Clustering Part 1. CSC 4510/9010: Applied Machine Learning. Dr. Paula Matuszek
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1 CSC 4510/9010: Applied Machine Learning 1 Clustering Part 1 Dr. Paula Matuszek Paula.Matuszek@villanova.edu Paula.Matuszek@gmail.com (610)
2 What is Clustering? 2 Given some instances with data: group instances such that examples within a group are similar examples in different groups are different These groups are clusters Unsupervised learning the instances do not include a class attribute.
3 Clustering Example Based on: 3
4 A Different Example 4 How would you group 'The price of crude oil has increased significantly 'Demand for crude oil outstrips supply' 'Some people do not like the flavor of olive oil' 'The food was very oily' 'Crude oil is in short supply' 'Oil platforms extract crude oil' 'Canola oil is supposed to be healthy' 'Iraq has significant oil reserves' 'There are different types of cooking oil
5 Another (Familiar) Example 5
6 Introduction Real Applications: Emerging Applications 8
7 In the Real World A technique demanded by many real world tasks Bank/Internet Security: fraud/spam pattern discovery Biology: taxonomy of living things such as kingdom, phylum, class, order, family, genus and species City-planning: Identifying groups of houses according to their house type, value, and geographical location Climate change: understanding earth climate, find patterns of atmospheric and ocean Finance: stock clustering analysis to uncover correlation underlying shares Image Compression/segmentation: coherent pixels grouped Information retrieval/organisation: Google search, topic-based news Land use: Identification of areas of similar land use in an earth observation database Marketing: Help marketers discover distinct groups in their customer bases, and then use this knowledge to develop targeted marketing programs Social network mining: special interest group automatic discovery 9
8 Clustering Basics 8 Collect examples Compute similarity among examples according to some metric Group examples together such that examples within a cluster are similar examples in different clusters are different Summarize each cluster Sometimes -- assign new instances to the most similar cluster
9 Measures of Similarity 9 In order to do clustering we need some kind of measure of similarity. This is basically our critic Vector of values, depends on domain: documents: bag of words, linguistic features purchases: cost, purchaser data, item data census data: most of what is collected Multiple different measures available
10 Measures of Similarity 10 Semantic similarity -- but this is hard. Similar attribute counts Number of attributes with the same value. Appropriate for large, sparse vectors, such as BOW. More complex vector comparisons: Euclidian Distance Cosine Similarity
11 Euclidean Distance 11 Euclidean distance: distance between two measures summed across each feature Squared differences to give more weight to larger difference dist(xi, xj) = sqrt((xi1-xj1) 2 +(xi2-xj2) (xin-xjn) 2 )
12 Euclidian 12 Calculate differences Ears: pointy? Muzzle: how many inches long? Tail: how many inches long? dist(x1, x2) = sqrt((0-1) 2 +(3-1) (2-4) 2 )=9 dist(x1, x3) = sqrt((0-0) 2 +(3-3) (2-3) 2 )=1
13 Cosine similarity measurement 13 Cosine similarity is a measure of similarity between two vectors by measuring the cosine of the angle between them. The result of the Cosine function is equal to 1 when the angle is 0, and it is less than 1 when the angle is of any other value. As the angle between the vectors shortens, the cosine angle approaches 1, meaning that the two vectors are getting closer, meaning that the similarity of whatever is represented by the vectors increases. Based on home.iitk.ac.in/~mfelixor/files/non-numeric-clustering-seminar.pp
14 Cosine Similarity 14 4 B(1,4) 3 A(3,2) C(3,3) Muzzle Tail
15 Clustering Algorithms 15 Flat K means Hierarchical Bottom up Top down (not common) Probabilistic Expectation Maximumization (E-M)
16 Partitioning (Flat) Algorithms 16 Partitioning method: Construct a partition of n documents into a set of K clusters Given: a set of documents and the number K Find: a partition of K clusters that optimizes the chosen partitioning criterion Globally optimal: exhaustively enumerate all partitions. Usually too expensive. Effective heuristic methods: K-means algorithm.
17 K-Means Clustering 17 Simplest hierarchical method, widely used Create clusters based on a centroid; each instance is assigned to the closest centroid K is given as a parameter. Heuristic and iterative
18 K-Means Clustering 18 Provide number of desired clusters, k. Randomly choose k instances as seeds. Form initial clusters based on these seeds. Calculate the centroid of each cluster. Iterate, repeatedly reallocating instances to closest centroids and calculating the new centroids Stop when clustering converges or after a fixed number of iterations. Based on: 18
19 K Means Example (K=2) 19 Pick seeds Reassign clusters Compute centroids Reasssign clusters x x x x Compute centroids Reassign clusters Converged! 22
20 K-Means 20 Tradeoff between having more clusters (better focus within each cluster) and having too many clusters. Overfitting again. Results can vary based on random seed selection. Some seeds can result in poor convergence rate, or convergence to sub-optimal clusterings. The algorithm is sensitive to outliers Data points that are far from other data points. Could be errors in the data recording or some special data points with very different values.
21 Problem! 21 Poor clusters based on initial seeds
22 Strengths of K-Means 22 Strengths: Simple: easy to understand and to implement Efficient: Time complexity: O(tkn), where n is the number of data points, k is the number of clusters, and t is the number of iterations. Since both k and t are small. k-means is considered a linear algorithm. K-means is most popular clustering algorithm. In practice, performs well, especially on text.
23 K-Means Weaknesses 23 Must choose K; poor choice can lead to poor clusters Clusters may differ in size or density All attributes are weighted Heuristic, based on initial random seeds; clusters may differ from run to run
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