1. Author / Bo Long, Zhongfei Zhang and Philip S. Yu
Source / ACM KDD05, August 21-24, 2005, pp. 635 pp. 640
Presenter / Allen Wu
Co-clustering by Block Value Decomposition
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2. Outline
Introduction
Block value decomposition
Derivation of the Algorithm
Empirical Evaluation
Conclusion
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3. Introduction
Dyadic data refer to a domain with two finite sets of objects in which observations are made for dyads.
Co-clustering can effectively deal with the high dimensional and sparse data between rows and columns.
In this paper, a new co-clustering framework, Block Value Decomposition(BVD), had been proposed.
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4. Introduction (cont.)
This paper develop a specific novel co-clustering algorithm for a special yet very popular case non-negative dyadic data.
The algorithm performs an implicitly adaptive dimensionality reduction, which works well for typical sparse data.
The dyadic data matrix is factorized into three components.
The row-coefficient matrix R
The block value matrix B
The column-coefficient matrix C
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5. The definition of dyadic data
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The notion dyadic refers to a domain with two sets of objects X={x1, , xn} and Y={y1, , ym}
The data can be organized as an n by m two-dimensional matrix Z.
Each w(x,y) corresponds to one element of Z.
6. 6


=
nk
k l
lm
nm
k l
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y1 y2y3y4
x1
x2
x3
x4


C
B
R
y1 y2y3 y4
=
y1 y2y3 y4
x1
x2
x3
x4
x1
x2
x3
x4
RBC
Z
8. Block value decomposition definition
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Non-negative block value decomposition of a non-negative data matrix Z nm(i.e. ij: Zij 0) is given by the minimization of
f(R, B, C) = ||Z RBC||2
subject to the constraints ij: Rij 0, Bij 0 and Cij 0, where R nk, B kl, C lm, k