Question? Leave a message!




Document clustering

Document clustering
Introduction to Information Retrieval Introduction to Information Retrieval Document clustering www.ThesisScientist.comIntroduction to Information Retrieval Today’s Topic: Clustering  Document clustering  Motivations  Document representations  Success criteria  Clustering algorithms  Partitional  Hierarchical www.ThesisScientist.comIntroduction to Information Retrieval Ch. 16 What is clustering  Clustering: the process of grouping a set of objects into classes of similar objects  Documents within a cluster should be similar.  Documents from different clusters should be dissimilar.  The commonest form of unsupervised learning  Unsupervised learning = learning from raw data, as opposed to supervised data where a classification of examples is given  A common and important task that finds many applications in IR and other places www.ThesisScientist.comIntroduction to Information Retrieval Ch. 16 A data set with clear cluster structure  How would you design an algorithm for finding the three clusters in this case www.ThesisScientist.comIntroduction to Information Retrieval Sec. 16.1 Applications of clustering in IR  Whole corpus analysis/navigation  Better user interface: search without typing  For improving recall in search applications  Better search results (like pseudo RF)  For better navigation of search results  Effective “user recall” will be higher  For speeding up vector space retrieval  Clusterbased retrieval gives faster search www.ThesisScientist.comIntroduction to Information Retrieval Yahoo Hierarchy isn’t clustering but is the kind of output you want from clustering www.yahoo.com/Science … (30) agriculture biology physics CS space ... ... ... ... ... dairy botany cell AI courses crops craft magnetism HCI missions agronomy evolution forestry relativity www.ThesisScientist.comIntroduction to Information Retrieval Google News: automatic clustering gives an effective news presentation metaphor www.ThesisScientist.comIntroduction to Information Retrieval Sec. 16.1 Scatter/Gather: Cutting, Karger, and Pedersen www.ThesisScientist.comIntroduction to Information Retrieval For visualizing a document collection and its themes  Wise et al, “Visualizing the nonvisual” PNNL  ThemeScapes, Cartia  Mountain height = cluster size www.ThesisScientist.comIntroduction to Information Retrieval Sec. 16.1 For improving search recall  Cluster hypothesis Documents in the same cluster behave similarly with respect to relevance to information needs  Therefore, to improve search recall:  Cluster docs in corpus a priori  When a query matches a doc D, also return other docs in the cluster containing D  Hope if we do this: The query “car” will also return docs containing automobile  Because clustering grouped together docs containing car with those containing automobile. Why might this happen www.ThesisScientist.comIntroduction to Information Retrieval www.ThesisScientist.com yippy.com – grouping search resultsIntroduction to Information Retrieval Sec. 16.2 Issues for clustering  Representation for clustering  Document representation  Vector space Normalization  Centroids aren’t length normalized  Need a notion of similarity/distance  How many clusters  Fixed a priori  Completely data driven  Avoid “trivial” clusters too large or small  If a cluster's too large, then for navigation purposes you've wasted an extra user click without whittling down the set of documents much. www.ThesisScientist.comIntroduction to Information Retrieval Notion of similarity/distance  Ideal: semantic similarity.  Practical: termstatistical similarity  We will use cosine similarity.  Docs as vectors.  For many algorithms, easier to think in terms of a distance (rather than similarity) between docs.  We will mostly speak of Euclidean distance  But real implementations use cosine similarity www.ThesisScientist.comIntroduction to Information Retrieval Clustering Algorithms  Flat algorithms  Usually start with a random (partial) partitioning  Refine it iteratively  K means clustering  (Model based clustering)  Hierarchical algorithms  Bottomup, agglomerative  (Topdown, divisive) www.ThesisScientist.comIntroduction to Information Retrieval Hard vs. soft clustering  Hard clustering: Each document belongs to exactly one cluster  More common and easier to do  Soft clustering: A document can belong to more than one cluster.  Makes more sense for applications like creating browsable hierarchies  You may want to put a pair of sneakers in two clusters: (i) sports apparel and (ii) shoes  You can only do that with a soft clustering approach.  We won’t do soft clustering today. See IIR 16.5, 18 www.ThesisScientist.comIntroduction to Information Retrieval Partitioning Algorithms  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  Intractable for many objective functions  Ergo, exhaustively enumerate all partitions  Effective heuristic methods: Kmeans and K medoids algorithms www.ThesisScientist.com See also Kleinberg NIPS 2002 – impossibility for natural clusteringIntroduction to Information Retrieval Sec. 16.4 KMeans  Assumes documents are realvalued vectors.  Clusters based on centroids (aka the center of gravity or mean) of points in a cluster, c:  1 μ(c) x   c xc  Reassignment of instances to clusters is based on distance to the current cluster centroids.  (Or one can equivalently phrase it in terms of similarities) www.ThesisScientist.comIntroduction to Information Retrieval Sec. 16.4 KMeans Algorithm Select K random docs s , s ,… s as seeds. 1 2 K Until clustering converges (or other stopping criterion): For each doc d : i Assign d to the cluster c such that dist(x , s ) is minimal. i j i j (Next, update the seeds to the centroid of each cluster) For each cluster c j s = (c ) j j www.ThesisScientist.comIntroduction to Information Retrieval Sec. 16.4 K Means Example (K=2) Pick seeds Reassign clusters Compute centroids Reassign clusters x x x Compute centroids x x x Reassign clusters Converged www.ThesisScientist.comIntroduction to Information Retrieval Sec. 16.4 Termination conditions  Several possibilities, e.g.,  A fixed number of iterations.  Doc partition unchanged.  Centroid positions don’t change. Does this mean that the docs in a cluster are unchanged www.ThesisScientist.comIntroduction to Information Retrieval Sec. 16.4 Convergence  Why should the Kmeans algorithm ever reach a fixed point  A state in which clusters don’t change.  Kmeans 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 www.ThesisScientist.comIntroduction to Information Retrieval Sec. 16.4 Lower case Convergence of KMeans  Define goodness measure of cluster k as sum of squared distances from cluster centroid: 2  G = Σ (d – c ) (sum over all d in cluster k) k i i k i  G = Σ G k k  Reassignment monotonically decreases G since each vector is assigned to the closest centroid. www.ThesisScientist.comIntroduction to Information Retrieval Sec. 16.4 Convergence of KMeans  Recomputation monotonically decreases each G k since (m is number of members in cluster k): k 2  Σ (d – a) reaches minimum for: i  Σ –2(d – a) = 0 i  Σ d = Σ a i  m a = Σ d K i  a = (1/ m ) Σ d = c k i k  Kmeans typically converges quickly www.ThesisScientist.comIntroduction to Information Retrieval Sec. 16.4 Time Complexity  Computing distance between two docs is O(M) where M is the dimensionality of the vectors.  Reassigning clusters: O(KN) distance computations, or O(KNM).  Computing centroids: Each doc gets added once to some centroid: O(NM).  Assume these two steps are each done once for I iterations: O(IKNM). www.ThesisScientist.comIntroduction to Information Retrieval Sec. 16.4 Seed Choice  Results can vary based on Example showing sensitivity to seeds random seed selection.  Some seeds can result in poor convergence rate, or convergence to suboptimal In the above, if you start clusterings. with B and E as centroids you converge to A,B,C  Select good seeds using a heuristic and D,E,F (e.g., doc least similar to any If you start with D and F existing mean) you converge to  Try out multiple starting points A,B,D,E C,F  Initialize with the results of another method. www.ThesisScientist.comIntroduction to Information Retrieval Sec. 16.4 Kmeans issues, variations, etc.  Recomputing the centroid after every assignment (rather than after all points are reassigned) can improve speed of convergence of Kmeans  Assumes clusters are spherical in vector space  Sensitive to coordinate changes, weighting etc.  Disjoint and exhaustive  Doesn’t have a notion of “outliers” by default  But can add outlier filtering Dhillon et al. ICDM 2002 – variation to fix some issues with small document clusters www.ThesisScientist.comIntroduction to Information Retrieval How Many Clusters  Number of clusters K is given  Partition n docs into predetermined number of clusters  Finding the “right” number of clusters is part of the problem  Given docs, partition into an “appropriate” number of subsets.  E.g., for query results ideal value of K not known up front though UI may impose limits.  Can usually take an algorithm for one flavor and convert to the other. www.ThesisScientist.comIntroduction to Information Retrieval K not specified in advance  Say, the results of a query.  Solve an optimization problem: penalize having lots of clusters  application dependent, e.g., compressed summary of search results list.  Tradeoff between having more clusters (better focus within each cluster) and having too many clusters www.ThesisScientist.comIntroduction to Information Retrieval K not specified in advance  Given a clustering, define the Benefit for a doc to be the cosine similarity to its centroid  Define the Total Benefit to be the sum of the individual doc Benefits. Why is there always a clustering of Total Benefit n www.ThesisScientist.comIntroduction to Information Retrieval Penalize lots of clusters  For each cluster, we have a Cost C.  Thus for a clustering with K clusters, the Total Cost is KC.  Define the Value of a clustering to be = Total Benefit Total Cost.  Find the clustering of highest value, over all choices of K.  Total benefit increases with increasing K. But can stop when it doesn’t increase by “much”. The Cost term enforces this. www.ThesisScientist.comIntroduction to Information Retrieval Ch. 17 Hierarchical Clustering  Build a treebased hierarchical taxonomy (dendrogram) from a set of documents. animal vertebrate invertebrate fish reptile amphib. mammal worm insect crustacean  One approach: recursive application of a partitional clustering algorithm. www.ThesisScientist.comIntroduction to Information Retrieval Dendrogram: Hierarchical Clustering  Clustering obtained by cutting the dendrogram at a desired level: each connected component forms a cluster. www.ThesisScientist.comIntroduction to Information Retrieval Sec. 17.1 Hierarchical Agglomerative Clustering (HAC)  Starts with each doc in a separate cluster  then repeatedly joins the closest pair of clusters, until there is only one cluster.  The history of merging forms a binary tree or hierarchy. Note: the resulting clusters are still “hard” and induce a partition www.ThesisScientist.comIntroduction to Information Retrieval Sec. 17.2 Closest pair of clusters  Many variants to defining closest pair of clusters  Singlelink  Similarity of the most cosinesimilar (singlelink)  Completelink  Similarity of the “furthest” points, the least cosinesimilar  Centroid  Clusters whose centroids (centers of gravity) are the most cosinesimilar  Averagelink  Average cosine between pairs of elements www.ThesisScientist.comIntroduction to Information Retrieval Sec. 17.2 Single Link Agglomerative Clustering  Use maximum similarity of pairs: sim(c ,c ) max sim(x,y) i j xc ,yc i j  Can result in “straggly” (long and thin) clusters due to chaining effect.  After merging c and c , the similarity of the i j resulting cluster to another cluster, c , is: k sim((cc ),c ) max(sim(c ,c ),sim(c ,c )) i j k i k j k www.ThesisScientist.comIntroduction to Information Retrieval Sec. 17.2 Single Link Example www.ThesisScientist.comIntroduction to Information Retrieval Sec. 17.2 Complete Link  Use minimum similarity of pairs: sim(c ,c ) min sim(x,y) i j xc ,yc i j  Makes “tighter,” spherical clusters that are typically preferable.  After merging c and c , the similarity of the resulting i j cluster to another cluster, c , is: k sim((cc ),c ) min(sim(c ,c ),sim(c ,c )) i j k i k j k C C C i j k www.ThesisScientist.comIntroduction to Information Retrieval Sec. 17.2 Complete Link Example www.ThesisScientist.comIntroduction to Information Retrieval Sec. 17.2.1 Computational Complexity  In the first iteration, all HAC methods need to compute similarity of all pairs of N initial instances, 2 which is O(N ).  In each of the subsequent N2 merging iterations, compute the distance between the most recently created cluster and all other existing clusters. 2  In order to maintain an overall O(N ) performance, computing similarity to each other cluster must be done in constant time. 3 2  Often O(N ) if done naively or O(N log N) if done more cleverly www.ThesisScientist.comIntroduction to Information Retrieval Sec. 17.3 Group Average  Similarity of two clusters = average similarity of all pairs within merged cluster. 1 sim(c ,c ) sim(x,y)  i j  cc (cc1) x(cc ) y(cc ):yx i j i j i j i j  Compromise between single and complete link.  Two options:  Averaged across all ordered pairs in the merged cluster  Averaged over all pairs between the two original clusters  No clear difference in efficacy www.ThesisScientist.comIntroduction to Information Retrieval Sec. 17.3 Computing Group Average Similarity  Always maintain sum of vectors in each cluster.  s(c ) x j  xc j  Compute similarity of clusters in constant time:  (s(c )s(c ))(s(c )s(c )) (c  c ) i j i j i j sim(c ,c ) i j (c  c )(c  c 1) i j i j www.ThesisScientist.comIntroduction to Information Retrieval Sec. 16.3 What Is A Good Clustering  Internal criterion: A good clustering will produce high quality clusters in which:  the intraclass (that is, intracluster) similarity is high  the interclass similarity is low  The measured quality of a clustering depends on both the document representation and the similarity measure used www.ThesisScientist.comIntroduction to Information Retrieval Sec. 16.3 External criteria for clustering quality  Quality measured by its ability to discover some or all of the hidden patterns or latent classes in gold standard data  Assesses a clustering with respect to ground truth … requires labeled data  Assume documents with C gold standard classes, while our clustering algorithms produce K clusters, ω , ω , …, ω with n members. 1 2 K i www.ThesisScientist.comIntroduction to Information Retrieval Sec. 16.3 External Evaluation of Cluster Quality  Simple measure: purity, the ratio between the dominant class in the cluster π and the size of i cluster ω i 1 Purity( ) max (n ) jC i j ij n i  Biased because having n clusters maximizes purity  Others are entropy of classes in clusters (or mutual information between classes and clusters) www.ThesisScientist.comIntroduction to Information Retrieval Sec. 16.3 Purity example    Cluster I Cluster II Cluster III Cluster I: Purity = 1/6 (max(5, 1, 0)) = 5/6 Cluster II: Purity = 1/6 (max(1, 4, 1)) = 4/6 Cluster III: Purity = 1/5 (max(2, 0, 3)) = 3/5 www.ThesisScientist.comIntroduction to Information Retrieval Sec. 16.3 Rand Index measures between pair decisions. Here RI = 0.68 Different Number of Same Cluster Clusters in points in clustering clustering Same class in 24 20 ground truth Different classes in 72 20 ground truth www.ThesisScientist.comIntroduction to Information Retrieval Sec. 16.3 Rand index and Cluster Fmeasure AD RI ABCD Compare with standard Precision and Recall: A A P R AB AC People also define and use a cluster F measure, which is probably a better measure. www.ThesisScientist.comIntroduction to Information Retrieval Final word and resources  In clustering, clusters are inferred from the data without human input (unsupervised learning)  However, in practice, it’s a bit less clear: there are many ways of influencing the outcome of clustering: number of clusters, similarity measure, representation of documents, . . .  Resources  IIR 16 except 16.5  IIR 17.1–17.3 www.ThesisScientist.com
sharer
Presentations
Free
Document Information
Category:
Presentations
User Name:
RyanCanon
User Type:
Teacher
Country:
United Arab Emirates
Uploaded Date:
20-07-2017