Dimensionality Reduction via Isomap with Lock-Step and Elastic Measures for Time Series Gene Expression Classification

Abstract

Isometric feature mapping (Isomap) has proven high potential for nonlinear dimensionality reduction in a wide range of application domains. Isomap finds low-dimensional data projections by preserving global geometrical properties, which are expressed in terms of the Euclidean distances among points. In this paper we investigate the use of a recent variant of Isomap, called double-bounded tree-connected Isomap (dbt-Isomap), for dimensionality reduction in the context of time series gene expression classification. In order to deal with the projection of temporal sequences dbt-Isomap is combined with different lock-step and elastic measures which have been extensively proposed to evaluate time series similarity. These are represented by three $\mathcal L_p$-norms, dynamic time warping and the distance based on the longest common subsequence model. Computational experiments concerning the classification of two time series gene expression data sets showed the usefulness of dbt-Isomap for dimensionality reduction. Moreover, they highlighted the effectiveness of $\mathcal L_1$-norm which appeared as the best alternative to the Euclidean metric for time series gene expression embedding.