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Recently, sparse representation-based classification (SRC) has been widely studied and has produced state-of-the-art results in various classification tasks. Learning useful and computationally convenient representations from complex redundant and highly variable visual data is crucial for the success of SRC. However, how to find the best feature representation to work with SRC remains an open question. In this paper, we present a novel discriminative projection learning approach with the objective of seeking a projection matrix such that the learned low-dimensional representation can fit SRC well and that it has well discriminant ability. More specifically, we formulate the learning algorithm as a bilevel optimization problem, where the optimization includes an $\ell _{1}$ -norm minimization problem in its constraints. Through the bilevel optimization model, the relationship between sparse representation and the desired feature projection can be explicitly exploited during the learning process. Therefore, SRC can achieve a better performance in the transformed subspace. The optimization model can be solved by using a stochastic gradient ascent algorithm, and the desired gradient is computed using implicit differentiation. Furthermore, our method can be easily extended to learn a dictionary. The extensive experimental results on a series of benchmark databases show that our method outperforms many state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Consider the problem of investigating the structure of a set of sample points in a very high dimensional (Euclidean) space. This case is paradigmatic, for instance, in postgenomic applications. The high dimensionality and small sample size make statistical inference and optimization difficult problems, such that selecting a model or choosing a learning algorithm face the evidence that currently no consensus guidelines exist. Usually, the intervention of linear or nonlinear projection method is required to map the observations into a low-dimensional space with the most salient data features preserved. This step usually involves computing statistics from the low-dimensional projected space of features and then inferring on the highly dimensional original structures (the genes). This work deals with model validation for gene selection and regulation dynamics. The analysis is conducted through a mix of quantitative methods and qualitative aspects. A regularized inference approach is employed based on dimensionality reduction, data denoising, and feature extraction tasks. Each task requires the implementation of statistics and machine learning algorithms. We focus on the complex problem of inferring the coregulation from the coexpression gene dynamics in the presence of limited biological information and time course perturbation experiments. In particular, both separation and interference gene dynamics are considered and validated to design the most coherent underlying transcriptional regulatory map. [ABSTRACT FROM AUTHOR]