Abstract
BackgroundThe search for cluster structure in microarray datasets is a base problem for the so-called "-omic sciences". A difficult problem in clustering is how to handle data with a manifold structure, i.e. data that is not shaped in the form of compact clouds of points, forming arbitrary shapes or paths embedded in a high-dimensional space, as could be the case of some gene expression datasets.ResultsIn this work we introduce the Penalized k-Nearest-Neighbor-Graph (PKNNG) based metric, a new tool for evaluating distances in such cases. The new metric can be used in combination with most clustering algorithms. The PKNNG metric is based on a two-step procedure: first it constructs the k-Nearest-Neighbor-Graph of the dataset of interest using a low k-value and then it adds edges with a highly penalized weight for connecting the subgraphs produced by the first step. We discuss several possible schemes for connecting the different sub-graphs as well as penalization functions. We show clustering results on several public gene expression datasets and simulated artificial problems to evaluate the behavior of the new metric.ConclusionsIn all cases the PKNNG metric shows promising clustering results. The use of the PKNNG metric can improve the performance of commonly used pairwise-distance based clustering methods, to the level of more advanced algorithms. A great advantage of the new procedure is that researchers do not need to learn a new method, they can simply compute distances with the PKNNG metric and then, for example, use hierarchical clustering to produce an accurate and highly interpretable dendrogram of their high-dimensional data.
Highlights
The search for cluster structure in microarray datasets is a base problem for the so-called “-omic sciences”
Evaluation on artificial datasets In a first series of experiments we used artificial datasets to evaluate the behavior of the new metric in controlled situations, in which we change the difficulty of the clustering problem by setting, for example, the dimensionality of the input space or the distance between the clusters
This dataset simulates a problem in which all genes are still correlated, but the correlation matrix is different for each experimental condition, which leads to a better separation when using correlation as base metric
Summary
The search for cluster structure in microarray datasets is a base problem for the so-called “-omic sciences”. A difficult problem in clustering is how to handle data with a manifold structure, i.e. data that is not shaped in the form of compact clouds of points, forming arbitrary shapes or paths embedded in a highdimensional space, as could be the case of some gene expression datasets. Several problems can be faced with this technology It can be used for the identification of differentially expressed genes [1], which could highlight possible gene targets for more detailed molecular studies or drug treatments. Another application is to assign samples to known classes (class prediction) [2], using genetic profiles to improve, for example, the diagnosis of cancer patients. Dealing with high dimensional spaces is a known challenge for clustering procedures, as they usually fail to handle manifold-structured data, i.e. data that form low-dimensional, arbitrary shapes or paths through a high-dimensional space
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