From Bicluster to Tricluster An Alternative Approach

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From Bicluster to TriclusterAn Alternative
Approach

• Presented by
• Morshed Osmani

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Outline

• Problem Definition
• Related Works
• My Idea
• Further Improvement
• Suggestion and Comments

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Problem Statement

• Bicluster has increased popularity in finding
  cluster in gene expression data. However this
  method works well in two dimensional space
  ((Gene, Sample), (Gene, Time), (Sample, Time)).
• Tricluster use all those three dimensions to
  cluster data.
• We want an algorithm which will use the bicluster
  approach to find the cluster in three dimensions.

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Related Works

• There are lots of biclustering algorithm to
  cluster data in 2D.1
• 2 uses all three dimensions but biclustering
  only in (Gene, Sample) dimensions.
• Tricluster 3 clusters data in all those three
  dimensions.
• Most of the other algorithms cluster along the 2D.

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My Idea

• Correct those mathematical notation
• Develop method for pruning large search space
• Implement the modified solution and get some
  simulation result
• Compare the modified algorithm with original
  papers algorithm

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Original Paper

• TRICLUSTER An Effective Algorithm for Mining
  Coherent Clusters in 3D Microarray Data
• Lizhuang Zhao, Mohammed J. Zaki
• Rensselaer Polytechnic Institute, New York
• ACM SIGMOD international conference on Management
  of data, 2005

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Introduction

• Traditional clustering algorithms work in the
  full dimensional space.
• Biclustering, on the other hand, does not have
  such a strict requirement. If some points are
  similar in several dimensions (a subspace), they
  will be clustered together in that subspace.
• Biclustering is able to identify the
  co-expression patterns of a subset of genes that
  might be relevant to a subset of the samples of
  interest.

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Introduction (Cont.)

• There has been a lot of interest in mining gene
  expression patterns across time. These approaches
  are also mainly two-dimensional, i.e., finding
  patterns along the gene-time dimensions.
• The paper deals with mining tri-clusters, i.e.,
  mining coherent clusters along the
  gene-sample-time (temporal) or gene-sample-region
  (spatial) dimensions.
• The authors claim TRICLUSTER is the first 3D
  microarray subspace clustering method.

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Related Work

• There has been work on mining gene expression
  patterns across time.
• There are many full-space and biclustering
  algorithms designed to work with microarray
  datasets, such as feature based clustering, graph
  based clustering and pattern based clustering.
• There is no previous method that mines
  tri-clusters.

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Challenges

• Biclustering itself is known to be a NP-hard
  problem. So heuristic methods or probabilistic
  approximations are used .
• Microarray data is inherently susceptible to
  noise, due to varying experimental conditions,
  thus it is essential that the methods be robust
  to noise.
• As we do not understand the complex gene
  regulation circuitry in the cell, clustering
  methods should allow overlapping clusters that
  share subsets of genes, samples or
  time-courses/spatial regions.
• Furthermore, the methods should be flexible
  enough to mine several (interesting) types of
  clusters, and should not be too sensitive to
  input parameters.

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Mathematical Notations Used
Let
be a set of n genes,
let
be a set of m biological samples (e.g.,
different tissues or experiments)
be a set of l experimental time points.
let
matrix
A three dimensional microarray dataset is a
real-valued
whose three dimensions correspond to genes,
samples and times respectively
A tricluster C is a submatrix of the dataset D,
provided certain conditions of homogeneity are
satisfied.
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Problems with Notation

• Used unconventional notation system which seems
  to be incorrect.
• May confuse the reader to comprehend the actual
  meaning.
• Wrong use of Cartesian product.
• May be solved by using mapping (function).

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The TRICLUSTER Algorithm

• 3D microarray datasets have more genes than
  samples, and perhaps an equal number of time
  points and samples, i.e.,
• Due to the symmetric property, TRICLUSTER always
  transposes the input 3D matrix such that
• the dimension with the largest cardinality (say
  G) is 1st dimension
• then make S as the 2nd and T as the 3rd
  dimension.

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Steps of TRICLUSTER

• TRICLUSTER has following main steps
• For each GxS time slice matrix, find the valid
  ratio-ranges for all pair of samples, and
  construct a range multigraph
• Mine the maximal biclusters from the range
  multigraph
• Construct a graph based on the mined biclusters
  (as vertices) and get the maximal TRICLUSTERs
• Optionally, delete or merge clusters if certain
  overlapping criteria are met.

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Future Direction

• Reduce the search space
• - How (yet to be determined)
• Implement the modified algorithm
• Compare the result with result from previous
  algorithm

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Need Suggestion

• Here dataset D is a data cube. What are the
  benefits we may receive from the data cube
  model in this case?
• How can this problem be integrated to DataDEX (if
  there is a possibility)?
• How can we reduce the search space?
• Any other comments or suggestions are welcome.

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Reference

• S. C. Madeira and A. L. Oliveira. Biclustering
  algorithms for biological data analysis a
  survey. IEEE/ACM Transactions on Computational
  Biology and Bioinformatics, 1(1)2445, 2004.
• D. Jiang, J. Pei, M. Ramanathany, C. Tang, and A.
  Zhang. Mining coherent gene clusters from
  gene-sample-time microarray data. In 10th ACM
  SIGKDD Conference, 2004.
• Lizhuang Zhao and Mohammed J. Zaki. TRICLUSTER
  an effective algorithm for mining coherent
  clusters in 3D microarray data. Proceedings of
  the 2005 ACM SIGMOD international conference on
  Management of data, Baltimore, Maryland, 2005