Advanced Multimedia Text Clustering Tamara Berg. Reminder - Classification Given some labeled training documents Determine the best label for a test (query)

Advanced Multimedia

Text ClusteringTamara Berg

Reminder - Classification

• Given some labeled training documents• Determine the best label for a test (query)

document

What if we don’t have labeled data?

• We can’t do classification.


• We can’t do classification.• What can we do?

– Clustering - the assignment of objects into groups (called clusters) so that objects from the same cluster are more similar to each other than objects from different clusters.




– Often similarity is assessed according to a distance measure.




– Often similarity is assessed according to a distance measure.

– Clustering is a common technique for statistical data analysis, which is used in many fields, including machine learning, data mining, pattern recognition, image analysis and bioinformatics.

Any of the similarity metrics we talked about before (SSD, angle between vectors)

Document Clustering

Clustering is the process of grouping a set ofdocuments into clusters of similar documents.

Documents within a cluster should be similar.

Documents from different clusters should bedissimilar.

Source: Hinrich Schutze






Google newsFlickr Clusters

http://news.google.com/

http://www.flickr.com/photos/tags/apple/clusters/


How to cluster Documents

Reminder - Vector Space Model

Documents are represented as vectors in term space

A vector distance/similarity measure between two documents is used to compare documents

Slide from Mitch Marcus

Document Vectors:One location for each word.

nova galaxy heat h’wood film rolediet fur

10 5 3

5 10 10 8 7 9 10 5

10 10 9 10

5 7 9 6 10 2 8

7 5 1 3

ABCDEFGHI

“Nova” occurs 10 times in text A“Galaxy” occurs 5 times in text A“Heat” occurs 3 times in text A(Blank means 0 occurrences.)


Document Vectors

nova galaxy heat h’wood film rolediet fur

10 5 3

5 10 10 8 7

9 10 5 10 10 9 10

5 7 9 6 10 2 8

7 5 1 3

ABCDEFGHI

Document ids


TF x IDF Calculation

)/log(* kikik nNtfw

€

Tk = term k in document Ditf ik = frequency of term Tk in document Diidfk = inverse document frequency of term Tk in C

N = total number of documents in the collection C

nk = the number of documents in C that contain Tk

idfk = log Nkn( )


W1 W2 W3 … WnA

Features

F1 F2 F3 … FnA

Define whatever features you like:Length of longest string of CAP’sNumber of $’sUseful words for the task…

Similarity between documents

A = [10 5 3 0 0 0 0 0];G = [5 0 7 0 0 9 0 0];E = [0 0 0 0 0 10 10 0];

Sum of Squared Distances (SSD) =

SSD(A,G) = ?SSD(A,E) = ?SSD(G,E) = ?Which pair of documents are the most similar?

€

(X ii=1

n

∑ −Yi)2


source: Dan Klein

K-means clustering

• Want to minimize sum of squared Euclidean distances between points xi and their nearest cluster centers mk

k

ki

ki mxMXDcluster

clusterinpoint

2)(),(

source: Svetlana Lazebnik

K-means clustering

• Want to minimize sum of squared Euclidean distances between points xi and their nearest cluster centers mk

k

ki

ki mxMXDcluster

clusterinpoint

2)(),(


source: Dan Klein

source: Dan Klein

source: Dan Klein

Convergence of K Means

• K-means converges to a fixed point in a finite number of iterations.

Proof:




Proof:• The sum of squared distances (RSS) decreases during

reassignment.





reassignment.• (because each vector is moved to a closer centroid)





reassignment.• (because each vector is moved to a closer centroid)• RSS decreases during recomputation.





reassignment.• (because each vector is moved to a closer centroid)• RSS decreases during recomputation.• Thus: We must reach a fixed point.





reassignment.• (because each vector is moved to a closer centroid)• RSS decreases during recomputation.• Thus: We must reach a fixed point.• But we don’t know how long convergence will take!





reassignment.• (because each vector is moved to a closer centroid)• RSS decreases during recomputation.• Thus: We must reach a fixed point.• But we don’t know how long convergence will take!• If we don’t care about a few docs switching back and forth,

then convergence is usually fast (< 10-20 iterations).


source: Dan Klein

source: Dan Klein



Hierarchical clustering strategies

• Agglomerative clustering• Start with each point in a separate cluster• At each iteration, merge two of the “closest” clusters

• Divisive clustering• Start with all points grouped into a single cluster• At each iteration, split the “largest” cluster


source: Dan Klein

source: Dan Klein

Divisive Clustering

• Top-down (instead of bottom-up as in Agglomerative Clustering)

• Start with all docs in one big cluster• Then recursively split clusters• Eventually each node forms a cluster on its

own.


Flat or hierarchical clustering?

• For high efficiency, use flat clustering (e.g. k means)

• For deterministic results: hierarchical clustering• When a hierarchical structure is desired:

hierarchical algorithm• Hierarchical clustering can also be applied if K

cannot be predetermined (can start without knowing K)


For Thurs

• Read Chapter 6 of textbook