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Mining di dati web Clustering di Documenti Web: Le metriche di similarità A.A 2006/2007

Learning: What does it Means? ,[object Object],[object Object],[object Object],[object Object]

And… What about Clustering? ,[object Object],[object Object],[object Object]

What clustering is? d intra d inter

Clustering ,[object Object],[object Object]

Clustering: K-Means ,[object Object],[object Object],[object Object],[object Object]

K-means Clustering ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example 1: data points image the k-means clustering result.

Importance of Choosing Initial Guesses (1)

Importance of Choosing Initial Guesses (2)

Local optima of K-means ,[object Object],[object Object],[object Object],Supplement to K-means

Example 2: K-means clustering result

Limitations of K-means ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Clustering: K-Means ,[object Object],[object Object]

d_intra or d_inter? That is the question! ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Distance Functions ,[object Object],[object Object],[object Object],[object Object],[object Object]

Distance or Similarity? ,[object Object],d = 0.3 sim = 0.7 d = 0.1 sim = 0.9

What does similar (or distant) really mean? ,[object Object],[object Object],[object Object],[object Object]

The Ugly Duckling theorems The theorem gets its fanciful name from the following counter-intuitive statement: assuming similarity is based on the number of shared predicates, an ugly duckling is as similar to a beautiful swan A as a beautiful swan B is to A, given that A and B differ at all. It was proposed and proved by Satosi Watanabe in 1969.

Satosi’s Theorem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

The ugly duckling and 3 beautiful swans ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

The ugly duckling and 3 beautiful swans ,[object Object],[object Object],[object Object],[object Object],[object Object]

Wolpert’s No Free Lunch Theorem ,[object Object],[object Object]

So Let’s Get Back to Distances ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Minkowski Distance ,[object Object],[object Object],[object Object],[object Object]

p=1 . Manhattan Distance ,[object Object],[object Object]

p=2 . Euclidean Distance ,[object Object]

p=  . Chebyshev Distance ,[object Object],[object Object]

2D Cosine Similarity ,[object Object],[object Object], a b

Cosine Similarity ,[object Object]

Jaccard Distance ,[object Object]

Binary Jaccard Distance ,[object Object]

Edit Distance ,[object Object]

Binary Edit Distance ,[object Object],x=(0,1,0,0,1,1) y=(1,1,0,1,0,1) d(x,y)=3 The binary edit distance is equivalent to the Manhattan distance ( Minkowski p=1 ) for binary features vectors.

The Curse of High Dimensionality ,[object Object],[object Object]

Volume of the Unit-Radius Sphere

Sphere/Cube Volume Ratio ,[object Object]

Sphere/Sphere Volume Ratio ,[object Object]

Concentration of the Norm Phenomenon ,[object Object],[object Object]

Web Document Representation ,[object Object],[object Object],[object Object],[object Object],[object Object]

Bag-of-Words vs. Vector-Space ,[object Object],[object Object],[object Object],[object Object],[object Object]

Bag-of-Words ,[object Object],[object Object],[object Object],[object Object],d=[1,0,1,1,0,0,0,1]. Apple Peach Apple Banana Apple Banana Coffee Apple Coffee Apple Peach Apple Banana Apple Banana Coffee Apple Coffee d=[ 1 ,0, 1 , 1 ,0,0,0, 1 ].

Vector-Space ,[object Object],[object Object],[object Object],Apple Peach Apple Banana Apple Banana Coffee Apple Coffee Apple Peach Apple Banana Apple Banana Coffee Apple Coffee d=[4,0,2,2,0,0,0,1]. d=[ 4 ,0, 2 , 2 ,0,0,0, 1 ].

Typical Web Collection Dimensions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

We Need to Cope with High Dimensionality ,[object Object],[object Object]

Dimensionality reduction ,[object Object],[object Object],[object Object]

PCA - Principal Component Analysis ,[object Object],[object Object],[object Object]

The Method ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

The Method ,[object Object],[object Object],[object Object]

The Method ,[object Object],[object Object],Computationally expensive task

The Method ,[object Object],[object Object]

PCA Eigenvectors Projection ,[object Object]

Singular Value Decomposition ,[object Object],[object Object]

Locality-Sensitive Hashing ,[object Object],[object Object]

Locality-Sensitive Hashing ,[object Object]

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