Cluster Analysis

Cluster analysis divides data into groups that are meaningful or serve a purpose. The basic idea is to identify characteristics that seem to be common across groups within the data and also differentiates different groups. Essentially the outcome of a cluster analysis results in data groups that have the greatest similarity of key characteristics within the group but are dissimilar across groups.  For example, Toyota Camry buyers may share common demographics or psychographics which will be different from Lexus buyers.

Clustering is a critical component of a segmented marketing strategy.

This is useful in identifying similar groups that can be targeted separately in advertising and promotions. These groups are called clusters and individuals are assigned to a cluster based on their how close their values on different profiling variables are to the cluster average or ‘center’.

The graph below demonstrates how stores, outlets, dealerships or hotel locations can be clustered based on demographic structure and performance.

A common application is. assigning similar customers to groups based on their profile on different variables like age, income, geographic location, gender, family size and education.

Cluster Analysis Approaches

Partitional: Partitional Cluster Analysis directly divides data into disjoint groups- it doesn't consider subsets or groups within clusters. The "K-Means" algorithm is a common partitional clustering approach that attempts to divide n datapoints to K clusters. This is an iterative process, which starts with 2 assumptions- the number of clusters and their initial means for each clustering factor (the variables on the basis of which clustering will be done). The means may be randomly picked or explicitly provided based on prior beliefs. The algorithm then proceeds to assign each datapoint to the nearest mean (by minimizing the Euclidean distance or the sum of the squared distances across all clustering factors). Once all datapoints are assigned, cluster means are recalculated based on the datapoints they now contain and the assignment process is repeated, means recalculated and so on until the means do not change between iterations, at this point the algorithm would be considered to have converged. Partitional Clusters are also typically exclusive or "Hard" clusters- clusters are mutually exclusive and one point cannot be in two clusters at the same time.

Hierarchical: Hierarchical clusters do not consider clusters as disjoint but rather as forming a hierarchy, almost like a tree (actually a dendrogram)- at the lowest level, every point can potentially form it's own cluster, at the highest point, all points fall into one cluster. Hierarchical Cluster Analysis falls into two broad classes:

Agglomerative: Starts with each point as it's own cluster and progressively merges the two closest clusters together, forming a hierarchy, until you reach the "top of the tree" where all points fall into a single cluster.

Divisive: You start at the "top of the tree", with all points in one cluster and progressively divide datapoints into clusters. The first split involves separating out the datapoint that is farthest from the mean of the remaining points and then other points that are closer to this point than to the "centroid" of the other points are assigned to this new cluster. The two new clusters thus created are further separated into sets of two using the same process and so on until every single point becomes its own cluster- this will be the "root" of the tree.

Hierarchical clusters are "exclusive" within each level of the dendrogram or "tree".

Fuzzy Clusters: Not all clustering approaches are exclusive or hard- in Fuzzy clustering a data point can belong to two clusters at the same time. A common technique of Fuzzy clustering is the C-Means algorithm, where a point belongs to a cluster with some probability, and the centroid of the cluster is the probability weighted average of all the points. Fuzzy clusters aren't uncommon in business- for instance segmenting consumers into disjoint clusters for marketing purposes may not be optimal- different marketing programs may require different cluster structure. For instance a heavily income based cluster structure may be best for price promotion programs, whereas an ethnographics or psychographics weighted clustering structure may be optimal for advertising programs. Fuzzy clustering would provide an efficient approach to combining these different purposes.