Hierarchical Clustering of Gene Expression Data

1. Hierarchical Clustering of Gene Expression Data Author : Feng Luo, Kun Tang Latifur Khan Graduate : Chien-Ming Hsiao

2. Outline • Motivation • Objective • Introduction • Hierarchical Clustering • Self-Organizing Tree algorithm • hierarchical growing self-organizing tree algorithm • Preliminary result • Conclusions • Personal Opinion

3. Motivation • Rapid development of biological technologies generates a hug amount of data. • Analyzation and interpretation of these massive data is a challenging task. • we are interested in data analysis tools that can help researchers to detect patterns hidden behind these complex initial data.

4. Objective • toextract useful and rational fundamental patterns of gene expression inherent in these huge data.

5. introduction • Current approaches for measuring gene expression profiles • SAGE, RT/PCR, cDNA, oligonucleotide microarray • Sample of Microarray

6. introduction • Two classes ofalgorithms have been successfully used to analyze gene expression data. • hierarchical clustering • a self-organizing tree

7. Hierarchical Clustering

8. Self-Organizing Tree algorithm • Self-Organizing Tree algorithm (SOTA) • based on the Kohonen’s self-organizing map (SOM) and Fritzke’s growing cell structures • output of SOTA is a binary tree topological neural network

9. Node Node Cell Node m w Cell Cell w s Cell Cell A B Self-Organizing Tree algorithm • Step 1: Initially the system as a binary tree with three nodes (A) Initial Architecture of SOTA. (B) Two Difference Reference Vector Updating Schemas.

10. Self-Organizing Tree algorithm • Step 2: Present all data and compute distances from each data to all external Cells (tree leaves) • Euclidean distances • cosine distances • Step 3: Select output winning cell c with minimum distance dij for each data.

11. Self-Organizing Tree algorithm • Step 4: Update reference vector of winning cell and its neighbors Where (t) is the learning function: The(t) is the learning rate function, (t) = 1/t  is a learning constant.  will have a different value for the winning cell and Its neighbors.

12. Self-Organizing Tree algorithm • Step 2,3,4 form a Cycle. While relative error of the entire tree is greater than a threshold repeat the cycle. • Step 5: If a cycle finished, increase the network size: two new cells are attached to the cell with highest resources. This cell becomes a node. • Resources: an average of the distances of the input data associated this cell to itself. • Step 6: Repeat Step 2 until convergence (resources are below a threshold).

13. Self-Organizing Tree algorithm • Time Complexity of SOTA is O( n log N) • Space Complexity of SOTA is O (n)

14. The incorrect capture of the hierarchical relationship SOTA

15. hierarchical growing self-organizing tree algorithm • hierarchical growing self-organizing tree algorithm (HGSOT) • The HGSOT grows • vertical grows • adds descendents • the same strategy used in SOTA • horizontal grows • adds more siblings • a level threshold : controlling growth in the sibling generation

16. hierarchical growing self-organizing tree algorithm • To determine horizontal growth

17. hierarchical growing self-organizing tree algorithm

18. The pseudo code of HGSOT • Initialization • initially the tree only has one root node. Initialize its reference vector with the centroid of entire data and all data will be associated with the root. • Vertical Growing • change the leaf cell to a node and add two children to each. The reference vector of a new cell is initialized as the node’s reference vector. • Distribution • distribute each input datum between two newly created cells; find the winning cell (using KLD, see 2.2.1), and then update the reference vector of the winning cell and its neighbor. • Error • when the error of the entire tree is larger than a threshold, called error threshold (TE), repeat Step 3.

19. The pseudo code of HGSOT • Horizontal Growing • when the difference between the minimum and maximum distance of all children cells of a node (x) is less than a threshold, called level threshold (TL), a child is added to this node; on the other hand if the difference is greater than the TL, a child is deleted from this node, and the horizontal growth terminated. • Distribution • distribute the input data associated with x into its descendents along siblings; find the winning cell (using KLD, see 2.2.), then update the reference vector of the winning cell and its neighbor. • Error • if the error of the entire tree is greater than (TE), then repeat Step 6. • if there are more levels to grow in the hierarchy, and then return to Step 2, otherwise, stop.

20. Hierarchical Cluster Algorithms • How we can distribute input data of selected node among these new created cells. • Similar to the SOTA approach. • Input data of selected node will be distributed not only its new created cells but also its neighbor cells. • We determine K level apart ancestor node of selected node. • We determine sub-tree of rooted by the ancestor node and input data of selected cell will be distributed among all cells (leaf) of this sub-tree. The latter approach is known as K level distribution (KLD).

21. Hierarchical Cluster Algorithms • KLD: We need to distribute data associated with node M to new created cells. For K=1, Data of node M will be distributed to cells, B, C, D & E. If K=0, data of M will be distributed between B and C.

22. Preliminary result • Experiment setup • Experiment Data • 112 genes expression data of rat central nervous system (CNS) • Four Gene Families: Neuro-Glial Markers Family (NGMs), Neurotransmitter receptors Family (NTRs), Peptide Signaling Family (PepS) and Diverse • These gene expression data were measured by using RT-PCR in mRNA expression in rat’s cervical spinal cord tissue over nine different developmental time points from embryonic days 11 through 21, postnatal days 0 through 14 and adult. • For each gene, data are normalized to the maximal expression level among the nine time points

23. Preliminary result • Experiment setup • The Parameters of HGSOT • The winner learning rate w and sibling learning rates of HGSOT is 0.15 and 0.015. • The error threshold is 0.001. • The level threshold is 0.8, which means the minimum distance will not be less than 80% of the maximum distance. • The distribution level K is equal to 4. • Euclidean distance is used to calculate the similarity.

24. Preliminary result

25. Preliminary result

26. Conclusions • can successfully gain five clusters similar to Wen et al’s original HAC result and gives a better hierarchical structure. • this algorithm can detect more subtle patterns at the lower hierarchical levels, and it shows a more suitable clustering than HAC on some genes.

27. Personal Opinion • we would like to do more experiments on different data sets