1. ZHANGXI LIN TEXAS TECH UNIVERSITY Lecture Notes 10 CRM Segmentation - Introduction

2. Outline CRM and Segmentation Review of Clustering Data Mining  Types of Clustering  K-Means Clustering  Hierarchical Clustering

3. Segmentation in the Context of CRM Segmentation: Subdividing the population according to known good discriminators Applying clustering data mining can help segmentation

4. Segmentation Types and Methods Interchangeable between segmentation and record classification in the context of CRM Customer profiling: to gain insight of the 4W – Who, what, where, and when Customer likeness clustering RFM cell classification grouping Purchase affinity clustering

5. Mass Customization vs. Mass Marketing Mass customization: tailor product/service/promotion to each individual customer, or a few customer, or a segment Fact: 29% of all marketing services are classified as a mass marketing segment

6. Promotions or Communications by Segment Groups Case: Three groups of customer profile  Medium-sized companies. Good customer, purchasing from direct channels.  Small-sized companies. Purchase only a few products. Need specific services  Large companies. Not loyal enough

7. Long Tail Theory The phrase The Long Tail (as a proper noun with capitalized letters) was first coined by Chris Anderson in an October 2004 Wired magazine article to describe the niche strategy of businesses, such as Amazon.com or Netflix, that sell a large number of unique items, each in relatively small quantities.proper nounChris AndersonAmazon.com Netflix The distribution and inventory costs of these businesses allow them to realize significant profit out of selling small volumes of hard-to-find items to many customers, instead of only selling large volumes of a reduced number of popular items. The group of persons that buy the hard-to-find or "non-hit" items is the customer demographic called the Long Tail. Given a large enough availability of choice, a large population of customers, and negligible stocking and distribution costs, the selection and buying pattern of the population results in a power law distribution curve, or Pareto distribution. This suggests that a market with a high freedom of choice will create a certain degree of inequality by favoring the upper 20% of the items ("hits" or "head") against the other 80% ("non-hits" or "long tail").power law Pareto distribution

8. Long Tail Theory

9. Demonstration Dataset: Buytest Tasks  Distributions of variables

10. Types of Clustering

11. Data & Text Mining 11 Types of Clustering A clustering is a set of clusters Important distinction between hierarchical and partitional sets of clusters Partitional Clustering  A division data objects into non-overlapping subsets (clusters) such that each data object is in exactly one subset Hierarchical clustering  A set of nested clusters organized as a hierarchical tree

12. Data & Text Mining 12 Partitional Clustering Original Points A Partitional Clustering

13. Data & Text Mining 13 Hierarchical Clustering Traditional Hierarchical Clustering Non-traditional Hierarchical Clustering Non-traditional Dendrogram Traditional Dendrogram

14. Data & Text Mining 14 Other Distinctions Between Sets of Clusters Exclusive versus non-exclusive  In non-exclusive clustering, points may belong to multiple clusters.  Can represent multiple classes or ‘border’ points Fuzzy versus non-fuzzy  In fuzzy clustering, a point belongs to every cluster with some weight between 0 and 1  Weights must sum to 1  Probabilistic clustering has similar characteristics Partial versus complete  In some cases, we only want to cluster some of the data Heterogeneous versus homogeneous  Cluster of widely different sizes, shapes, and densities

15. Data & Text Mining 15 Types of Clusters – the outcomes of clustering Well-separated clusters Center-based clusters Contiguous clusters Density-based clusters Property or Conceptual Described by an Objective Function

16. Data & Text Mining 16 Types of Clusters: Well-Separated Well-Separated Clusters:  A cluster is a set of points such that any point in a cluster is closer (or more similar) to every other point in the cluster than to any point not in the cluster. 3 well-separated clusters

17. Data & Text Mining 17 Types of Clusters: Center-Based Center-based  A cluster is a set of objects such that an object in a cluster is closer (more similar) to the “center” of a cluster, than to the center of any other cluster  The center of a cluster is often a centroid, the average of all the points in the cluster, or a medoid, the most “representative” point of a cluster 4 center-based clusters

18. Data & Text Mining 18 Types of Clusters: Contiguity-Based Contiguous Cluster (Nearest neighbor or Transitive)  A cluster is a set of points such that a point in a cluster is closer (or more similar) to one or more other points in the cluster than to any point not in the cluster. 8 contiguous clusters

19. Data & Text Mining 19 Types of Clusters: Density-Based Density-based  A cluster is a dense region of points, which is separated by low-density regions, from other regions of high density.  Used when the clusters are irregular or intertwined, and when noise and outliers are present. 6 density-based clusters

20. Data & Text Mining 20 Types of Clusters: Conceptual Clusters Shared Property or Conceptual Clusters  Finds clusters that share some common property or represent a particular concept.. 2 Overlapping Circles

21. Data & Text Mining 21 Types of Clusters: Objective Function Clusters Defined by an Objective Function  Finds clusters that minimize or maximize an objective function.  Enumerate all possible ways of dividing the points into clusters and evaluate the `goodness' of each potential set of clusters by using the given objective function. (NP Hard)  Can have global or local objectives.  Hierarchical clustering algorithms typically have local objectives  Partitional algorithms typically have global objectives  A variation of the global objective function approach is to fit the data to a parameterized model.  Parameters for the model are determined from the data.  Mixture models assume that the data is a ‘mixture' of a number of statistical distributions.

22. Data & Text Mining 22 Types of Clusters: Objective Function … Map the clustering problem to a different domain and solve a related problem in that domain  Proximity matrix defines a weighted graph, where the nodes are the points being clustered, and the weighted edges represent the proximities between points  Clustering is equivalent to breaking the graph into connected components, one for each cluster.  Want to minimize the edge weight between clusters and maximize the edge weight within clusters

23. Data & Text Mining 23 Distance of clusters

24. Data & Text Mining 24 Manhattan Distance (U 1,V 1 ) (U 2,V 2 ) L 1 = |U 1 - U 2 | + |V 1 - V 2 |

25. Data & Text Mining 25 Euclidean Distance (U 1,V 1 ) (U 2,V 2 ) L 2 = ((U 1 - U 2 ) 2 + (V 1 - V 2 ) 2 ) 1/2

26. Data & Text Mining 26 Euclidean Distance Distance Matrix

27. Data & Text Mining 27 Minkowski Distance Minkowski Distance is a generalization of Euclidean Distance Where r is a parameter, n is the number of dimensions (attributes) and p k and q k are, respectively, the kth attributes (components) or data objects p and q.

28. Data & Text Mining 28 Minkowski Distance: Examples r = 1. City block (Manhattan, taxicab, L 1 norm) distance.  A common example of this is the Hamming distance, which is just the number of bits that are different between two binary vectors r = 2. Euclidean distance r  . “supremum” (L max norm, L  norm) distance.  This is the maximum difference between any component of the vectors Do not confuse r with n, i.e., all these distances are defined for all numbers of dimensions.

29. Data & Text Mining 29 Minkowski Distance Distance Matrix

30. Data & Text Mining 30 Cosine Similarity If d 1 and d 2 are two document vectors, then cos( d 1, d 2 ) = (d 1  d 2 ) / ||d 1 || ||d 2 ||, where  indicates vector dot product and || d || is the length of vector d. Example: d 1 = 3 2 0 5 0 0 0 2 0 0 d 2 = 1 0 0 0 0 0 0 1 0 2 d 1  d 2 = 3*1 + 2*0 + 0*0 + 5*0 + 0*0 + 0*0 + 0*0 + 2*1 + 0*0 + 0*2 = 5 ||d 1 || = (3*3+2*2+0*0+5*5+0*0+0*0+0*0+2*2+0*0+0*0) 0.5 = (42) 0.5 = 6.481 ||d 2 || = (1*1+0*0+0*0+0*0+0*0+0*0+0*0+1*1+0*0+2*2) 0.5 = (6) 0.5 = 2.245 cos( d 1, d 2 ) =.3150

31. Data & Text Mining 31 K-Means clustering

32. Data & Text Mining 32 K-means Clustering Partitional clustering approach Each cluster is associated with a centroid (center point) Each point is assigned to the cluster with the closest centroid Number of clusters, K, must be specified The basic algorithm is very simple

33. Data & Text Mining 33 K-means Clustering – Details Initial centroids are often chosen randomly.  Clusters produced vary from one run to another. The centroid is (typically) the mean of the points in the cluster. ‘Closeness’ is measured by Euclidean distance, cosine similarity, correlation, etc. K-means will converge for common similarity measures mentioned above. Most of the convergence happens in the first few iterations.  Often the stopping condition is changed to ‘Until relatively few points change clusters’ Complexity is O( n * K * I * d )  n = number of points, K = number of clusters, I = number of iterations, d = number of attributes

34. Data & Text Mining 34 Two different K-means Clusterings Sub-optimal Clustering Optimal Clustering Original Points

35. Data & Text Mining 35 Importance of Choosing Initial Centroids

36. Data & Text Mining 36 Importance of Choosing Initial Centroids

37. Data & Text Mining 37 Evaluating K-means Clusters Most common measure is Sum of Squared Error (SSE)  For each point, the error is the distance to the nearest cluster  To get SSE, we square these errors and sum them.  x is a data point in cluster C i and m i is the representative point for cluster C i  can show that m i corresponds to the center (mean) of the cluster  Given two clusters, we can choose the one with the smallest error  One easy way to reduce SSE is to increase K, the number of clusters  A good clustering with smaller K can have a lower SSE than a poor clustering with higher K

38. Data & Text Mining 38 Importance of Choosing Initial Centroids

39. Data & Text Mining 39 Importance of Choosing Initial Centroids

40. Data & Text Mining 40 Problems with Selecting Initial Points If there are K ‘real’ clusters then the chance of selecting one centroid from each cluster is small.  Chance is relatively small when K is large  If clusters are the same size, n, then  For example, if K = 10, then probability = 10!/10 10 = 0.00036  Sometimes the initial centroids will readjust themselves in ‘right’ way, and sometimes they don’t  Consider an example of five pairs of clusters

41. Data & Text Mining 41 10 Clusters Example Starting with two initial centroids in one cluster of each pair of clusters

42. Data & Text Mining 42 10 Clusters Example Starting with two initial centroids in one cluster of each pair of clusters

43. Data & Text Mining 43 10 Clusters Example Starting with some pairs of clusters having three initial centroids, while other have only one.

44. Data & Text Mining 44 10 Clusters Example Starting with some pairs of clusters having three initial centroids, while other have only one.

45. Data & Text Mining 45 Hierarchical Clustering

46. Data & Text Mining 46 Hierarchical Clustering Produces a set of nested clusters organized as a hierarchical tree Can be visualized as a dendrogram  A tree like diagram that records the sequences of merges or splits

47. Data & Text Mining 47 Strengths of Hierarchical Clustering Do not have to assume any particular number of clusters  Any desired number of clusters can be obtained by ‘cutting’ the dendogram at the proper level They may correspond to meaningful taxonomies  Example in biological sciences (e.g., animal kingdom, phylogeny reconstruction, …)

48. Data & Text Mining 48 Hierarchical Clustering Two main types of hierarchical clustering  Agglomerative:  Start with the points as individual clusters  At each step, merge the closest pair of clusters until only one cluster (or k clusters) left  Divisive:  Start with one, all-inclusive cluster  At each step, split a cluster until each cluster contains a point (or there are k clusters) Traditional hierarchical algorithms use a similarity or distance matrix  Merge or split one cluster at a time

49. Data & Text Mining 49 Agglomerative Clustering Algorithm More popular hierarchical clustering technique Basic algorithm is straightforward 1. Compute the proximity matrix 2. Let each data point be a cluster 3. Repeat 4. Merge the two closest clusters 5. Update the proximity matrix 6. Until only a single cluster remains Key operation is the computation of the proximity of two clusters  Different approaches to defining the distance between clusters distinguish the different algorithms

50. Data & Text Mining 50 Starting Situation Start with clusters of individual points and a proximity matrix p1 p3 p5 p4 p2 p1p2p3p4p5......... Proximity Matrix

51. Data & Text Mining 51 Intermediate Situation After some merging steps, we have some clusters C1 C4 C2 C5 C3 C2C1 C3 C5 C4 C2 C3C4C5 Proximity Matrix

52. Data & Text Mining 52 Intermediate Situation We want to merge the two closest clusters (C2 and C5) and update the proximity matrix. C1 C4 C2 C5 C3 C2C1 C3 C5 C4 C2 C3C4C5 Proximity Matrix

53. Data & Text Mining 53 After Merging The question is “How do we update the proximity matrix?” C1 C4 C2 U C5 C3 ? ? ? ? ? C2 U C5 C1 C3 C4 C2 U C5 C3C4 Proximity Matrix

54. Data & Text Mining 54 How to Define Inter-Cluster Similarity p1 p3 p5 p4 p2 p1p2p3p4p5......... Similarity? MIN MAX Group Average Distance Between Centroids Other methods driven by an objective function  Ward’s Method uses squared error Proximity Matrix

55. Data & Text Mining 55 How to Define Inter-Cluster Similarity p1 p3 p5 p4 p2 p1p2p3p4p5......... Proximity Matrix MIN MAX Group Average Distance Between Centroids Other methods driven by an objective function  Ward’s Method uses squared error

56. Data & Text Mining 56 How to Define Inter-Cluster Similarity p1 p3 p5 p4 p2 p1p2p3p4p5......... Proximity Matrix MIN MAX Group Average Distance Between Centroids Other methods driven by an objective function  Ward’s Method uses squared error

57. Data & Text Mining 57 How to Define Inter-Cluster Similarity p1 p3 p5 p4 p2 p1p2p3p4p5......... Proximity Matrix MIN MAX Group Average Distance Between Centroids Other methods driven by an objective function  Ward’s Method uses squared error

58. Data & Text Mining 58 How to Define Inter-Cluster Similarity p1 p3 p5 p4 p2 p1p2p3p4p5......... Proximity Matrix MIN MAX Group Average Distance Between Centroids Other methods driven by an objective function  Ward’s Method uses squared error 

59. Data & Text Mining 59 Cluster Similarity: MIN or Single Link Similarity of two clusters is based on the two most similar (closest) points in the different clusters  Determined by one pair of points, i.e., by one link in the proximity graph. 12345

60. Data & Text Mining 60 Hierarchical Clustering: MIN Nested ClustersDendrogram 1 2 3 4 5 6 1 2 3 4 5

61. Data & Text Mining 61 Strength of MIN Original Points Two Clusters Can handle non-elliptical shapes

62. Data & Text Mining 62 Limitations of MIN Original Points Two Clusters Sensitive to noise and outliers

63. Data & Text Mining 63 Cluster Similarity: MAX or Complete Linkage Similarity of two clusters is based on the two least similar (most distant) points in the different clusters  Determined by all pairs of points in the two clusters 12345

64. Data & Text Mining 64 Hierarchical Clustering: MAX Nested ClustersDendrogram 1 2 3 4 5 6 1 2 5 3 4

65. Data & Text Mining 65 Strength of MAX Original Points Two Clusters Less susceptible to noise and outliers

66. Data & Text Mining 66 Limitations of MAX Original Points Two Clusters Tends to break large clusters Biased towards globular clusters

67. Data & Text Mining 67 Cluster Similarity: Group Average Proximity of two clusters is the average of pairwise proximity between points in the two clusters. Need to use average connectivity for scalability since total proximity favors large clusters 12345

68. Data & Text Mining 68 Hierarchical Clustering: Group Average Nested ClustersDendrogram 1 2 3 4 5 6 1 2 5 3 4

69. Data & Text Mining 69 Hierarchical Clustering: Group Average Compromise between Single and Complete Link Strengths  Less susceptible to noise and outliers Limitations  Biased towards globular clusters

70. Data & Text Mining 70 Cluster Similarity: Ward’s Method Similarity of two clusters is based on the increase in squared error when two clusters are merged  Similar to group average if distance between points is distance squared Less susceptible to noise and outliers Biased towards globular clusters Hierarchical analogue of K-means  Can be used to initialize K-means