1 CSCI 5417 Information Retrieval Systems Jim Martin!Lecture 15 10/13/2011 10/17/11 CSCI5417-IR 2Today 10/13 More Clustering Finish flat clustering Hierarchical clustering2 10/17/11 CSCI5417-IR 3K-Means Assumes documents are real-valued vectors. Clusters based on centroids (aka the center of gravity or mean) of points in a cluster, c: Iterative reassignment of instances to clusters is based on distance to the current cluster centroids. (Or one can equivalently phrase it in terms of similarities) € µ(c) =1| c | x x ∈c∑10/17/11 CSCI5417-IR 4K-Means Algorithm Select K random docs {s1, s2,… sK} as seeds. Until stopping criterion: For each doc di: Assign di to the cluster cj such that dist(di, sj) is minimal. For each cluster c_j s_j = m(c_j)3 10/17/11 CSCI5417-IR 5K Means Example (K=2) Pick seeds Assign clusters Compute centroids x x Reassign clusters x x x x Compute centroids Reassign clusters Converged! 10/17/11 CSCI5417-IR 6Termination conditions Several possibilities A fixed number of iterations Doc partition unchanged Centroid positions don’t change4 Convergence Why should the K-means algorithm ever reach a fixed point? A state in which clusters don’t change. K-means is a special case of a general procedure known as the Expectation Maximization (EM) algorithm. EM is known to converge. Number of iterations could be large. But in practice usually isn’t Sec. 16.4 Seed Choice Results can vary based on random seed selection. Some seeds can result in poor convergence rate, or convergence to sub-optimal clusterings. Select good seeds using a heuristic (e.g., doc least similar to any existing mean) Try out multiple starting points Initialize with the results of another method. Sec. 16.45 Do this with K=2 10/17/11 CSCI5417-IR 910/17/11 CSCI5417-IR 10Hierarchical Clustering Build a tree-based hierarchical taxonomy (dendrogram) from a set of unlabeled examples. animal vertebrate fish reptile amphib. mammal worm insect crustacean invertebrate6 Dendrogram: Hierarchical Clustering Traditional clustering partition is obtained by cutting the dendrogram at a desired level: each connected component forms a cluster. 11Break Past HW Best score on part 2 is .437 Best approaches Multifield indexing of title/keywords/abstract Snowball (English), Porter Tuning the stop list Ensemble (voting) Mixed results Boosts Relevance feedback 10/17/11 CSCI5417-IR 127 Descriptions For the most part, your approaches were pretty weak (or your descriptions were) Failed to report R-Precision Use of some kind of systematic approach X didn’t work Interactions between approaches Lack of details Use relevance feedback and it gave me Z I changed the stop list Boosted the title field Etc. 10/17/11 CSCI5417-IR 13Next HW Due 10/25 I have a new untainted test set So don’t worry about checking for the test document; it won’t be there 10/17/11 CSCI5417-IR 148 10/17/11 CSCI5417-IR 15 Agglomerative (bottom-up): Start with each document being a single cluster. Eventually all documents belong to the same cluster. Divisive (top-down): Start with all documents belong to the same cluster. Eventually each node forms a cluster on its own. Does not require the number of clusters k to be known in advance But it does need a cutoff or threshold parameter condition Hierarchical Clustering algorithms 10/17/11 CSCI5417-IR 16Hierarchical -> Partition Run the algorithm to completion Take a slice across the tree at some level Produces a partition Or insert an early stopping condition into either top-down or bottom-up9 10/17/11 CSCI5417-IR 17Hierarchical Agglomerative Clustering (HAC) Assumes a similarity function for determining the similarity of two instances and two clusters. Starts with all instances in separate clusters and then repeatedly joins the two clusters that are most similar until there is only one cluster. The history of merging forms a binary tree or hierarchy. 10/17/11 CSCI5417-IR 18Hierarchical Clustering Key problem: as you build clusters, how do you represent each cluster, to tell which pair of clusters is closest?10 10/17/11 CSCI5417-IR 19“Closest pair” in Clustering Many variants to defining closest pair of clusters Single-link Similarity of the most cosine-similar Complete-link Similarity of the “furthest” points, the least cosine-similar “Center of gravity” Clusters whose centroids (centers of gravity) are the most cosine-similar Average-link Average cosine between all pairs of elements 10/17/11 CSCI5417-IR 20Single Link Agglomerative Clustering Use maximum similarity of pairs: Can result in “straggly” (long and thin) clusters due to chaining effect. After merging ci and cj, the similarity of the resulting cluster to another cluster, ck, is:11 10/17/11 CSCI5417-IR 21Single Link Example 10/17/11 CSCI5417-IR 22Complete Link Agglomerative Clustering Use minimum similarity of pairs: Makes “tighter,” spherical clusters that are typically preferable. After merging ci and cj, the similarity of the resulting cluster to another cluster, ck, is:12 10/17/11 CSCI5417-IR 23Complete Link Example 10/17/11 CSCI5417-IR 24Misc. Clustering Topics Clustering terms Clustering people Feature selection Labeling clusters13 10/17/11 CSCI5417-IR 25Term vs. document space So far, we clustered docs based on their similarities in term space For some applications, e.g., topic analysis for inducing navigation structures, you can “dualize”: Use docs as axes Represent (some) terms as vectors Cluster terms, not docs
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