Clustering Expression Data. Clustering Expression Data

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1 Subscribe if you Din t get msg last night Clustering Exression Data Why cluster gene exression ata? Tissue classification Fin biologically relate genes First ste in inferring regulatory networks Look for common romoter elements Hyothesis generation One of the tools of choice for exression analysis Clustering Exression Data What has been one? Hierarchical average-link [Eisen et al. ] Self Organizing Mas SOM) [Tamayo et al. ] CAST [Ben-Dor et al. ] Suort Vector Machines SVM) [Gruny et al. ] etc. etc. etc. Why so many methos? Clustering is NP-har even with simle objectives ata Har roblem: high imensionality noise many heuristic local search aroximation algorithms No clear winner Clustering Algorithms Partitional CAST Ben-Dor et al. ) k-means variously initialize Hartigan ) Hierarchical single-link average-link comlete-link Ranom as a control) Ranomly assign genes to clusters Others

2 The following slies largely from htt://staff.washington.eu/kayee/research.html Errors are mine. Clustering Ka Yee Yeung Center for Exression Arrays University of Washington Overview What is clustering? Similarity/istance metrics Hierarchical clustering algorithms Mae oular by Stanfor ie. [Eisen et al. ] K-means Mae oular by many grous eg. [Tavazoie et al. ] Self-organizing ma SOM) Mae oular by Whitehea ie. [Tamayo et al. ] What is clustering? Grou similar objects together Objects in the same cluster grou) are more similar to each other than objects in ifferent clusters Data exloratory tool genes How to efine similarity? Exeriment X genes n s X n Y Raw matrix genes Similarity metric: A measure of airwise similarity or issimilarity Examles: Correlation coefficient Eucliean istance Y n Similarity matrix

3 Eucliean istance Similarity metrics X[ Y[ ) j Correlation coefficient X[ X ) Y[ Y ) j X[ X ) Y[ Y ) j j where X j X[ X - Y Z - W - Examle Correlation XY) Distance XY) Correlation XZ) - Distance XZ). Correlation XW) Distance XW). X Y Z W Lessons from the examle Correlation irection only Eucliean istance magnitue irection Min attributes exeriments) to comute airwise similarity > attributes for Eucliean istance > attributes for correlation Array ata is noisy nee many exeriments to robustly estimate airwise similarity Clustering algorithms Inuts: Raw ata matrix or similarity matrix Number of clusters or some other arameters Many ifferent classifications of clustering algorithms: Hierarchical vs artitional Heuristic-base vs moel-base Soft vs har

4 Hierarchical Clustering [Hartigan ] Agglomerative bottom-u) Algorithm: Initialize: each item a cluster Iterate: enrogram select two most similar clusters merge them Halt: when require number of clusters is reache Hierarchical: Single Link cluster similarity similarity of two most similar members - Potentially long an skinny clusters Fast Examle: single link Examle: single link ) ) ) ) ) ) ) ) ) min{ min{ min{ min{ min{ min{ ) ) min{ min{ ) ) min{ min{

5 Examle: single link ) ) ) ) min{ ) ) )) Sometimes rawn to a scale Hierarchical: Comlete Link cluster similarity similarity of two least similar members tight clusters - slow Examle: comlete link ) ) max{ max{ max{ max{ max{ max{ ) ) ) Examle: comlete link ) ) ) ) ) ) max{ max{ max{ max{ ) ) ) ))

6 Examle: comlete link ) ) ) ) ) ) max{ ) )) )) Hierarchical: Average Link cluster similarity average similarity of all airs tight clusters - slow Examle: average link... ) ). ). ). ) ) ) ) Examle: average link... ) ). ) ) ) ) ) ) ) ))

7 Examle: average link ) )... ) )) ) ). ) ) Hierarchical: Centroi Link cluster centroi average of all oints cluster similarity istance between centrois In Exression literature often calle Average link faster - iscars shae // Software: TreeView [Eisen et al. ] Fig in Eisen s PNAS aer Time course of serum stimulation of rimary human fibrolasts cdna arrays with arox sots Similar to average-link Free ownloa at: htt://rana.lbl.gov/eisensoftware.htm Another Goo Package: TMEV htt:// Hierarchical ivisive clustering algorithms To own Start with all the objects in one cluster Successively slit into smaller clusters Ten to be less efficient than agglomerative Resolver imlemente a eterministic annealing aroach from [Alon et al. ]

Partitional: K-Means [MacQueen ] Details of k-means Iterate until converge: Assign each ata oint to the closest centroi Comute new centroi Objective function: Minimize Proerties of k-means Fast Prove

8 Partitional: K-Means [MacQueen ] Details of k-means Iterate until converge: Assign each ata oint to the closest centroi Comute new centroi Objective function: Minimize Proerties of k-means Fast Prove to converge to local otimum In ractice converge quickly Ten to rouce sherical equal-size clusters Relate to the moel-base aroach Self-organizing mas SOM) [Kohonen ] Basic iea: ma high imensional ata onto a D gri of noes Neighboring noes are more similar than oints far away

SOM Gri geometry of noes) Inut vectors that are close to each other mae to the same or neighboring noes Proerties of SOM Partial structure Easy visualization Tons of arameters to tune Sensitive to

9 SOM Gri geometry of noes) Inut vectors that are close to each other mae to the same or neighboring noes Proerties of SOM Partial structure Easy visualization Tons of arameters to tune Sensitive to arameters Summary Definition of clustering Pairwise similarity: Correlation Eucliean istance Clustering algorithms: Hierarchical single-link comlete-link average-link) K-means SOM Different clustering algorithms ifferent clusters Which clustering algorithm shoul I use? Goo question No efinite answer: on-going research Feel free to rea my thesis: htt://staff.washington.eu/kayee/research

10 General Suggestions Avoi single-link Try: K-means Average-link/ comlete-link If you are intereste in caturing atterns of exression use correlation instea of Eucliean istance Visualization of ata Eisen-gram Denrogram PCA MDS etc Misc Notes Greey algorithms. Can get trae in local minima. Can be sensitive to aition of new oints orer of oints simle intuitive algorithms reasonably fast ok on simle ata no obvious reconcetion about structure - no moel of structure; biases unclear

Clustering gene expression data

Clustering gene expression data 1 How Gene Expression Data Looks Entries of the Raw Data matrix: Ratio values Absolute values Row = gene s expression pattern Column = experiment/condition s profile genes