More%20Microarray%20Analysis:%20Unsupervised%20Approaches

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More Microarray AnalysisUnsupervised Approaches

• Matt Hibbs
• Troyanskaya Lab

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Outline

• Gene Expression vs. DNA applications
• A little more normalization (missing values)
• Unsupervised Analysis
• Basic Clustering
• Statistical Enrichment
• PCA/SVD
• Advanced Clustering
• Search-based Approaches

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Expression / DNA

• Some similar concepts to analysis, but often very
  different goals
• Expression clustering, guilt by association,
  functional enrichment
• DNA signal processing, spatial relationships,
  motif finding
• Visualized differently (Heat maps vs. karyoscope)

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The missing value problem

• Microarrays can have systematic or random missing
  values
• Some algorithms cant deal with missing values
  (PCA/SVD in particular)
• Instead of hoping missing values wont bias the
  analysis, better to estimate them accurately

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Spatial Defects
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KNN Impute

• Idea use genes with similar expression profiles
  to estimate missing values

2 5 7 3 1
Gene X
2 4 5 7 3 2
Gene A
8 9 2 1 4 9
Gene B
3 5 6 7 3 2
Gene C
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Imputation affects downstream analysis

 
Complete data set
Data set with missing values estimated by
KNNimpute algorithm
Data set with 30 entries missing and filled with
zeros (zero values appear black)
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Unsupervised Analysis

• Supervised techniques great if you have starting
  information (e.g. labels)
• But, we often we dont know enough beforehand to
  apply these methods
• Unsupervised techniques are exploratory
• Let the data organize itself, then try to find
  biological meaning
• Approaches to understand whole data
• Visualization often helpful

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Clustering

• Let the data organize itself
• Reordering of genes (or conditions) in the
  dataset so that similar patterns are next to each
  other (or in separate groups)
• Identify subsets of genes (or experiments) that
  are related by some measure

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Quick Example
Conditions
Genes
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Why cluster?

• Guilt by association if unknown gene X is
  similar in expression to known genes A and B,
  maybe they are involved in the same/related
  pathway
• Visualization datasets are too large to be able
  to get information out without reorganizing the
  data

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Clustering Techniques

• Algorithm (Method)
• Hierarchical
• K-means
• Self Organizing Maps
• QT-Clustering
• NNN
• .
• .
• .

• Distance Metric
• Euclidean (L2)
• Pearson Correlation
• Spearman Correlation
• Manhattan (L1)
• Kendalls t
• .
• .
• .

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Distance Metrics

• Choice of distance measure is important for most
  clustering techniques
• Pair-wise metrics compare vectors of numbers
• e.g. genes x y, ea. with n measurements

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Distance Metrics
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Hierarchical clustering

• Imposes (pair-wise) hierarchical structure on all
  of the data
• Often good for visualization
• Basic Method (agglomerative)
• Calculate all pair-wise distances
• Join the closest pair
• Calculate pairs distance to all others
• Repeat from 2 until all joined

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Hierarchical clustering
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Hierarchical clustering
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Hierarchical clustering
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Hierarchical clustering
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Hierarchical clustering
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Hierarchical clustering
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HC Interior Distances

• Three typical variants to calculate interior
  distances within the tree
• Average linkage mean/median over all possible
  pair-wise values
• Single linkage minimum pair-wise distance
• Complete linkage maximum pair-wise distance

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Hierarchical clustering problems

• Hard to define distinct clusters
• Genes assigned to clusters on the basis of all
  experiments
• Optimizing node ordering hard (finding the
  optimal solution is NP-hard)
• Can be driven by one strong cluster a problem
  for gene expression b/c data in row space is
  often highly correlated

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HC Real Example

• Demo in JavaTreeView HIDRA
• Spellman et al., 1998 yeast alpha-factor sync
  cell cycle timecourse

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HC Another Example

• Expression of tumors hierarchically clustered
• Expression groups by clinical class

Garber et al.
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K-means Clustering

• Groups genes into a pre-defined number of
  independent clusters
• Basic algorithm
• Define k number of clusters
• Randomly initialize each cluster with a seed
  (often with a random gene)
• Assign each gene to the cluster with the most
  similar seed
• Recalculate all cluster seeds as means (or
  medians) of genes assigned to the cluster
• Repeat 3 4 until convergence
• (e.g. No genes move, means dont change much,
  etc.)

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K-means example
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K-means example
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K-means example
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K-means problems

• Have to set k ahead of time
• Ways to choose optimal k minimize
  within-cluster variation compared to random data
  or held out data
• Each gene only belongs to exactly 1 cluster
• One cluster has no influence on the others (one
  dimensional clustering)
• Genes assigned to clusters on the basis of all
  experiments

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K-means Real Example

• Demo in TIGR MeV
• Spellman et al. alpha-factor cell cycle

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Clustering Tweaks

• Fuzzy clustering allows genes to be partially
  in different clusters
• Dependent clusters consider between-cluster
  distances as well as within-cluster
• Bi-clustering look for patterns across subsets
  of conditions
• Very hard problem (NP-complete)
• Practical solutions use heuristics/simplifications
  that may affect biological interpretation

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Cluster Evaluation

• Mathematical consistency
• Compare coherency of clusters to background
• Look for functional consistency in clusters
• Requires a gold standard, often based on GO,
  MIPS, etc.
• Evaluate likelihood of enrichment in clusters
• Hypergeometric distribution, etc.
• Several tools available

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Gene Ontology

• Organization of curated biological knowledge
• 3 branches biological process, molecular
  function, cellular component

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Hypergeometric Distribution

• Probability of observing x or more genes in a
  cluster of n genes with a common annotation
• N total number of genes in genome
• M number of genes with annotation
• n number of genes in cluster
• x number of genes in cluster with annotation
• Multiple hypothesis correction required if
  testing multiple functions (Bonferroni, FDR,
  etc.)
• Additional genes in clusters with strong
  enrichment may be related

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GO term Enrichment Tools

• SGDs Princetons GoTermFinder
• http//go.princeton.edu
• GOLEM (http//function.princeton.edu/GOLEM)
• HIDRA

Sealfon et al., 2006
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More Unsupervised Methods

• Search-based approaches
• Starting with a query gene/condition, find most
  related group
• Singular Value Decomposition (SVD) Principal
  Component Analysis (PCA)
• Decomposition of data matrix into patterns
  weights and contributions
• Real names are principal componentssingular
  values and left/right eigenvectors
• Used to remove noise, reduce dimensionality,
  identify common/dominant signals

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SVD ( PCA)

• SVD is the method, PCA is performing SVD on
  centered data
• Projects data into another orthonormal basis
• New basis ordered by variance explained

Singular values
Eigen-genes
Original Data matrix
Eigen-conditions
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SVD
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SVD Real Example

• Demo in TIGR MeV
• Spellman et al., 1998 cell cycle time courses
• alpha-factor sync
• cdc15 sync

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DNA arrays / Sequence-based Analysis

• Methods so far focused on expression data
• Other uses of microarrays often sequence based
  CGH, ChIP-chip, SNP scanner
• Data has important, inherent order
• Most analysis methods developed from signal
  processing techniques (e.g. sound)
• View data in chromosomal order (karyoscope)
• Tools JavaTreeView, IGB, Chippy

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CGH Example

• Demo in JavaTreeView

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Aneuploidy affects expression too
rpl20aD/ rpl20aD, Chromosome XV
(data from Hughes et al. (2000))
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Software Tools

• JavaTreeView viz, karyoscope
• HIDRA viz, mult. datasets, search
• Cluster (Eisen lab) clustering
• TIGR MeV clustering, viz
• IGB Affys CGH browser
• ChIPpy ChIP-chip analysis

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Summary

• Unsupervised Analysis
• Let the data organize itself, find patterns
• Clustering Distance Metric Algorithm
• SVD/PCA auto find dominant patterns
• Impute missing values (KNN)
• CGH Karyoscope view
• Questions?