customer segmentation in retail [closed]

Question

I have a large sales database of a 'home and construction' retail. And I need to know who are the electricians, plumbers, painters, etc. in the store.

My first approach was to select the articles related to a specialty (wires [article] is related to an electrician [specialty], for example) And then, based on customer sales, know who the customers are.

But this is a lot of work.

My second approach is to make a cluster segmentation first, and then discover which cluster belong to a specialty. (this is a lot better because I would be able to discover new segments)

But, how can I do that? What type of clustering should I occupy? Kmeans, fuzzy? What variables should I take to that model? Should I use PCA to know how many cluster to search?

The header of my data (simplified):

customer_id | transaction_id | transaction_date | item_article_id | item_group_id | item_category_id | item_qty | sales_amt

Any help would be appreciated (sorry my english)

Answer 1

You want to identify classes of customers based on what they buy (I presume this is for marketing reasons). This calls for a clustering approach. I will talk you through the entire setup.

The clustering space

Let us first consider what exactly you are clustering: either orders or customers. In either case, the way you characterize the items and the distances between them is the same. I will discuss the basic case for orders first, and then explain the considerations that apply to clustering by customers instead.

For your purpose, an order is characterized by what articles were purchased, and possibly also how many of them. In terms of a space, this means that you have a dimension for each type of article (item_article_id), for example the "wire" dimension. If all you care about is whether an article is bought or not, each item has a coordinate of either 0 or 1 in each dimension. If some order includes wire but not pipe, then it has a value of 1 on the "wire" dimension and 0 on the "pipe" dimension.

However, there is something to say for caring about the quantities. Perhaps plumbers buy lots of glue while electricians buy only small amounts. In that case, you can set the coordinate in each dimension to the quantity of the corresponding article (presumably item_qty). So suppose you have three articles, wire, pipe and glue, then an order described by the vector (2, 3, 0) includes 2 wire, 3 pipe and 0 glue, while an order described by the vector (0, 1, 4) includes 0 wire, 1 pipe and 4 glue.

If there is a large spread in the quantities for a given article, i.e. if some orders include order of magnitude more of some article than other orders, then it may be helpful to work with a log scale. Suppose you have these four orders:

1. 2 wire, 2 pipe, 1 glue
2. 3 wire, 2 pipe, 0 glue
3. 0 wire, 100 pipe, 1 glue
4. 0 wire, 300 pipe, 3 glue

The former two orders look like they may belong to electricians while the latter two look like they belong to plumbers. However, if you work with a linear scale, order 3 will turn out to be closer to orders 1 and 2 than to order 4. We fix that by using a log scale for the vectors that encode these orders (I use the base 10 logarithm here, but it does not matter which base you take because they differ only by a constant factor):

1. (0.30, 0.30, 0)
2. (0.48, 0.30, -2)
3. (-2, 2, 0)
4. (-2, 2.48, 0.48)

Now order 3 is closest to order 4, as we would expect. Note that I have used -2 as a special value to indicate the absence of an article, because the logarithm of 0 is not defined (log(x) tends to negative infinity as x tends to 0). -2 means that we pretend that the order included 1/100th of the article; you could make the special value more or less extreme, depending on how much weight you want to give to the fact that an article was not included.

The input to your clustering algorithm (regardless of which algorithm you take, see below) will be a position matrix with one row for each item (order or customer), one column for each dimension (article), and either the presence (0/1), amount, or logarithm of the amount in each cell, depending on which you choose based on the discussion above. If you cluster by customers, you can simply sum the amounts from all orders that belong to that customer before you calculate what goes into each cell of your position matrix (if you use the log scale, sum the amounts before taking the logarithm).

Clustering by orders rather than by customers gives you more detail, but also more noise. Customers may be consistent within an order but not between them; perhaps a customer sometimes behaves like a plumber and sometimes like an electrician. This is a pattern that you will only find if you cluster by orders. You will then find how often each customer belongs to each cluster; perhaps 70% of somebody's orders belong to the electrician type and 30% belong to the plumber type. On the other hand, a plumber may only buy pipe in one order and then only buy glue in the next order. Only if you cluster by customers and sum the amounts of their orders, you get a balanced view of what each customer needs on average.

From here on I will refer to your position matrix by the name my.matrix.

The clustering algorithm

If you want to be able to discover new customer types, you probably want to let the data speak for themselves as much as possible. A good old fashioned hierarchical clustering with complete linkage (CLINK) may be an appropriate choice in this case. In R, you simply do hclust(dist(my.matrix)) (this will use the Euclidean distance measure, which is probably good enough in your case). It will join closely neighbouring items or clusters together until all items are categorized in a hierarchical tree. You can treat any branch of the tree as a cluster, observe typical article amounts for that branch and decide whether that branch represents a customer segment by itself, should be split in sub-branches, or joined with a sibling branch instead. The advantage is that you find the "full story" of which items and clusters of items are most similar to each other and how much. The disadvantage is that the outcome of the algorithm does not tell you where to draw the borders between your customer segments; you can cut up the clustering tree in many ways, so it's up to your interpretation how you want to identify your customer types.

On the other hand, if you are comfortable fixing the number of clusters (k) beforehand, k-means is a very robust way to get just any segmentation of your customers in k distinct types. In R, you would do kmeans(my.matrix, k). For marketing purposes, it may be sufficient to have (say) 5 different profiles of customers that you make custom advertisement for, rather than treating all customers the same. With k-means you don't explore all of the diversity that is present in your data, but you might not need to do so anyway.

If you don't want to fix the number of clusters beforehand, but you also don't want to manually decide where to draw the borders between the segments afterwards, there is a third possibility. You start with the k-means algorithm, where you let it generate an amount of cluster centers that is much larger than the number of clusters that you hope to end up with (for example, if you hope to end up with somewhere about 10 clusters, let the k-means algorithm look for 200 clusters). Then, use the mean shift algorithm to further cluster the resulting centers. You will end up with a smaller number of compact clusters. The approach is explained in more detail by James Li over here. You can use the mean shift algorithm in R with the ms function from the LPCM package, see this documentation.

About using PCA

PCA will not tell you how many clusters you need. PCA answers a different question: which variables seem to represent a common underlying (hidden) factor. In a sense, it is a way to cluster variables, i.e. properties of entities, not to cluster the entities themselves. The number of principal components (common underlying factors) is not indicative of the number of clusters needed. PCA can still be interesting if you want to learn something about the predictive value of each article about a customer's interests.

Sources

• Michael J. Crawley, 2005. Statistics. An Introduction using R.
• Gerry P. Quinn and Michael J. Keough, 2002. Experimental Design and Data Analysis for Biologists.
• Wikipedia: hierarchical clustering, k-means, mean shift, PCA