4 - Discovery of overlapping clustering

One of the most useful statistical analysis technique for gene expression data is clustering. The clustering of the samples groups them together on the basis of their expression profile. It reveals differences between groups of samples, like for instance between previously unidentified sub-types of cancer. There can be more than one meaningful way to cluster the samples. For instance, in a study about tumors, samples could be clustered according to their pathological status or their inflammation level. If the complete data set, with all genes, is clustered, the result could be any of those clustering, or a chimerical clustering where some samples are grouped based on one concept and others based on some other concept. Getz et al. (2000) have shown that by clustering on only a subset of genes, different clusterings of the samples appear, each with its own biological interpretation. The problem is to get the appropriate clustering for the application at hand. A first approach is to keep all genes. In this case, the clustering which appears is the one supported by the largest number of genes. This might be a reasonable strategy if it is expected that most of the variation in the data is due to the phenomenon of interest. However, if the appropriate clustering is not the most prominent, it is likely to be missed. A related approach is to select a set of genes on which a well defined clustering can be found (Dash et al. 1997, Devney and Ram 1997, Xing and Carp 2000). Those techniques are based on the idea that some genes are irrelevant, that is, consist of noise. But as Getz et al. have shown, the problem is not so much the presence of noise than the existence of different organizations of the data. The genes which are irrelevant for one clustering can be relevant to another. The methods working by feature selection are not well adapted to such case. Another approach is to select the genes based on some knowledge of the data (Alizadeh et al. 2000). Alizadeh et al. selected a cluster of genes using some biological insights (they selected genes which defines germinal centre B-cell signature), and performed their analysis using only this subset of genes. This might be an effective method for data where the genes are clearly defined, so that the choice of genes determines the question asked. For instance, a clustering made on genes expressed only in lymphocytes could separate the samples according to their inflammation level. In high-throughput gene expression experiments however, the genes are usually only succinctly annotated. This means that this approach can bias the results, as the choice of genes might be made to obtain the clustering expected by the investigator. It can also hide important, unexpected, features of the data. Getz et al. (2000) proposed to search for tight groups of highly correlated genes, and to cluster the samples on those groups. This approach has two weaknesses: firstly, the sample clustering is done on only a handful of genes which have essentially all the same values. Secondly, it only works for correlated genes, hence showing a linear dependence, while relationships that are more complex can exist. For instance, some genes oscillate with time during the cell cycle, hence they show a similar profile. However, two oscillating genes with a 90° phase difference are not correlated. Von Heydebreck et al. (2001) proposed to search for sets of genes for which a clear binary separation of the samples can be found. This technique searches only binary separations. The algorithm must be extended to find more complex clustering.