Data visualization and clustering: an application to gene expression data

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1 Data visualization and clustering: an application to gene expression data Francesco Napolitano Università degli Studi di Salerno Dipartimento di Matematica e Informatica DAA Erice, April 2007

2 Thanks to Dipartimento di Matematica e Informatica, University of Salerno A. Ciaramella (*), F. Iorio (**), G. Raiconi, R. Tagliaferri. Dipartimento di Scienze Fisiche, University Federico II of Naples G. Miele, A. Staiano (*), G. Longo Complex Disease Genetics Unit, Dpt. of Cellular and Molecular Biology and Pathology "L. Califano" University Federico II of Naples S. Cocozza, M. Pinelli (*) Currently with Parthenope University of Naples (**) Currently with Telethon Institute of Genetics and Medicine, Naples

3 Introduction Genomic data analysis is an example of hard data mining challenge. In fact genomic datasets are usually noisy and big, both in the number of genes to be analized and in their dimensionality. We propose a visual and interactive approach applied to the analysis of the HeLa Cell dataset.

4 Human Cell Cycle Gene Expression Data The complete dataset was obtained by a DNA microarray (*). The extracted values refer to the ratio between the two microarray channels (Cy5/Cy3). In (**) 1334 were extracted basing on the periodicity of their expression values. They also performed an hierarchical clustering on the dataset. We used the data from the experiment which provided more information and less missing values (TT3 in the next figure) and tried to explore more clustering possibilities. (*) (**) M. L. Whitfield, G. Sherlock, A. J. Saldanha, J. I. Murray, C. A. Ball, K. E. Alexander, J. C. Matese, C. M. Perou, M. M. Hurt, P. O. Brown, D. Botstein. (2002) Identification of Genes Periodically Expressed in the Human Cell Cycle and Their Expression in Tumors, Molecular Biology of the Cell, vol. 13,

5 Dataset overview

6 The space of clusterizations for a dataset Clusterization 1 Initialization 1 Clusterization 2 dataset Clustering Method 1 Clustering Method 2 Parameter set 1 Parameter set 2 Parameter set N Initialization 2 Which one is the best? Initialization P Clusterization Q Clustering Method M

7 Which one is the best? Which ones are good?

8 Clustering the HeLa cell dataset We try various approaches to explore other solutions for the clustering of the HeLa cell dataset. We seek for both similar and different solutions to the one proposed in the referred paper. The clustering process will always be divided into two steps, the first of which will enable human interaction for the second by reducing the number of objects to deal with.

9 How many clusters? Stability of the clusterization of a dataset is seen as how much it is likely to be produced by a clustering procedure. This phenomenon can be estimated through the comparison of clusterings performed on subsamples of the dataset. Comparison between clusterizations is performed through classical measures (such as Mionkowski Index, Jaccard Coefficient, correlation) or entropy based measures (such as the entropy of the confusion matrix between clusterizations). Averaging over the similarities between the clusterizations of subsamples, a final value for the stability of the clusterization of the whole dataset is found. A good choice for the number of clusters can be the one giving maximum stability.

10 Clusterization 1 We choose PPS Parameter set 1 Initialization 1 Initialization 2 Clusterization 2 Clustering Method 1 Parameter set 2 Clusterization Q dataset Clustering Method 2 Parameter set N Initialization P We choose PCA We use random projections of the preprocessed HeLa dataset Clustering Method M We vary the number of neurons between 12 and 150

11 Stability of the HeLa cell clusterization through PPS

12 Clusters reliability Once chosen a set of parameters, the reliability of the clusters obtained using it can be assessed by means of subsampling techniques.

13 Clusterization 1 We choose PPS Parameter set 1 Initialization 1 Initialization 2 Clusterization 2 Clustering Method 1 Parameter set 2 Clusterization Q dataset Clustering Method 2 Parameter set N Initialization P We choose PCA We use subsets of the preprocessed HeLa dataset Clustering Method M We choose some parameter set according to the previous analysis

14 Clusters reliability: The Fuzzy Similarity Tool Exploiting the fuzzy similarity information, a subset of the patterns obeying a given reliability threshold can be extracted. The higher the requested reliability, the more the presence of outliers and the smaller the clusters.

15 The 62 clusters obtained with PPS We choose 62 as the number of clusters, being a good compromise between the stability of the clusterization and the reliability of the clusters. Also, 62 is a number of objects a human can directly deal with, thus allowing the next interactive step.

16 Interactive agglomeration The next phase consists in merging the clusters found in the first phase through the interactive agglomeration tool.

17 Interactive Hierarchical Agglomeration

18 Biological findings: cluster comparison 8 our cluster 6 4 Whitfield cluster Whitfield unlabelled Cluster associated with DNA replication in Whitfield et al. turned out to be less characterized than our corresponding cluster. Many of the unlabelled clusters, in fact, are actually associated with DNA replication.

19 Further exploring the space of clusterizations Clusterization 1 We try PPS, SOM and K-means Initialization 1 Clusterization 2 Clustering Method 1 Parameter set 1 Parameter set 2 Initialization 2 Clusterization Q dataset We start form the preprocessed HeLa dataset Clustering Method 2 Clustering Method M Parameter set N Initialization P We choose 60 As the number of neurons (62 for PPS) We try random initializations

20 K-means Clustering Map KMS Clustering Map for HeLa Distorsion Histogram Distances Histogram K-means is performed 100 times with K=60 and random initialization. Using MDS, each clusterization is mapped to a point on the plane, exploiting an entropy based similarity measure. The map is colored according to a fitness function, defined as the sum of clusters distorsions. Clusterizations 34, 65, 66 are extracted for next steps

21 SOM Clustering Map SOM Clustering Map for HeLa Distorsion Histogram Distances Histogram SOM clustering is performed 100 times with K=60 and random initialization. Using MDS, each clusterization is mapped to a point on the plane, exploiting an entropy based similarity measure. The map is colored according to a fitness function, defined as the sum of clusters distorsions. Clusterizations 42, 49, 100 are extracted for next steps

22 PPS Clustering Map PPS Clustering Map for HeLa Distorsion Histogram Distances Histogram PPS clustering is performed 100 times with K=62 and random initialization. Using MDS, each clusterization is mapped to a point on the plane, exploiting an entropy based similarity measure. The map is colored according to a fitness function, defined as the sum of clusters distorsions. Clusterization 88 is extracted for next steps

23 Comparison between SOM and K- Means candidate clusterizations F0.5 SOM 100 SOM 42 SOM 49 KMS 34 KMS 66 KMS 65 SOM ,7192 0,6788 0,7179 0,7068 0,6841 SOM42 0, ,704 0,7398 0,7243 0,7111 SOM49 0,6786 0, ,708 0,7184 0,6821 KMS65 0,7177 0,7346 0, ,7139 0,6939 KMS66 0,7068 0,7194 0,7186 0, ,6956 KMS34 0,6881 0,7103 0,6863 0,6981 0,6996 1

24 Comparison of the biological functionalities of our clusters (SOM 42) with the ones in Whitfield et al. Other DNA Repl. early DNA Repl. late Histone Tubulin Spindle Assembly Mitotic Surv Cell Adhesion Chromosome metab RAS Signal. Trasd. Description establishment and/or maintenance of chromatin architecture nucleotide biosynthesis neurophysiological process response to DNA damage stimulus transcription from RNA polymerase II promoter transport cell proliferation development sister chromatid segregation cell cycle

25 Comparing biological functionalities of our clusters (KMS 34) with the ones in Whitfield et al. Other DNA Repl. early DNA Repl. late Histone Tubulin Spindle Assembly Mitotic Surv Cell Adhesion Chromosome metab RAS Signal. Trasd. Description signal transduction development cell proliferation DNA replication transport DNA repair cell cycle chromosome organization and biogenesis nitrogen compound metabolism sister chromatid segregation

26 Comparing biological functionalities of our clusters (PPS) with the ones in Whitfield et al. Other DNA Repl. early DNA Repl. late Histone Tubulin Spindle Assembly Mitotic Surv Cell Adhesion Chromosome metab RAS Signal. Trasd. Description DNA metabolism cell cycle regulation of transcription, DNA-dependent cell proliferation sister chromatid segregation transport neurophysiological process

27 Conclusions The problem of clustering is complex, allowing for many feasible solutions to be investigated. Such complexity can be dealt with the help of visual and interactive tools together in addition to standard analytic techniques. Understanding of datasets such as HeLa cell, that is hard both in size and complexity, is greatly helped by visual inspection and data interaction.

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