Spectral embedding finds meaningful (relevant) structure in image and microarray data

We present the results of applying the spectral method of Lafon, a nonlinear DR method based on the weighted graph Laplacian, that minimizes the requirements for such parameter optimization for two biological data types. We demonstrate that it is successful in determining implicit ordering of brain slice image data and in classifying separate species in microarray data, as compared to two conventional linear methods and three nonlinear methods (one of which is an alternative spectral method). This spectral implementation is shown to provide more meaningful information, by preserving important relationships, than the methods of DR presented for comparison.Tuning parameter fitting is simple and is a general, rather than data type or experiment specific approach, for the two datasets analyzed here. Tuning parameter optimization is minimized in the DR step to each subsequent classification method, enabling the possibility of valid cross-experiment comparisons.Results from the spectral method presented here exhibit the desirable properties of preserving meaningful nonlinear relationships in lower dimensional space and requiring minimal parameter fitting, providing a useful algorithm for purposes of visualization and classification across diverse datasets, a common challenge in systems biology.Dimensionality reduction (DR) is the process of rendering high dimensional complex data in a low dimensional space. Provided the process is calculated accurately, this low dimensional representation is preferred for use in inference and summarization for multiple reasons, among which are ease of visualization in a reduced variable space and clarity (i.e. ready interpretation) of clustering or classification. Other benefits include the insights into the data structure that can be obtained from the projected axes and the obvious denoising effect attained in some types of DR. Reduction strategies often rely on linear approaches defined by a method that represents x1, ..., xn ∈ ？q as