CAFÉ-Map : context aware feature mapping for mining high dimensional biomedical data

Feature selection and ranking is of great importance in the analysis of biomedical data. In addition to reducing the number of features used in classification or other machine learning tasks, it allows us to extract meaningful biological and medical information from a machine learning model. Most existing approaches in this domain do not directly model the fact that the relative importance of features can be different in different regions of the feature space. In this work, we present a context aware feature ranking algorithm called CAFÉ-Map. CAFÉ-Map is a locally linear feature ranking framework that allows recognition of important features in any given region of the feature space or for any individual example. This allows for simultaneous classification and feature ranking in an interpretable manner. We have benchmarked CAFÉ-Map on a number of toy and real world biomedical data sets. Our comparative study with a number of published methods shows that CAFÉ-Map achieves better accuracies on these data sets. The top ranking features obtained through CAFÉ-Map in a gene profiling study correlate very well with the importance of different genes reported in the literature. Furthermore, CAFÉ-Map provides a more in-depth analysis of feature ranking at the level of individual examples

Operators for transforming kernels into quasi-local kernels that improve SVM accuracy

Motivated by the crucial role that locality plays in various learning approaches, we present, in the framework of kernel machines for classification, a novel family of operators on kernels able to integrate local information into any kernel obtaining quasi-local kernels. The quasi-local kernels maintain the possibly global properties of the input kernel and they increase the kernel value as the points get closer in the feature space of the input kernel, mixing the effect of the input kernel with a kernel which is local in the feature space of the input one. If applied on a local kernel the operators introduce an additional level of locality equivalent to use a local kernel with non-stationary kernel width. The operators accept two parameters that regulate the width of the exponential influence of points in the locality-dependent component and the balancing between the feature-space local component and the input kernel. We address the choice of these parameters with a data-dependent strategy. Experiments carried out with SVM applying the operators on traditional kernel functions on a total of 43 datasets with di®erent characteristics and application domains, achieve very good results supported by statistical significance

Information Preserving Component Analysis: Data Projections for Flow Cytometry Analysis

Flow cytometry is often used to characterize the malignant cells in leukemia and lymphoma patients, traced to the level of the individual cell. Typically, flow cytometric data analysis is performed through a series of 2-dimensional projections onto the axes of the data set. Through the years, clinicians have determined combinations of different fluorescent markers which generate relatively known expression patterns for specific subtypes of leukemia and lymphoma -- cancers of the hematopoietic system. By only viewing a series of 2-dimensional projections, the high-dimensional nature of the data is rarely exploited. In this paper we present a means of determining a low-dimensional projection which maintains the high-dimensional relationships (i.e. information) between differing oncological data sets. By using machine learning techniques, we allow clinicians to visualize data in a low dimension defined by a linear combination of all of the available markers, rather than just 2 at a time. This provides an aid in diagnosing similar forms of cancer, as well as a means for variable selection in exploratory flow cytometric research. We refer to our method as Information Preserving Component Analysis (IPCA).Comment: 26 page

Parsimonious Mahalanobis Kernel for the Classification of High Dimensional Data

The classification of high dimensional data with kernel methods is considered in this article. Exploit- ing the emptiness property of high dimensional spaces, a kernel based on the Mahalanobis distance is proposed. The computation of the Mahalanobis distance requires the inversion of a covariance matrix. In high dimensional spaces, the estimated covariance matrix is ill-conditioned and its inversion is unstable or impossible. Using a parsimonious statistical model, namely the High Dimensional Discriminant Analysis model, the specific signal and noise subspaces are estimated for each considered class making the inverse of the class specific covariance matrix explicit and stable, leading to the definition of a parsimonious Mahalanobis kernel. A SVM based framework is used for selecting the hyperparameters of the parsimonious Mahalanobis kernel by optimizing the so-called radius-margin bound. Experimental results on three high dimensional data sets show that the proposed kernel is suitable for classifying high dimensional data, providing better classification accuracies than the conventional Gaussian kernel