Clustering and Network

Transcription

1 Clustering and Network Jing-Dong Jackie Han Copy Right: Jing-Dong Jackie Han

2 What is clustering? A way of grouping together data samples that are similar in some way - according to some criteria that you pick A form of unsupervised learning you don t know before hand how the data should be grouped together So, it is a method of data exploration a way of looking for patterns or structure in the data that are of interest

3 Clustering Choosing (dis)similarity measures a critical step in clustering Euclidean distance Pearson Linear Correlation Clustering algorithms Hierarchical agglomerative clustering K-means clustering and quality measures

4 Pediatric ALL classifier Clustering 535 Caucasian gene expression profiles based on our predicted marker genes Li et al. Blood, 2009 Collaborators: Huyong Zheng. Shilai Bao

5 How do we define similarity? The similarity measure is often more important than the clustering algorithm used don t overlook this choice!

6 Euclidean distance d euc ( x, y) = n i= 1 ( x i y i 2 ) Here n is the number of dimensions in the data vector. For instance: Number of time-points/conditions (when clustering genes) Number of genes (when clustering samples)

7 d euc = d euc = d euc = These examples of Euclidean distance match our intuition of dissimilarity pretty well

8 d euc =1.41 d euc =1.22 But what about these? Magnitude vs shape

9 Correlation We might care more about the overall shape of expression profiles rather than the actual magnitudes That is, we might want to consider genes similar when they are up and down together When might we want this kind of measure? What experimental issues might make this appropriate?

10 Pearson Linear Correlation We re shifting the expression profiles down (subtracting the means) and scaling by the standard deviations (i.e., making the data have mean = 0 and std = 1) = = = = = = n i i n i i n i i n i i i n i i y n y x n x y y x x y y x x 1 1 ) ( ) ( ) )( ( ), ( y x ρ

11 Pearson Linear Correlation Pearson linear correlation (PLC) is a measure of shape similarity Always between 1 and +1 (perfectly anti-correlated and perfectly correlated) This is a similarity measure, but we can easily make it into a dissimilarity measure: d p = 1 ρ( x, y) 2

12 Hierarchical Agglomerative Clustering We start with every data point in a separate cluster We keep merging the most similar pairs of data points/clusters until we have one big cluster left This is called a bottom-up or agglomerative method

13 Hierarchical Clustering (cont.) This produces a binary tree or dendrogram The final cluster is the root and each data item is a leaf The height of the bars indicate how close the items are

14 Hierarchical Clustering Demo

15 Hierarchical Clustering Issues Distinct clusters are not produced sometimes this can be good, if the data has a hierarchical structure w/o clear boundaries There are methods for producing distinct clusters, but these usually involve specifying somewhat arbitrary cutoff values What if data doesn t have a hierarchical structure?

16 K-means Clustering Choose a number of clusters k Initialize cluster centers µ 1, µ k Could pick k data points and set cluster centers to these points Or could randomly assign points to clusters and take means of clusters For each data point, compute the cluster center it is closest to (using some distance measure) and assign the data point to this cluster Re-compute cluster centers (mean of data points in cluster) Stop when there are no new re-assignments

17 K-means Clustering (cont.) How many clusters do you think there are in this data? How might it have been generated?

18 K-means Clustering Demo

19 K-means Clustering Issues Random initialization means that you may get different clusters each time; Completely random initialization of cluster centers is not optimal. (Not taken into account the spatial distribution of data points) Implicit assumptions about the shapes of clusters; You have to pick the number of clusters

20 Super k-means choosing initial centers based on data distribution Choose first center uniformly at random Repeat until k centers: Add a new center Choose x 0 with probability D( x ) D( x) x X D( x 2 0) D(x) = distance between x and closest center

21 k-means++ Example: (k=3)

22 Example: (k=3) Choose 1 st center uniformly at random

23 k-means++ Example: D 2 = D 2 = D 2 = D 2 = (k=3) Choose 2 nd center probability proportional to D 2

24 k-means++ Example: D 2 = D 2 = D 2 = (k=3) Choose 3 rd center probability proportional to D 2

25 k-means++ Example: (k=3) Now run k- means as normal

26 Sum of squared distances (SSD) k SSD d ( X, µ ) =," " i= 1 X C i 2 i where"d"is"the"euclidean"distance"in"k2means"clustering.

27 Super k-means is better than k-means in Cluster 3.0 More compact Loose Distributions of the sum of squared Euclidean distances (SSD) from data to cluster center in 20 runs Liu et al. Cell Res, 2013.

28 De novo discovery of ovarian cancer subtypes by adaptive clustering log- rank test P = 2.96e- 07 Zhang et al. Cell Reports, 2013.

29 Networks What is a network? Why network? High-throughput component identification by comparative genomics, functional genomics and proteomics Network prediction/inference/reverse engineering Network properties and their biological relevance Network simulations

30 I. What is a network?

31 Elements of a Network Degree (k): number of edges a node has. Node Hub: a node with high degree Edge Cliquishness: clustering, triangle Characteristic path length (CPL) of a network: the average shortest path length (smallest number of hops) between any two connected nodes.

32 II. Why network?

33 Complex phenotypes are formed through molecular networks Aging, Stem cell differentiation Han, Cell Res., 2008

34 Pathways to Networks Xia et al. Unpublished Data

35 Temporal parameters of the networks Souchelnytskyi Proteomics 2005

36 Spatial parameters of the networks Tissue localizations Subcellular localizations

37 III. Construction of networks

38 High-throughput interaction identifications Protein-protein interactions post-translation Undirected:Y2H, AP-MS Directed biochemical protein modifications: 2D gels, MS and specific antibodies (α-ptypr) activating and inhibitory protein binding: protein activities, not possible for high-throughput yet Protein-DNA interactions ChIP-chip, ChIP-seq, Y1H (directed) ncrna/mirna-mrna interactions mirna array, mirna beads Genetic interactions Synthetic lethality no direction RNAi epistasis: activator, repressor -> signs Correlations between same type molecules co-expression, co-phenotype, co-localization, co-evolution

39 High-throughput omics Transcriptome Interactome Cis- trome Promoterome Integration Cell Localizome Phenome Tissue Localizome

40 Expression profiling compendium" 549 data point" ~20,000" predicted" genes" Gene 1 Parallel expression profiles: mrna increase and decrease at the same time PCC measures the level of co-expression or parallel -ness between two sets of expression profiles, it ranges from -1 to 1. Conditions Gene 2 Gene 3

41 Molecular machines in C. elegans early embryogenesis Gunsalus et al. Nature 2005

42 Data integration to generate Breast Cancer Network Pujana, Han et al. Nature Genetics, 2007

43 Breast Cancer Gene Network

44 Case study

45 Tightly regulated gene expression clusters

46 Function, gene set and transcription factor, epigenetic target enrichment GO, KEGG pathway enrichment: DAVID Gene set enrichment: GSEA Co-citation enrichment: CoCiter (can be used for your customized terms) Transcription factor target enrichment: MEME, JASPAR, HOMER, FactorBook Epigenetic factor target enrichment: HOMER

47 Transcriptionally regulated modules

48 References All of my papers are freely downloadable from my lab website