Cluster validation Integration

Cluster validation Integration

ICES Bioinformatics

Overview

INTRODUCTION

MICROARRAY ANALYSIS

VALIDATION OF THE RESULTS

• Statistical validation

• Biological validation INTEGRATION

Cluster validation

Preprocessing 1

Clustering Algorithm 1

Preprocessing 2

Clustering Algorithm 2

Clustering Algorithm 3

Parameter

Setting 1 Parameter

Setting 2 Parameter Setting 3

Validation

Why cluster validation?

• Different algorithms, parameters

• Intrinsic properties of the dataset (sensitivity to noise, to outliers)

STATISTICAL VALIDATION

• Sensitivity analysis

– Leaf one out cross validation (FOM) – Sensitivity analysis

• Gaussian noise

• ANOVA

• Cluster coherence testing

– Euclidean distance score – Gap statistics

Statistical validation

Validation

Figure of Merit (sensitivity towards an experiment)

• Tested cluster algorithm is applied to all experimental conditions except the left out condition

• Hypothesis: if the cluster algorithm is robust it can predict the measured values of the left out condition

• To estimate the predictive power of the algorithm FOM is calculated

FOM is the root mean square deviation in the left-out condition e of the individual gene expression levels relative to their

cluster means

This is repeated for all conditions and the average FOM is calculated

Statistical validation

Validation

Yeung et al., 2001

Sensitivity analysis towards the signal to noise ratio

Sensitivity analysis = A way of assigning confidence to the cluster membership

– create new in silico replica's of the dataset of interest by adding a small amount of noise on the original data – treat new datasets as the original one and cluster

– Genes consistently clustered together over all in silico replicas are considered as robust towards adding noise

How to determine the noise?

Statistical validation

Validation

• Gaussian noise with  0 and standard deviation 

estimated as the median standard deviation for the log-ratios for all genes across the different experiment Bittner et al. 2000

How to determine the noise? How to generate simulated datasets?

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• noise based on the appropriate ANOVA model

 describes the noise term

•The values are the estimates from the original fit

•The are drawn with replacement from the studentized residuals of the original fit

Clustering is repeated on the simulated datasets

Statistical validation

Validation

Comparing cluster results

• cluster label known:

determine the stability of a gene: the percent of bootstrap cluster experiments in which the gene matches to the same cluster

• cluster label unknown:

• Identify pairs of genes that cluster together in C^ and count the frequency with which such pairs cluster together in the bootstrapped clusters C^*. When each pair of genes clusters together reliably stable clusters will emerge

• RAND INDEX (Yeung et al. 2001)

• Jaccard coefficient (Ben-Hur et al. 2002)

Approximate the confidence in the clustering output of a gene

Statistical validation

Validation

Cluster exp 1 C1

Cluster exp 2 C1

Cluster exp 3 C1

Cluster exp 4 C1

Cluster exp 1 C1

C2 C3

…

Cluster exp 2 C1

C2 C3

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Cluster exp 3 C1

C2 C3

…

Cluster exp 4 C1

C2 C3

…

RAND index

• statistic designed to assess the degree of agreement between two partitions

• Usually an unknown partition against an external standard Adjusted RAND index

• adjusted so that the expected value of the RAND index between two random partions is zero

Statistical validation

Validation

d c

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d RAND a

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a: the number of object pairs that are clustered together in data set 1 and in dataset 2 b: the number of object pairs that are clustered together in data set 1 but not in dataset 2 c: the number of object pairs that are clustered together in data set 2 but not in dataset 1 d: the number of object pairs that are put in different clusters in both datasets

a, d: agreement between cluster results b, c: disagreement between cluster results

The rand index is defined as the fraction of agreement that is the number of pairs of objects that are either in same groups in both partitions (a) or in different groups in both partitions (b) divided by the total number of pairs of objects (a + b + c +d).

The rand index lies between 0 and 1.

• Jaccard coefficient

Statistical validation

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Matrix A:

cluster results of dataset 1

# genes

# genes

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Matrix B:

cluster results of dataset 2

# genes

# genes

C_ij=1: if x_iand x_jbelong to the same cluster; 0 otherwise

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Matrix A:

cluster results of dataset 1

# genes

# genes

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Matrix B:

cluster results of dataset 2

# genes

# genes

C_ij=1: if x_iand x_jbelong to the same cluster; 0 otherwise

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Jaccard coefficient J

Based on the clusters of one dataset, binary pair vectors are calculated, where each element corresponds to a unique pair of genes and had a value one if both genes were clustered into the same cluster and zero otherwise.

From two such pairvectors, where one was derived from the first dataset and the other from the second dataset, the jaccard coefficient is computed. This coefficient compares the correlation between both obtained binary matrices.

Cluster coherence testing

k points (genes) in cluster p experiments (dimensions)

average profile of cluster

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Vw:

• Variance of the genes about the the cluster average averaged over all experiments

•Maximizes coherence of the genes within a cluster

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Statistical validation

Euclidian distance

Validation

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p experiments Cluster

average profile

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VB:

•Describes how the average at each experimental point oscillates around the average of the average cluster profile

•Maximizes variance across experiments

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Statistical validation

Gap score

Validation

Score function:

•R² select clusters containing tightly co-expressed genes (minimal Vw) showing a high variable profile (high V_B) across the experiments (ie affected by the

signal studied).

•Score is compared to a similar score calculated based on a randomly generated cluster (bootstrapping)

•The difference between the score of the randomly generated cluster and the cluster of interest is calculated. (gapstatistics)

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Gap statistics

Statistical validation

Validation

Overview

INTRODUCTION

MICROARRAY ANALYSIS

VALIDATION OF THE RESULTS

• Statistical validation

• Biological validation INTEGRATION

Biological validation

dataset

small clusters

• contain genes with highly similar profile (+)

• some information given up in first step (-)

validate “core” clusters

Motif finding DNA level

literature/

knowledge

extend clusters

big clusters

• contain all real positives (+)

• increasing number of false positives (-)

Validation

Microarrays and TextMining

Rationale:

Clustering Accession Nrs

AC0020

D11428 SRS,

Medline, GeneCards,..

Manual Query : huge task

data Literature/

knowledge

Validation

Biological validation

Controlled vocabularies

Cluster number Graphical representatio n of cluster Number of ORFs MIPS functional category (top-level) ORFs within functional category P-value (- log10)

1 426 energy

transport facilitation 47

40 10 5 3 196 cell growth, cell

division and DNA synthesis

48 5

4 149 protein synthesis cellular organisation

71 107

50 19 5 159 cell rescue, defense,

cell death and ageing 20 4 6 171 cell growth, cell

division and DNA synthesis

76 24

9 78 cell growth, cell division and DNA synthesis

23 4

37 11 metabolism 9 6

Cumulative

hypergeometric distribution

Biological validation

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p-value that this degree of enrichment could have occurred by chance (implemented in Ontoexpress)

² test or Fisher exact test (as implemented in FATIGO software)

Biological validation

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N1: number of genes on the chip

N2: number of differentially expressed genes

Microarrays and Motif Finding

cDNA arrays

Motif finding

Clustering Preprocessing of the data

EMBL BLAST Upstream regions

Gibbs sampling

Validation

Biological validation

Overview

INTRODUCTION

MICROARRAY ANALYSIS

VALIDATION OF THE RESULTS

• Statistical validation

• Biological validation INTEGRATION

• IT level

• Algorithmic level

Integration

Integration

Need for integrated tool Validation

Overview

INTRODUCTION

MICROARRAY ANALYSIS

VALIDATION OF THE RESULTS

• Statistical validation

• Biological validation INTEGRATION

• IT level

• Algorithmic level

Integration

Need for integrated algorithms Validation

• Retain high sensitivity (minimize number of false negatives)

• Reduce level of noise (minimize number of false positives)

• In corporate a priori information

• Combine data from different sources that can mutually confirm each other

• Example: sequence information and expression profiles

• Server rMotif (Lapidot and Pilpel, 2003)

• Selects genes from a microarray if

– Contain a motif

– Have a highly correlated expression profile

Integration

Validation

• Motif diagnosis tool

• measures the extent to which a set of genes that contain a

given motif in their promoter) display expression profiles similar to each other at a given set of conditions (analyzed by

microarrays)

• score (EC expression coherence) of a set of N genes is defined as the number of p pairs of genes in the set for which the Euclidean distance between the mean and variance normalized profiles falls below a threshold D, divided by the total number of pairs in the set

• EC= p/[(0.5(N)(N-1)]

Integration

Validation

Integration

Validation