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Basic Machine Learning: Clustering
CS 315 – Web Search and Data Mining
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Supervised vs. Unsupervised Learning
Two Fundamental Methods in Machine LearningSupervised Learning (“learn from my example”)
Goal: A program that performs a task as good as humans. TASK – well defined (the target function) EXPERIENCE – training data provided by a human PERFORMANCE – error/accuracy on the task
Unsupervised Learning (“see what you can find”) Goal: To find some kind of structure in the data. TASK – vaguely defined No EXPERIENCE No PERFORMANCE (but, there are some evaluations metrics)
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What is Clustering?
The most common form of Unsupervised Learning
Clustering is the process of grouping a set of physical or abstract objects
into classes (“clusters”) of similar objects
It can be used in IR: To improve recall in search For better navigation of search results
Ex1: Cluster to Improve Recall
Cluster hypothesis: Documents with similar text are related
Thus, when a query matches a document D, also return other documents in the cluster containing D.
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Ex2: Cluster for Better Navigation
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Clustering Characteristics
Flat Clustering vs Hierarchical Clustering Flat: just dividing objects in groups (clusters) Hierarchical: organize clusters in a hierarchy
Evaluating Clustering Internal Criteria
The intra-cluster similarity is high (tightness) The inter-cluster similarity is low (separateness)
External Criteria Did we discover the hidden classes?
(we need gold standard data for this evaluation)
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Clustering for Web IR
Representation for clustering Document representation Need a notion of similarity/distance
How many clusters? Fixed a priori? Completely data driven? Avoid “trivial” clusters - too large or small
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Recall: Documents as vectors
Each doc j is a vector of tf.idf values, one component for each term.
Can normalize to unit length.
Vector space terms are axes - aka features N docs live in this space even with stemming, may have 20,000+ dimensions
What makes documents related?
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ijijin
i ji
ji
j
jj idftfw
w
w
d
dd
,,
1 ,
, where
Intuition for relatedness
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t 1
D2
D1
D3
D4t 2
x
y
Documents that are “close together” in vector space talk about the same things.
What makes documents related?
Ideal: semantic similarity.Practical: statistical similarity
We will use cosine similarity.
We will describe algorithms in terms of cosine similarity.
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n
i kiw
jiw
jdsim
dd
kd
kj
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:, normalized of similarity Cosine
,
This is known as the “normalized inner product”.
Clustering Algorithms
Hierarchical algorithms Bottom-up, agglomerative clustering
Partitioning “flat” algorithms Usually start with a random (partial) partitioning Refine it iteratively
The famous k-means partitioning algorithm: Given: a set of n documents and the number k Compute: a partition of k clusters that
optimizes the chosen partitioning criterion
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K-means
Assumes documents are real-valued vectors.Clusters based on centroids of points in a cluster, c (= the center of gravity or mean) :
Reassignment of instances to clusters is based on distance to the current cluster centroids.
See Animation
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cx
xc
||
1(c)μ
K-Means Algorithm
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Let d be the distance measure between instances.
Select k random instances {s1, s2,… sk} as seeds.
Until clustering converges or other stopping criterion: For each instance xi: Assign xi to the cluster cj such that d(xi, sj) is minimal. (Update the seeds to the centroid of each cluster) For each cluster cj
sj = (cj)
K-means: Different Issues
When to stop? When a fixed number of iterations is reached When centroid positions do not change
Seed Choice Results can vary based on random seed selection. Try out multiple starting points
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Example showingsensitivity to seeds
A B
D E
C
F
If you start with centroids: B and Eyou converge to
If you start with centroids D and Fyou converge to:
Hierarchical clustering
Build a tree-based hierarchical taxonomy (dendrogram) from a set of unlabeled examples.
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animal
vertebrate
fish reptile amphib. mammal worm insect crustacean
invertebrate
Hierarchical Agglomerative Clustering
We assume there is a similarity function that determines the similarity of two instances.
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Start with all instances in their own cluster.Until there is only one cluster: Among the current clusters, determine the two clusters, ci and cj, that are most similar. Replace ci and cj with a single cluster ci cj
Algorithm:
Watch animation of HAC
What is the most similar cluster?
Single-link Similarity of the most cosine-similar (single-link)
Complete-link Similarity of the “furthest” points, the least cosine-similar
Group-average agglomerative clustering Average cosine between pairs of elements
Centroid clustering Similarity of clusters’ centroids
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Single link clustering
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1) Use maximum similarity of pairs:
),(max),(,
yxsimccsimji cycx
ji
2) After merging ci and cj, the similarity of the resulting cluster to another cluster, ck, is:
)),(),,(max()),(( kjkikji ccsimccsimcccsim
Complete link clustering
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1) Use minimum similarity of pairs:
2) After merging ci and cj, the similarity of the resulting cluster to another cluster, ck, is:
Major issue - labeling
After clustering algorithm finds clusters - how can they be useful to the end user?
Need a concise label for each cluster In search results, say “Animal” or “Car” in the jaguar example. In topic trees (Yahoo), need navigational cues.
Often done by hand, a posteriori.
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How to Label Clusters
Show titles of typical documents Titles are easy to scan Authors create them for quick scanning! But you can only show a few titles which may not fully represent
cluster
Show words/phrases prominent in cluster More likely to fully represent cluster Use distinguishing words/phrases But harder to scan
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Further issues
Complexity: Clustering is computationally expensive. Implementations need
careful balancing of needs.
How to decide how many clusters are best?
Evaluating the “goodness” of clustering There are many techniques, some focus on implementation issues
(complexity/time), some on the quality of
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