Methods and tools for consumer segmentation. Review of cluster analysis methods and assessment of their applicability for solving the consumer market segmentation problem Results of segmentation using the multidimensional scaling method

Segmentation methods

Some "basic" segmentation methods can be distinguished. The most important of them is the cluster analysis of consumers (taxonomy). Clusters of consumers are formed by grouping together those who give similar answers to the questions asked. Buyers can be clustered if they are of similar age, income, habits, etc. Similarity between buyers is based on different measures, but a weighted sum of the squared differences between buyers' responses to a question is often used as a measure of similarity. The output of clustering algorithms can be hierarchical trees or the union of consumers into groups. There are a fairly large number of cluster algorithms.

For example, in the United States, a cluster analysis of systems called PRIZM is widely used. , which starts clustering by reducing the set of 1000 possible socio-demographic indicators. This system forms socio-demographic segments for the entire territory of the USA. Thus, cluster 28 was singled out - the families that fell into this cluster include persons with the most successful professional or managerial career. This cluster also reflects high income, education, property, and approximately average age. Although this cluster represents only 7% of the US population, it is critical for entrepreneurs selling high-end products.

There are other examples of consumer segmentation based on cluster analysis. For example, among the "psychological" sectors, a very important place is occupied by "the attitude of the consumer to the novelty of the product" (Fig. 3)

Figure 3

As can be seen from the above data, the largest number of consumers refers to the number of ordinary buyers.

Consumer segmentation based on cluster analysis is a "classic" method. At the same time, there are techniques for segmenting the market based on the so-called "product segmentation" or market segmentation by product parameters. It is especially important in the production and marketing of new products. Of particular importance is segmentation by product, based on the study of long-term market trends. The process of development and production of a new product, the completion of large investment programs require a fairly long period, and the correctness of the results of market analysis and assessment of its capacity is especially important here. In the conditions of work on the traditional market of standard products, the calculation of its capacity can be carried out by using the summation of markets method. In modern conditions, in order to increase its competitiveness and correctly determine the market capacity, it is no longer enough for an enterprise to segment the market in only one direction - the definition of consumer groups according to some criteria. Within the framework of integrated marketing, it is also necessary to segment the product itself according to the most important parameters for its promotion on the market. For this purpose, the method of compiling functional cards- carrying out a kind of double segmentation, by product and consumer.

Functional maps" can be single-factor (segmentation is carried out according to one factor and for a homogeneous group of products) and multi-factor (analysis of which consumer groups a particular product model is intended for and which parameters are most important for promoting products on the market) By compiling functional cards, you can determine which market segment a given product is designed for, which of its functional parameters correspond to certain consumer needs.

When developing a new product, this technique assumes that all factors reflecting the system of consumer preferences should be taken into account, and at the same time the technical parameters of the new product, with which you can satisfy the needs of the consumer; consumer groups are defined, each with its own set of requests and preferences; all selected factors are ranked according to the degree of significance for each of the consumer groups.

This approach allows you to see at the development stage what parameters of the product need design improvement, or to determine whether there is a sufficiently capacious market for this model.

Let us give an example of such a market analysis in relation to the project of computers under development "Apple" (Table 1) (see the next page)

Table 1." Segmentation of the personal computer market and factors taken into account when developing products for it (1982) "

Factors	Market segments by consumer groups						Model
	Houses	At school	At the university	To the house. office	In small business	In corporation	A	V
Technical specifications	*	*	***	**	**	**	***	**
Price	***	***	**	***	***	**	0	**
Special qualities	*	*	**	*	*	*	**	*
Reliability	**	*	*	**	**	*	0	**
Ease of use	**	**	*	**	*	0	***	***
Compatibility	0	0	0	0	0	***	0	0
Peripheral equipment	0	0	0	0	0	***	0	0
Software	*	*	**	**	**	***	*	**

*** is a very important factor

** - important factor

* - unimportant factor

0 - negligible factor

This simple analysis shows that model A is a computer without a market, and model B is the most suitable product for universities and small businesses.

The company once bet on computer A and lost.

In general, in world practice, 2 fundamental approaches to marketing segmentation are used - (see: the general scheme of segment analysis (Fig. 4)) (next page)

Within the first method. referred to as "a priori", the signs of segmentation, the number of segments, their number, characteristics, map of interests are previously known. That is, it is assumed that the segment groups in this method have already been formed. The "a priori" method is used in cases where segmentation is not part of the current study, but serves as an auxiliary basis for solving other marketing problems. Sometimes this method is used when market segments are very clearly defined, when the variance of market segments is not high. "A priory" is also acceptable in the formation of a new product focused on a known market segment.

Within the framework of the second method, called "post hoc (cluster based)," the uncertainty of the signs of segmentation and the essence of the segments themselves is implied. The researcher preliminarily selects a number of variables that are interactive with respect to the respondent (the method involves conducting a survey) and then, depending on the expressed attitude to a certain group of variables, Respondents belong to the relevant segment, while the interest map identified in the subsequent analysis is considered as secondary.This method is used when segmenting consumer markets, the segment structure of which is not defined in relation to the product being sold.

Segmentation by method " a priori "

When choosing the number of segments into which the market should be divided, they are usually guided by the objective function - determining the most promising segment. Obviously, when forming a sample, it is superfluous to include segments in it, whose purchasing potential is rather small in relation to the product under study. The number of segments, as studies show, should not exceed 10, the excess is usually associated with excessive detailing of segmentation features and leads to unnecessary "blurring" of features.

For example, when segmenting by income level, it is recommended to break down all potential buyers into segments of equal volume, taking into account that the volume of each of the segments is at least not less than the estimated volume of sales of services based on knowledge of the production capacity of the enterprise. The most successful example explaining the above and demonstrating the possibility of dividing potential consumers into stable segment groups can be the segmentation of the population based on income, when the entire population is divided into five 20% groups. The presented distribution of income for five 20% groups of the population is given regularly in statistical collections and reports, similarly to that presented in Table. 2

table 2 ."Distribution of income by population groups. %"

The convenience of working with such segment groups is obvious, especially in terms of tracking their capacity.

March 10th, 2015

Entering any market with a product - consumer, industrial - the manufacturer must understand that he cannot serve all his customers, even with sufficient production capacity. After all, buyers use this product in different ways, and most importantly, they buy it, guided by various motives. Therefore, I usually make a breakdown of buyers (segmentation) according to these motives and other characteristics, and only then - the offer of goods produced with the maximum consideration of these characteristics. It is no exaggeration to say that the ideal approach to planning marketing activities from the point of view of meeting the needs of consumers can be considered the adaptation of products and services to the requirements of each individual consumer.

Until 1960, the theory and practice of business was dominated by an orientation towards an aggregated, mass market. This was explained by the fact that, focusing on a common, undistributed market, the manufacturing firm was able to produce a large number of goods and obtain economies of scale. But since the 60s. The trend towards the need to distinguish the specifics of consumer demand, which is reflected in the segmentation of the sales market, began to gain strength.

In modern conditions of increased competition in the sales markets, the problem of the need to increase the competitiveness of domestic industrial products in the domestic and foreign markets is actualized. Under these conditions, the key issue is the search for reserves to reduce costs is the economic basis of price and profit. As a result, a significant number of industrial enterprises are pursuing a low-cost strategy, focusing on various ways of its implementation: rejection of expensive related services; cost savings by creating models of products that are cheaper to manufacture, and the like. But direct costs are largely determined by production technology, the level of loading of the enterprise-commodity producer, and the possibilities for reducing management costs by improving the efficiency of managing the functional areas of enterprises remain underused.

One of the modern tools is to reduce management costs and ensure an increase in the quality of management, which can be interpreted as the accuracy of forecasting profits, profitability for each cluster (a group of industrial enterprises of the same type of economic activity) compared to the initial situation, or the accuracy of forecasting the profitability of the functional areas of these activities. enterprises is a cluster analysis.

The importance of segmentation as an effective marketing tool is explained by the following features:

ü segmentation is a highly effective means of competition, since it focuses on identifying and meeting the specific needs of consumers;
ü focuses the activities of the company on a specific market niche, this is especially true for firms that begin their market activities;
ü market segmentation helps to more reasonably determine the marketing directions of the company;
ü with the help of segmentation, it becomes possible to set realistic marketing goals;
ü successful market segmentation affects the effectiveness of marketing as a whole, from market and consumer research to the formation of an appropriate sales and promotion system.

In marketing theory, the concept S TP -marketing . It is formed from the abbreviation of the first letters of English wordssegmenting(segmentation),targeting(target market selection) andpositioning(positioning). S TP -marketing is the core of modern strategic marketing.

Market segmentation - this is the division of consumers into groups based on differences in needs, characteristics or behavior and the development for each of the groups of a separate marketing mix.

Market segment consists of consumers responding in the same way to the same set of marketing incentives.

1. Market segmentation- the stage of allocation of individual groups of consumers within the common market.
2. Selecting target markets- among the selected market segments, target segments are selected, that is, those on which the company focuses its activities.
3. Positioning- identification of the firm's product among analogue products.

The ultimate goal of segmenting the target market is the choice of a segment (or segments) of consumers, the satisfaction of whose needs the company's activities will be oriented.
Marketers believe that the correct allocation of the market segment is half the commercial success, and they constantly recall the modification of the well-known Pareto law (law 80:20).

Market segmentation methods:

a priori method;

· Cluster method;

· Method of flexible segmentation;

· Component segmentation method.

At a priori methods the market segmentation hypothesis is first put forward and then tested in the course of marketing research. Therefore, this method is called a priori, i.e. inexperienced. This method of market segmentation is the most commonly used today, due to its relative simplicity, the availability of methods brought to practical implementation, and the low cost of implementation.

Cluster Methods imply that the market structure is unknown. They do not define a dependent variable, but look for natural clusters found in a database of consumers obtained through market research. In this case, the respondents are first grouped from among potential consumers using a special analytical procedure into natural clusters - market segments. After that, variables are defined, with the help of which it would be possible to formally define the market segment.

Compared with a priori segmentation, when segments are determined by the estimated variables at the beginning of the study, and with cluster segmentation, when the selected segments are formed from the results of cluster analysis, the models flexible segmentation offer a dynamic approach to the problem. Using this approach, a large number of different segments can be developed and tested, each including consumers or organizations with a similar perception of new "trial" products (identified by configuration of specific product characteristics). Flexible segmentation combines the results of coupled analysis and computer modeling of consumer behavior when choosing a product.

Component segmentation shifts the focus of market segmentation to personality characteristics (described by a set of demographic and psychographic characteristics) that would be better matched by product features. In component-by-component segmentation, the researcher is interested in comparing the parameters of the value of the product and the various characteristics of the respondent. Having defined these two sets of parameters, the researcher can make suggestions for the development of any possible product properties for any type of consumer.

Market Segmentation Process

The segmentation process occurs in eight steps.

Market Coverage Strategy

The first step is to choose a segmentation method.

The second stage is to check the homogeneity of the segment, i.e. we check whether the consumer's reaction to the product of this segment is the same.

The third stage is to check the level of differentiation of the segment, i.e. we check for how many segments the product is calculated and what variety of goods the organization offers.

The fourth stage is an assessment of the level of accessibility of the segment, i.e. it is necessary to assess whether the enterprise has a sufficient number of channels for the sale of its products, what is the throughput of these channels, whether the enterprise can ensure the sale of the entire volume of products, whether the system for delivering products to consumers is sufficiently reliable.

The fifth stage is to check the level of profitability of the segment, i.e. the possible price of the product when working in this segment and its cost are determined, taking into account the adaptation of the product for this segment. (Profitability ≈ Profitability)

The sixth stage is the assessment of segment stability.

The seventh stage is the choice of the target segment.

The eighth stage is the market coverage strategy.

Assessment of the attractiveness of segments and the concept of the target market

The attractiveness of a market segment is determined in accordance with criteria that each company determines independently.

Not all criteria are of equal importance and therefore each of them must be considered separately. The purpose of the attractiveness analysis is to calculate the weighted significance of a criterion that characterizes the “attractiveness” of a particular product.

The target market is the most suitable and profitable group of market segments (or one segment) for the enterprise, to which its activities are directed.

The company should promote those differences of its product that are most attractive to the target market.

In evaluating market segments, two factors are taken into account: (1) their overall attractiveness, and (2) the goals and resources of the company developing it.

Criteria for assessing the attractiveness of the target market

1. Size (capacity) of the market - Under the capacity of the commodity market is understood the possible volume of sales of goods (specific products of the enterprise) at a given level and ratio of different prices. The market capacity is characterized by the size of the demand of the population and the size of the commodity supply.

2. Geographic location

3. Actual and potential sales
Actual sales volume - the amount of goods and services that the organization can realistically sell under the existing conditions of operation, the estimated costs of advertising and the price level that it intends to establish.

Potential sales volume (offer) - the share of the potential market that the organization hopes to occupy and, accordingly, the maximum number of goods that it can count on for sale with its capabilities.

4. Actual and potential level and intensity of competition

the real and potential ability of companies to design, manufacture and market products that are more attractive in terms of price and non-price parameters than competitors' products.

the intensity of competition and, consequently, the level of competitiveness of the company are determined by the potential of the market; ease of entry into it; type of goods; market homogeneity; the structure of the industry or the competitive positions of firms; opportunities for technological innovation, etc.

5. Possibility of market coverage

The number of potential outlets and centers through which the product will be distributed.

6. Real and potential promotion costs

7. Stage of the market life cycle - i.e. product development, implementation stage, development (growth) stage, maturity stage or decline stage

8. Market trends, i.e. direction of development, prospects

9. Additional consumer requirements for the product

10. Real and potential price level

11. Consumer expectation and actual response to product marketing efforts

SMEs should identify and select two to three key success factors as a result of analyzing the attractiveness of each market segment. Critical success factors will be the "motto" of the company, and they must be constantly remembered. They are the most important circumstances that must or must not occur in order for a company to be successful in a particular product market.

Market Coverage Strategies

Having completed the segmentation, the company must determine which segment to target its activities. According to the degree of market coverage, three types of strategies are possible:

1. Single segment (concentrated marketing)

the firm focuses on a large share of one or more submarkets. For example, Volkswagen has focused its efforts on the small car market. Through concentrated marketing, the firm secures a strong market position in the segments it serves because it knows the needs of those segments better than anyone else and enjoys a certain reputation. Moreover, as a result of the specialization of production, distribution and promotion measures, the firm achieves economies in many areas of its activity. However, this strategy is associated with an increased level of risk: the selected segment may not meet expectations. In this regard, many firms choose to diversify their activities, covering several different market segments.

This approach is sometimes referred to as a "niche strategy" because This is often done with limited resources.

2. Multiple segments (differential marketing)

An increasing number of firms are adopting this strategy.

By offering a variety of products, the firm hopes to achieve sales growth and deeper penetration into each of its market segments. She expects that by strengthening her position in several market segments, she will be able to identify in the mind of the consumer the firm with this product category. Moreover, she expects an increase in repeat purchases, since it is the company's product that corresponds to the desires of consumers, and not vice versa.

3. Full market coverage (undifferentiated marketing)

Most marketing professionals believe that this strategy is limited in scope.

In this case, the firm focuses not on how the needs of customers differ from each other, but on what these needs have in common. It develops a product and marketing program that will appeal to as many customers as possible. It relies on methods of mass distribution and mass advertising. It strives to give the product an image of superiority in people's minds. As an example of undifferentiated marketing, we can cite the actions of the Krasny Oktyabr company, which several years ago offered a chocolate brand for everyone.

Undifferentiated marketing is economical. The costs of producing a product, maintaining its inventory and transporting it are low. Advertising costs with undifferentiated marketing are also kept low. The absence of the need for marketing research of market segments and planning broken down by these segments helps to reduce the cost of marketing research and product management.

The concept of positioning

Positioning is the process of finding a market position for a company, product or service that will favorably distinguish it (him) from the position of competitors. Positioning is carried out taking into account a specific target group of consumers, for which advantages and uniqueness are created and offered. Without a clear idea of ​​what the position is aimed at, it is very difficult, even almost impossible, to align marketing decisions. The definition of competitive positioning often dictates the most effective combinations of marketing tools.
Summarizing, we can say that positioning is a marketing strategy to create a strong connection of your brand (product or company) with certain associations, or better, with benefits.

Thus, positioning involves:
- creation in the head of the consumer of a stable association of a product or company with a certain place in the market,
- maintaining the association (chosen position) in the long term.

The position of the product in the market the place a given product occupies in the minds of consumers compared to similar competing products from the consumer's point of view.
Positioning strategy is a set of measures aimed at conveying the concept of positioning to consumers. Positioning exists only in the mind of the consumer.
- Strategy for offering goods (services)
- Pricing strategy
- Product distribution strategy
- Strategy for promoting goods (services)
Positioning constraint
- Target market
- Real and potential competitors
- Company strategy

Repositioning- changes in the position of a product or service in marketing and advertising, when they are given a new image, another target audience is determined, arguments for sales and advertising information, packaging, etc. change.
Reasons for repositioning:
- Questionable positioning
- Underpositioning
- Indistinct positioning
- Useless positioning
- Overpositioning

Place of residence, etc. From this it should be clear that the market segment is

There is a group of consumers who in some respects behave in the same way in the market.

Market segmentation, in turn, breaks down into a number of stages.

• 2. The choice of a market segment lies in the fact that each of the segments is evaluated in terms of its attractiveness (the ability to bring the desired result to the enterprise). Based on these estimates, the most attractive segment (or segments) is selected.
• 3. Finally, the third stage is product positioning. After the market segment is selected, it is necessary to think about how the product that the company offers on the market will be presented on the market. In addition, a detailed marketing mix must also be developed. It is these tasks that are solved at this stage.

In marketing, several features have been identified that can improve the effectiveness of segmentation. These signs do not concern consumers, but the segments themselves.

• 1. The segment must be meaningful. This means that the attribute that underlies segmentation must at least to some extent adjust with consumer behavior. Thus, being overweight matters in terms of how much bread a person consumes, or whether they have trouble buying clothes. However, this sign is unlikely to be significant in connection with what cosmetics he uses.
• 2. The market segment must be large enough in size to be able to generate the profit that is necessary for the success of the firm. If the segment is too small from this point of view, the development and implementation of a marketing program focused on it simply does not make sense.
• 3. The segment must be measurable. This means that the feature that underlies segmentation must provide the possibility of a clear and unambiguous separation of a group of consumers from their other groups. Age is an example of a measurable trait. We can always easily divide all consumers into groups depending on the value that this variable takes.

An example of a feature that is not fully measurable can also be, oddly enough, the frequency of consumption of a product, consumer preferences in some cases can be extremely variable. A much more reliable sign from this point of view is brand loyalty: even if the consumer buys a product infrequently, he will always choose only one brand, rejecting all others.

Here, one should also consider whether the interviewee will be sincere when answering the researcher's question. From this point of view, signs of the type of sexual orientation are poorly measurable. Although the degree of tolerance of our society towards sexual minorities is constantly growing (and this is a sign of any sufficiently developed society), not every representative of these minorities will dare to openly declare their sexual orientation.

3. The segment must be accessible. This quality implies not only accessibility for research, but also the availability of additional information. If an enterprise can be expected to be able to influence a segment of the jerk with the means at its disposal and then evaluate its impact by comparing the initial state with the state after the impact, the segment can be considered accessible. It is clear that this is possible only if there is access to information.

In marketing practice, three segmentation methods are most often used: grouping, multivariate sequential segmentation with a dependent variable, and cluster analysis. This list does not exhaust all possible segmentation methods, but it is quite enough to get a general idea of ​​\u200b\u200bthis procedure and the complexities associated with it.

1. The easiest way to segment is the division of the market into groups traditionally identified in marketing and sociology based on the features listed above. In this case, it is simply assumed that consumer groups, identified on the basis of such characteristics as gender, age, or profession, are characterized by a fairly standard set of needs and behaviors.

This method is most appropriate in the case of choosing a new field of activity, for example, in the case when the company is just starting to operate on the market or decides to enter a new market.

The disadvantage of this segmentation method is that it is based on assumptions, hypotheses. The division of consumers based on age, gender, profession, income level or social status is traditional for marketing research, but it is not at all obvious that these variables are associated with the process of "finishing" consumers. In other words, it is far from always possible to assert that the activity of consumers directly depends, for example, on their age. Therefore, by resorting to such segmentation, the marketer selects arbitrary and insufficiently weighty reasons for selecting segments.

When segmenting the market, it must be borne in mind that the features underlying the allocation of certain groups have different importance. On the one hand, we can talk about signs that are directly related to the goals of the enterprise. Such a sign would be, for example, the willingness to purchase a new product that has a set of certain qualities: on this basis, we can distinguish a group of consumers who are ready to do this, and a group of consumers who are not ready for this.

Since the enterprise is interested in the sale of goods, this parameter is directly related to its goals. On the other hand, there are less significant parameters that are not in the same close connection with the goals of the enterprise. An example of such a trait would be age. So, this or that product can be intended for the age category of people after 30 years. But this does not mean that every person who is over thirty will buy this product. Consequently, age as a segmentation parameter is less related to the immediate goals of the enterprise.

If the number of really significant factors is very large, they can be reduced using the so-called factor analysis. It involves the selection of groups of related features (parameters), which are combined into one feature. So, for example, the level of income is closely related to the size of the house, the presence of a car, the number of tourist trips, visits to establishments such as restaurants and clubs, and therefore these signs can be combined into one.

It is advisable to give this feature some name. In our case, we could call the new feature "the amount of income", but interpret it broadly, not only as the amount of money that a person receives in a month or a year. Similarly, one can link income level, occupation and education, income level and political preferences, etc.

2. Multivariate sequential segmentation with a dependent variable is most appropriate when the company already has experience in the market. In this case, segmentation is aimed at identifying the most preferred market segment in terms of the results already available.

Since the main result that the company strives for is to extract maximum profit, in this case, for example, the company's income can be chosen as a dependent variable. Preliminary segmentation is aimed at this aspect: it is necessary to identify groups of consumers that, from the point of view of the enterprise, bring him the greatest income.

It is clear that the lower limit of income is generally determined subjectively and represents a compromise between the real and the desired situation. It is conditionally possible to distinguish, for example, three groups: consumers who bring a large income, consumers who bring an average (satisfactory) income, and consumers who bring too little income.

The second stage of segmentation is the identification of the second variable, which is most closely related to the first variable. This variable is usually:

• a) the frequency of use of the product or service sold by the firm;
• b) the level of income brought by the consumer to the company;
• c) consumer loyalty to the brand. For example, in marketing research it turns out that people from 25 to 33 years old bring the greatest income to the company. Therefore, all consumers should be divided into at least three groups: 1) up to 25 years; 2) from 25 to 33 years old; and 3) over 33 years old.

When using this method, only the most profitable segment of the market is subjected to further segmentation. In our case, this is the category of consumers aged 25 to 33 years. At the subsequent stages, the bases for segmentation are again found, which are most related to the level of profitability.

The division limit in this case is the segment, which must have the following qualities:

• 1) the consumers belonging to it bring the greatest income to the company (for example, the income received by the company in this segment, which accounts for only 20% of the market, is 70% of the total income);
• 2) the segment must not be fully mastered;
• 3) it must be large enough to make it worth investing in its additional development;
• 4) further division of the segment should be impossible (this is the preferred feature).

The advantage of this segmentation method is that it is based on the most significant variables. This method also has disadvantages. First of all, it does not take into account the interaction between different variables. In addition, segments that are quickly allocated with its help turn out to be too small. At the same time, in general, this method is quite productive.

When using it, you can see which segments are really the most preferable, which ones can be, and which ones should be abandoned altogether. In particular, the use of this method makes it possible to formulate very realistic tasks, for example, increasing the income received from one or another group of consumers. Finally, it allows you to identify weaknesses in the company's activities.

3. Unlike the two previous segmentation methods, in which the marketer begins the market analysis with the entire population of consumers and gradually divides them into groups, with cluster analysis, the direction is reversed: the analysis begins with individual consumers. For this reason, cluster analysis requires that the marketer has data on a sufficiently large number of real consumers, as a rule, their number should be at least 200 people.

Cluster analysis includes several steps.

• 1) First, the marketer randomly selects one consumer and begins to look for another who will be as similar as possible to him in terms of known parameters. When two such consumers are found, they are combined into a cluster. Other clusters are identified in a similar way.
• 2) The next step is the unification of individual consumers and their groups into broader communities. It should be borne in mind that both individual consumers or already allocated clusters, as well as a consumer and a cluster, can be combined into clusters. The merger is carried out until a more or less satisfactory number of clusters is obtained, that is, segments that, in terms of their volume, correspond to the interests of the enterprise.
• 3) Control over the correctness of the selection of clusters is that the marketer conducts segmentation a second time and checks whether the same segmentation can be obtained using other similarity measures. The results of the main and control segmentation based on cluster analysis are compared, after which adjustments are made to the main segmentation.

The undoubted advantage of this method is that it allows you to start from specific data about consumers. A marketer using this method is less likely to choose a segmentation parameter that is actually of little value.

The disadvantage of this method is that when using it, clusters can be selected that do not actually exist. This means that the resulting groups of consumers will not in fact be characterized by the same behavior. That is why various control procedures should be an obligatory part of cluster analysis.

Product positioning on the market is a direction of marketing activity for the selection of target markets, which involves the analysis of the elements of the marketing mix and product positions in selected market segments in order to identify those parameters that contribute to gaining competitive advantages.

If all enterprises produce the same products with the same characteristics, use the same methods of promoting and delivering the product, and provide similar services, then for consumers they will all be the same.

At the same time, it is important to take into account the position that the product occupies on the market at the present time. The position of the product is the opinion of consumers on the most important parameters of the product. It characterizes the place occupied by a particular product in the minds of consumers in relation to the product of competitors. Unlike the image of a product, which is more of an emotional characteristic, the position of a product is formed, as a rule, on the basis of quantitatively measured parameters (market share, product characteristics, price, etc.).

• The choice of a market segment involves a certain procedure, consisting of three stages.
• Market segmentation in its own, narrow sense of the word - the allocation of consumer groups that differ in their needs, financial capabilities, habits,

I work in the email marketing industry for a site called MailChimp.com. We help clients create newsletters for their advertising audience. Every time someone calls our work "mail stuffing", I feel an unpleasant chill in my heart.

Why? Yes, because email addresses are no longer black boxes that you bombard with messages like grenades. No, in email marketing (as with other forms of online contact, including tweets, Facebook posts, and Pinterest campaigns), businesses gain insights into how an audience makes contact on an individual level through click tracking, online orders, distribution of statuses in social networks, etc. This data is not just interference. They characterize your audience. But for the uninitiated, these operations are akin to the wisdom of the Greek language. Or Esperanto.

How do you collect transaction data from your customers (users, subscribers, etc.) and use their data to better understand your audience? When you're dealing with a lot of people, it's hard to study each client individually, especially if they all contact you in different ways. Even if you could theoretically reach out to everyone personally, in practice this is hardly feasible.

You need to take the customer base and find a middle ground between random bombing and personalized marketing for each individual customer. One way to achieve this balance is to use clustering to segment your customer market so that you can reach different segments of your customer base with different targeted content, offers, etc.

Cluster analysis is the collection of various objects and their division into groups of their own kind. By working with these groups—determining what their members have in common and what makes them different—you can learn a lot about the messy dataset you have. This knowledge will help you make better decisions, and at a more detailed level than before.

In this context, clustering is called exploratory data mining because these techniques help you "pull" information about relationships in huge datasets that you can't visually capture. And the discovery of connections in social groups is useful in any industry - to recommend films based on the habits of the target audience, to identify the criminal centers of the city, or to justify financial investments.

One of my favorite uses of clustering is image clustering: piling up image files that "look the same" to a computer. For example, on image hosting services like Flickr, users produce tons of content and simple navigation becomes impossible due to the large number of photos. But using clustering techniques, you can combine similar images, allowing the user to navigate between these groups even before detailed sorting.

Supervised or unsupervised machine learning?

In exploratory data mining, by definition, you don't know ahead of time what kind of data you're looking for. You are a researcher. You can clearly explain when two customers look similar and when they look different, but you don't know the best way to segment your customer base. So asking a computer to segment the customer base for you is called unsupervised machine learning, because you don't control anything - you don't tell the computer how to do its job.

In contrast to this process, there is supervised machine learning, which usually appears when artificial intelligence hits the front page. If I know that I want to divide customers into two groups - say "likely to buy" and "unlikely to buy" - and feed the computer with historical examples of such buyers, applying all the innovations to one of these groups, then this is control.

If instead I say, “Here's what I know about my clients, and here's how to tell if they're different or the same. Tell me something interesting, ”is the lack of control.

This chapter discusses the simplest method of clustering called k-means, which dates back to the 1950s and has since become the standard in database knowledge discovery (KDR) across industries and governments.

The k-means method is not the most mathematically accurate of all methods. It was created, first of all, for reasons of practicality and common sense - like African American cuisine. She does not have such a chic pedigree as the French one, but she often caters to our gastronomic whims. Clustering with k-means, as you will soon see, is part mathematics and part history (about the company's past, if the comparison is in management education). Its undoubted advantage is intuitive simplicity.

Let's see how this method works with a simple example.

Girls dance with girls, guys scratch their heads

The goal of k-means clustering is to pick a few points in space and turn them into k groups (where k is any number you choose). Each group is defined by a dot in the center, like a flag planted in the moon, signaling, “Hey, here's the center of my group! Join if you are closer to this flag than to the others!” This group center (officially called the cluster centroid) is the mean of the k-means name.

Consider, for example, school dances. If you have managed to erase the horror of this "entertainment" from your memory, I am very sorry for bringing back such painful memories.

The heroes of our example - students of Makakne High School, who came to the dance evening under the romantic name "Ball at the Bottom of the Sea", are scattered around the assembly hall, as shown in Fig. 1. I even painted on the parquet in Photoshop to make it easier to imagine the situation.

Rice. one. Makakne High School students lined up in the auditorium

And here are some examples of songs that these young leaders of the free world will clumsily dance to (in case you want a musical accompaniment, for example, on Spotify):

• Styx: Come Sail Away
• Everything But the Girl: Missing
• Ace of Base: All that She Wants
• Soft Cell: Tainted Love
• Montell Jordan
• Eiffel 65: Blue

Now clustering by k-means depends on the number of clusters into which you want to divide those present. Let's start with three clusters (later in this chapter, we will consider the choice of k). The algorithm places three flags on the floor of the assembly hall in some valid way, as shown in Fig. 2, where you see 3 initial flags distributed by gender and marked with black circles.

Rice. 2. Placement of initial centers of clusters

In k-means clustering, the dancers are tied to their closest cluster center, so that a line of demarcation can be drawn between any two centers on the floor. Thus, if the dancer is on one side of the line, he belongs to one group, if on the other side, then to the other (as in Fig. 3).

Rice. 3. The lines mark the boundaries of the clusters

Using these demarcation lines, we divide the dancers into groups and color them accordingly, as in fig. 4. This diagram, which divides space into polygons defined by proximity to one or another cluster center, is called the Voronoi diagram.

Rice. 4. Grouping by clusters marked with different background patterns on the Voronoi diagram

Let's look at our initial division. Something's wrong, isn't it? The space is divided in a rather strange way: the lower left group remains empty, and on the border of the upper right group, on the contrary, there are many people.

The k-means clustering algorithm moves cluster centers around the floor until it reaches the best result.

How to determine the "best result"? Each person present is some distance away from their cluster center. The shorter the average distance from the participants to the center of their group, the better the result.

Now we introduce the word "minimization" - it will be very useful to you in optimizing the model for a better location of cluster centers. In this chapter, you will make Solver move cluster centers countless times. The way that Solver uses to find the best location for cluster centers is to slowly iteratively move them around the surface, fixing the best results found, and combining them (literally mating like racehorses) to find the best position.

So if the diagram in Fig. 4 looks rather pale, "Search for a solution" can suddenly arrange the centers as in fig. 5. Thus, the average distance between each dancer and his center will decrease slightly.

Rice. 5. Slightly shifting the centers

It is obvious that sooner or later the Search for a Solution will realize that the centers should be placed in the middle of each group of dancers, as shown in fig. 6.

Rice. 6. Optimal clustering at school dances

Fine! This is what ideal clustering looks like. Cluster centers are located at the center of each group of dancers, minimizing the average distance between a dancer and the nearest center. Now that the clustering is done, it's time to move on to the fun part, which is trying to figure out what these clusters mean.

If you know the hair color of the dancers, their political preferences, or the time they traveled a hundred meters, then clustering does not make much sense.

But once you decide to determine the age and gender of those present, you will begin to see some general trends. The small group at the bottom are elderly people, most likely accompanying. The group on the left is all boys, and the group on the right is all girls. And everyone is very afraid to dance with each other.

Thus, the k-means method allowed you to divide many dance attendees into groups and correlate the characteristics of each attendee with belonging to a particular cluster in order to understand the reason for the separation.

Now you are probably saying to yourself: “Come on, what nonsense. I already knew the answer before the start. You're right. In this example, yes. I gave such a "toy" example on purpose, being sure that you can solve it just by looking at the dots. The action takes place in a two-dimensional space, in which clustering is performed elementarily with the help of the eyes.

But what if you run a store that sells thousands of products? Some buyers have made one or two purchases in the last two years. Others are dozens. And everyone bought something different.

How do you cluster them on such a "dance floor"? Let's start with the fact that this dance floor is not two-dimensional, and not even three-dimensional. This is a thousand-dimensional space of the sale of goods, in which the buyer has purchased or not purchased the product in each dimension. See how quickly the problem of clustering starts to go beyond the ability of the “eyeball of the first category”, as my military friends like to say.

Real Life: K-Means Clustering in Email Marketing

Let's move on to a more specific case. I'm in email marketing, so I'll give an example from the life of Mailchimp.com, where I work. This same example will work for retail, ad conversion, social media, and more. It interacts with almost any type of data related to delivering promotional material to customers, after which they unconditionally choose you.

Wholesale Wine Empire Joey Bag O'Donuts

Imagine for a moment that you live in New Jersey, where you run the Joey Bag O'Donuts Wholesale Wine Empire. This is an import-export business whose purpose is to bring huge amounts of wine from abroad and sell it to certain liquor stores around the country. The way the business works is that Joey travels all over the world looking for incredible deals with lots of wine, he ships it to him in Jersey, and it's up to you to put it in stores and make a profit.

You find buyers in many ways: a Facebook page, a Twitter account, sometimes even direct mail - after all, emails "promote" most types of business. Last year, you sent one letter a month. Usually each letter describes two or three deals, say one with champagne and the other with malbec. Some deals are just amazing - 80% off or more. As a result, you made about 32 deals in a year, and all of them went more or less smoothly.

But just because things are going just fine, doesn't mean they can't get better. It would be useful to understand the motives of their customers a little deeper. Of course, when you look at a particular order, you see that one Adams bought some sparkling in July at a 50% discount, but you can't determine what made him buy. Did he like the minimum order quantity of one carton of six bottles or the price that hasn't reached its maximum yet?

It would be nice to be able to split the list of clients into interest groups. Then you could edit the letters to each group separately and, perhaps, would promote the business even more. Any deal suitable for this group could become the subject of the letter and go in the first paragraph of the text. This type of targeted mailing can cause a massive sales explosion!

It is possible to let the computer do the work for you. Using k-means clustering, you can find the best grouping and then try to figure out why it's the best.

Initial dataset

The Excel document that we will analyze in this chapter is located on the book's website. It contains all the original data in case you want to work with them. Or you can just follow the text by looking at the rest of the sheets in the document.

To start, you have two interesting data sources:

• metadata for each order is stored in a spreadsheet, including varietal, minimum quantity of wine per order, retail discount, whether a price cap has been passed, and country of origin. This data is placed in a tab called OfferInformation, as shown in Fig. 7;
• knowing which customers are ordering what, you can shake that information out of MailChimp and feed it to a spreadsheet with offer metadata in the Transactions tab. These are variable data presented as shown in Fig. 8, very simple: the buyer and his order.

Rice. 7. Details of the last 32 orders

Rice. eight. List of orders by customer

We determine the subject of measurements

And here is the task. In the problem of school dances, measuring the distance between those present and determining the cluster centers was not difficult, right? You just need to find the right roulette! But what to do now?

You know that last year there were 32 offers of deals and you have a list of 324 orders in a separate tab, broken down by buyers. But to measure the distance from each customer to the cluster center, you must place them in this 32-deal space. In other words, you need to figure out what deals they didn't make and create a deal-by-customer matrix where each customer gets their own column with 32 deals cells, filled with ones if deals were made and zeros if they didn't.

In other words, you need to take this row-oriented table of trades and turn it into a matrix with customers on the vertical and offers on the horizontal. Pivot tables are the best way to create it.

Action algorithm: on a worksheet with variable data, select columns A and B, and then insert a pivot table. Using the PivotTable Wizard, simply select deals as the row heading and buyers as the column heading and populate the table. The cell will have 1 if the client-deal pair exists, and 0 if it doesn't (in this case, 0 is displayed as an empty cell). The result is the table shown in Fig. 9.

Rice. 9. Pivot table "client-deal"

Now that you have your order information in a matrix format, copy the OfferInformation sheet and name it Matrix. In this new sheet, paste the values ​​from the pivot table (no need to copy and paste the deal number because it is already in the order information), starting with column H. You should end up with an expanded version of the matrix, complete with order information, like in fig. 10.

Rice. 10. Deal description and order data merged into a single matrix

Data standardization

In this chapter, each dimension of your data is represented in the same way, as binary information about orders. But in many clustering situations, we cannot do this. Imagine a scenario where people are clustered by height, weight, and salary. All these three types of data have different dimensions. Height can vary from 1.5 to 2 meters, while weight - from 50 to 150 kg.

In this context, measuring the distance between customers (like between dancers in a ballroom) becomes a confusing affair. Therefore, it is common to standardize each column of data by subtracting the mean and then dividing in turn by a measure of variation called the standard deviation. Thus, all columns are reduced to a single value, varying quantitatively around 0.

Let's start with four clusters

Well, now all your data is reduced to a single convenient format. To start clustering, you need to choose k - the number of clusters in the k-means algorithm. Often k-means are applied like this: take a set of different k and test them one by one (how to choose them, I will explain later), but we are just getting started - so we will choose only one.

You will need a number of clusters that is about right for what you want to do. You obviously don't intend to create 50 clusters and send out 50 targeted promotional emails to a couple of guys from each group. This immediately deprives our exercise of meaning. In our case, we need something small. Start this example with 4 - in an ideal world, you would probably divide your client list into 4 understandable groups of 25 people each (which is unlikely in reality).

So, if you have to divide the buyers into 4 groups, what is the best way to select them?

Instead of spoiling the pretty Matrix sheet, copy the data to a new sheet and name it 4MC. Now you can insert 4 bars after the price high in the H to K bars, which will be the cluster centers. (To insert a column, right-click on column H and select Paste. The column will appear on the left.) Name these clusters Cluster 1 through Cluster 4. You can also apply conditional formatting to them, and whenever you set them, you can see how different they are.

The 4MC sheet will appear as shown in fig. eleven.

Rice. eleven. Empty cluster centers placed on a 4MC sheet

In this case, all cluster centers are zeros. But technically, they can be anything and, what you will especially like - like at school dances, they are distributed in such a way that they minimize the distance between each customer and his cluster center.

Obviously, then these centers will have values ​​from 0 to 1 for each transaction, since all client vectors are binary.

But what does it mean to "measure the distance between the cluster center and the buyer"?

Euclidean distance: measuring distances straight ahead

For each customer, you have a separate column. How to measure the distance between them? In geometry, this is called the "shortest path" and the resulting distance is the Euclidean distance.

Let's go back to the assembly hall for a while and try to figure out how to solve our problem there.

Let us place the coordinate axes on the floor and in fig. 12 we will see that at the point (8,2) we have a dancer, and at (4,4) we have a cluster center. To calculate the Euclidean distance between them, you will have to remember the Pythagorean theorem, which you have been familiar with since school.

Rice. 12. Dancer at (8,2) and cluster center at (4,4)

These two points are 8 - 4 = 4 meters apart vertically and 4 - 2 = 2 meters horizontally. According to the Pythagorean theorem, the square of the distance between two points is 4L2 + 2L2 = 20 meters. From here we calculate the distance itself, which will be equal to the square root of 20, which is approximately 4.47m (as in Fig. 13).

Rice. thirteen. Euclidean distance is equal to the square root of the sum of the distances in each direction

In the context of newsletter subscribers, you have more than two dimensions, but the same concept applies. The distance between the buyer and the cluster center is calculated by taking the difference between the two points for each trade, squaring them, adding them, and taking the square root. For example, on sheet 4MC, you want to know the Euclidean distance between the center of cluster 1 in column H and customer Adams' orders in column L.

In cell L34, under the Adams orders, you can calculate the difference between the Adams vector and the cluster center, square it, add it up, and then take the root using the following array formula (check the absolute references, allowing you to drag this formula to the right or down without changing the reference to the cluster center):

(=ROOT(SUM(L$2:L$33-$H$2:$H$33)A2)))

An array formula (type the formula and press Ctrl+Shift+Enter or Cmd+Return on MacOS, as explained in Chapter 1) should be used because the (L2:L33-H2:H33)^2 part needs to know where refer to calculating the differences and squaring them, step by step. However, the final result is a single number, in our case 1.732 (as in Figure 14). It has the following meaning: Adams made three trades, but since the initial cluster centers are zeros, the answer will be equal to the square root of 3, namely 1.732.

Rice. 14. Distance between cluster center 1 and Adams

In the spreadsheet in fig. In Figure 2-14, I docked the top row (see Chapter 1) between columns G and H, and named row 34 in cell G34 "Distance to Cluster 1," just to see what's where when I scroll down the page.

Distances and belonging to a cluster for everyone!

Now you know how to calculate the distance between the order vector and the cluster center.

It's time to add Adams the calculation of distances to the rest of the cluster centers by dragging cell L34 down to L37, and then manually changing the reference to the cluster center from column H to column I, J and K in the cells below. The result should be the following 4 formulas in L34:L37:

(=SQRT(SUM((L$2:L$33-$H$2:$H$33)A2)))
(=SQRT(SUM((L$2:L$33-$I$2:$I$33)A2)))
(=SQRT(SUM((L$2:L$33-$J$2:$J$33)A2)))
(=SQRT(SUM((L$2:L$33-$K$2:$K$33)A2)))
(=ROOT(SUM((L$2:L$33-$H$2:$H$33)A2)))
(=ROOT(SUM((L$2:L$33-$I$2:$I$33)A2)))
(=ROOT(SUM((L$2:L$33-$J$2:$J$33)A2)))
(=ROOT(SUM((L$2:L$33-$K$2:$K$33)A2)))

Since you used absolute links for the cluster centers (which is exactly what the $ sign means in formulas, as discussed in Chapter 1), you can drag L34:L37 to DG34:DG37 to calculate the distance from each customer to all four cluster centers. Label the rows in column G in cells 35 through 37 "Distance to Cluster 2", etc. The newly calculated distances are shown in Figure 2. 15.

Rice. 15. Calculation of distances from each customer to all cluster centers

Now you know the distance of each client to all four cluster centers. Their distribution among clusters was made according to the shortest distance in two steps as follows.

First, let's go back to Adams in column L and calculate the minimum distance to the cluster center in cell L38. It's simple:

Min(L34:L37)
=min(L34:L37)

For the calculation, we use the match/searchpos formula (for more details, see Chapter 1). Putting it in L39, you can see the cell number from the interval L34:L37 (counting each in order from 1) that is at the minimum distance:

Match(L38,L34:L37,0) =searchpos(L38,L34:L37,0)

In this case, the distance is the same for all four clusters, so the formula selects the first one (L34) and returns 1 (Figure 16).

Rice. sixteen. Adding Cluster Bindings to the Sheet

You can also drag these two formulas onto DG38: DG39. For more organization, add row names 38 and 39 in cells 38 and 39 of column G "Minimum Cluster Distance" and "Assigned Cluster".

Finding Solutions for Cluster Centers

Your spreadsheet has been updated with distance calculation and cluster binding. Now, in order to determine the best location of cluster centers, you need to find those values ​​in columns from H to K that minimize the total distance between customers and the cluster centers to which they are associated, indicated in line 39 for each customer.

When you hear the word "minimize": the optimization phase begins, and optimization is performed using the "Search for a solution".

To use Search for a Solution, you will need a cell for results, so in A36 we will sum up all the distances between buyers and their cluster centers:

SUM(L38:DG38)
=CMMA(L3 8:DG3 8)

This sum of distances from clients to their closest cluster centers is exactly the objective function we encountered earlier during clustering of the McAcne High School auditorium. But the Euclidean distance with its powers and square roots is a monstrously non-linear function, so you have to use an evolutionary solution algorithm instead of the simplex method.

You already used this method in Chapter 1. The simplex algorithm, if it is possible to apply it, works faster than others, but it cannot be used to calculate roots, squares, and other non-linear functions. Just as useless is OpenSolver, which uses a simplex algorithm, even if it seems to have taken steroids.

In our case, the evolutionary algorithm built into Search for a Solution uses a combination of random search and an excellent “crossover” solution to, like evolution in a biological context, find efficient solutions.

You have everything you need to set the task before the “Search for a Solution”:

• goal: to minimize the total distances from buyers to their cluster centers (A36);
• variables: the vector of each transaction relative to the cluster center (Н2:К33);
• conditions: cluster centers must have values ​​between 0 and 1.

The presence of "Search for a solution" and a hammer is recommended. We set the task of "Searching for a solution": to minimize A36 by changing the values ​​of H2:K33 with the condition H2:K33<=1, как и все векторы сделок. Убедитесь, что переменные отмечены как положительные и выбран эволюционный алгоритм (рис. 17).

Rice. 17. Solver Settings for 4-Center Clustering

But setting a goal isn't everything. You will have to sweat a little, choosing the necessary options for the evolutionary algorithm by clicking the "Parameters" button in the "Search for a solution" window and going to the settings window. I advise you to set the maximum time to 30 more seconds, depending on how long you are willing to wait for the "Search for solutions" to cope with its task. On fig. 18 I set mine to 600 seconds (10 minutes). That way, I can run "Search for a Solution" and go to lunch. And if you feel like aborting it early, just hit Escape and exit with the best solution it could find.

Rice. eighteen. Evolutionary Algorithm Parameters

Click Run and watch Excel do its thing until the evolutionary algorithm converges.

The meaning of the results

As soon as "Search for a solution" gives you the optimal cluster centers, the fun begins. Let's move on to groups! On fig. In Figure 19, we can see that Solver found the optimal total distance of 140.7, and all four cluster centers - thanks to conditional formatting! - look completely different.

Rice. nineteen. Four optimal cluster centers

Keep in mind that your cluster centers may differ from those presented in the book, because the evolutionary algorithm uses random numbers and the answer is different every time. The clusters may be completely different or, more likely, in a different order (for example, my cluster 1 may be very close to your cluster 4, etc.).

Since you inserted trade descriptions in columns B through G when you created the sheet, you can now read the details in Fig. 19, which is important for understanding the idea of ​​cluster centers.

For cluster 1 in column H, the conditional formatting selects deals 24, 26, 17, and, to a lesser extent, 2. Reading the descriptions of these deals, you can see what they all have in common: they were all done on Pinot Noir.

Looking at column I, you can see that all of the green cells have a low minimum count. These are buyers who are unwilling to purchase huge lots during the transaction.

But the other two cluster centers, frankly speaking, are difficult to interpret. How about, instead of interpreting the cluster centers, look at the buyers themselves in the cluster and determine what kind of deals they like? This could bring clarity to the issue.

Rating of deals by the cluster method

Instead of finding out which distances to which cluster center are closer to 1, let's check who is tied to which cluster and which deals they prefer.

To do this, let's start by copying the OfferInformation sheet. Let's call the copy 4MS - TopDealsByCluster. Number the columns from H to K on this new sheet from 1 to 4 (as in Figure 20).

Rice. twenty. Creating a table sheet for calculating the popularity of deals using clusters

On the 4MC sheet, you had cluster anchors from 1 to 4 on row 39. All you need to do to count the deals by cluster is look at the column names from H to K on the 4MC sheet - TopDealsByCluster, see which worksheet 4MS was tied to this cluster in row 39, and then added up the number of their transactions in each row. Thus, we will get the total number of buyers in this cluster who have made transactions.

Let's start with cell H2, which contains the number of buyers of cluster 1 who accepted offer No. 1, namely the January malbec. You need to add the values ​​of the cells in the range L2: DG2 on a 4MC sheet, but only customers from 1 cluster, which is a classic example of using the sumif / sumif formula. It looks like this:

SUMIF("4MC"!$L$39:$DG$39,"4MC - TopDealsByCluster"! H$1,"4MC"!$L2:$DG2)
=CyMMEOra("4MC"!$L$39:$DG$39,"4MC - TopDealsByCluster"! H$1,"4MC"!$L2:$DG2)

This formula works like this: you supply it with some conditional values, which it checks in the first part of "4MC"!$L$39:$DG$39,"4MC, then compares it to 1 in the column header ("4MC - TopDealsByCluster"! H$1 ) and then, for each match, adds that value to row 2 in the third part of the "4MC"!$L2:$DG2 formula.

Note that you have used absolute references ($ in the formula) before anything related to the cluster binding, the row number in the column headings, and the column letter for completed trades. By making these links absolute, you can drag the formula anywhere from H2:K33 to calculate the number of deals for other cluster centers and combinations of deals, as in Figure 2. 21. To make these columns more readable, you can also apply conditional formatting to them.

Rice. 21. Total number of deals per offer, broken down by cluster

By selecting columns A through K and applying autofiltering, you can sort this data. By sorting column H from smallest to largest, you will see which transactions are the most popular in cluster 1 (Fig. 22).

Rice. 22. Cluster sorting 1. Pinot, Pinot, Pinot!

As I mentioned earlier, the four biggest trades for this cluster are pinos. These guys are clearly abusing the movie Sideways. If you sort cluster 2, then it will become quite clear to you that these are small wholesale buyers (Fig. 23).

But when you sort cluster 3, it's not so easy to understand anything. Large deals can be counted on the fingers, and the difference between them and the rest is not so obvious. However, the most popular deals still have something in common - pretty good discounts, 5 out of the 6 biggest deals are for sparkling wine, and France is the producer for 3 out of 4 of them. However, these assumptions are ambiguous.

As for cluster 4, these guys obviously liked the August offer for champagne for some reason. Also, 5 of the 6 largest transactions are for French wine, and 9 of the 10 largest deals are for a large volume of goods. Maybe this is a large wholesale cluster gravitating towards French wines? The intersection of clusters 3 and 4 is also worrisome.