Hyperspectral colon tissue cell classification

A novel algorithm to discriminate between normal and malignant tissue cells of the human colon is presented. The microscopic level images of human colon tissue cells were acquired using hyperspectral imaging technology at contiguous wavelength intervals of visible light. While hyperspectral imagery data provides a wealth of information, its large size normally means high computational processing complexity. Several methods exist to avoid the so-called curse of dimensionality and hence reduce the computational complexity. In this study, we experimented with Principal Component Analysis (PCA) and two modifications of Independent Component Analysis (ICA). In the first stage of the algorithm, the extracted components are used to separate four constituent parts of the colon tissue: nuclei, cytoplasm, lamina propria, and lumen. The segmentation is performed in an unsupervised fashion using the nearest centroid clustering algorithm. The segmented image is further used, in the second stage of the classification algorithm, to exploit the spatial relationship between the labeled constituent parts. Experimental results using supervised Support Vector Machines (SVM) classification based on multiscale morphological features reveal the discrimination between normal and malignant tissue cells with a reasonable degree of accuracy

Structured Sparsity: Discrete and Convex approaches

Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics applications: While the ambient dimension is vast in modern data analysis problems, the relevant information therein typically resides in a much lower dimensional space. However, many solutions proposed nowadays do not leverage the true underlying structure. Recent results in CS extend the simple sparsity idea to more sophisticated {\em structured} sparsity models, which describe the interdependency between the nonzero components of a signal, allowing to increase the interpretability of the results and lead to better recovery performance. In order to better understand the impact of structured sparsity, in this chapter we analyze the connections between the discrete models and their convex relaxations, highlighting their relative advantages. We start with the general group sparse model and then elaborate on two important special cases: the dispersive and the hierarchical models. For each, we present the models in their discrete nature, discuss how to solve the ensuing discrete problems and then describe convex relaxations. We also consider more general structures as defined by set functions and present their convex proxies. Further, we discuss efficient optimization solutions for structured sparsity problems and illustrate structured sparsity in action via three applications.Comment: 30 pages, 18 figure

Robust linear discriminant analysis using MOM-Qn and WMOM-Qn estimators: Coordinate-wise approach

Robust linear discriminant analysis (RLDA) methods are becoming the better choice for classification problems as compared to the classical linear discriminant analysis (LDA) due to their ability in circumventing outliers issue. Classical LDA relies on the usual location and scale estimators which are the sample mean and covariance matrix. The sensitivity of these estimators towards outliers will jeopardize the classification process. To alleviate the issue, robust estimators of location and covariance are proposed. Thus, in this study, two RLDA for two groups classification were modified using two highly robust location estimators namely Modified One-Step M-estimator (MOM) and Winsorized Modified One-Step M-estimator (WMOM). Integrated with a highly robust scale estimator, Qn, in the trimming criteria of MOM and WMOM, two new RLDA were developed known as RLDAMQ and RLDAWMQ respectively. In the computation of the new RLDA, the usual mean is replaced by MOM-Qn and WMOM-Qn accordingly. The performance of the new RLDA were tested on simulated as well as real data and then compared against the classical LDA. For simulated data, several variables were manipulated to create various conditions that always occur in real life. The variables were homogeneity of covariance (equal and unequal), samples (balanced and unbalanced), dimension of variables, and the percentage of contamination. In general, the results show that the performance of the new RLDA are more favorable than the classical LDA in terms of average misclassification error for contaminated data, although the new RLDA have the shortcoming of requiring more computational time. RLDAMQ works best under balanced sample sizes while RLDAWMQ surpasses the others under unbalanced sample sizes. When real financial data were considered, RLDAMQ shows capability in handling outliers with lowest misclassification error. As a conclusion, this research has achieved its primary objective which is to develop new RLDA for two groups classification of multivariate data in the presence of outliers

Automated design of robust discriminant analysis classifier for foot pressure lesions using kinematic data

In the recent years, the use of motion tracking systems for acquisition of functional biomechanical gait data, has received increasing interest due to the richness and accuracy of the measured kinematic information. However, costs frequently restrict the number of subjects employed, and this makes the dimensionality of the collected data far higher than the available samples. This paper applies discriminant analysis algorithms to the classification of patients with different types of foot lesions, in order to establish an association between foot motion and lesion formation. With primary attention to small sample size situations, we compare different types of Bayesian classifiers and evaluate their performance with various dimensionality reduction techniques for feature extraction, as well as search methods for selection of raw kinematic variables. Finally, we propose a novel integrated method which fine-tunes the classifier parameters and selects the most relevant kinematic variables simultaneously. Performance comparisons are using robust resampling techniques such as Bootstrap$632+$and k-fold cross-validation. Results from experimentations with lesion subjects suffering from pathological plantar hyperkeratosis, show that the proposed method can lead to$sim 96$correct classification rates with less than 10% of the original features

Robust computation of linear models by convex relaxation

Consider a dataset of vector-valued observations that consists of noisy inliers, which are explained well by a low-dimensional subspace, along with some number of outliers. This work describes a convex optimization problem, called REAPER, that can reliably fit a low-dimensional model to this type of data. This approach parameterizes linear subspaces using orthogonal projectors, and it uses a relaxation of the set of orthogonal projectors to reach the convex formulation. The paper provides an efficient algorithm for solving the REAPER problem, and it documents numerical experiments which confirm that REAPER can dependably find linear structure in synthetic and natural data. In addition, when the inliers lie near a low-dimensional subspace, there is a rigorous theory that describes when REAPER can approximate this subspace.Comment: Formerly titled "Robust computation of linear models, or How to find a needle in a haystack