Feature selection in weakly coherent matrices
نویسندگان
چکیده
A problem of paramount importance in both pure (Restricted Invertibility problem) and applied mathematics (Feature extraction) is the one of selecting a submatrix of a given matrix, such that this submatrix has its smallest singular value above a specified level. Such problems can be addressed using perturbation analysis. In this paper, we propose a perturbation bound for the smallest singular value of a given matrix after appending a column, under the assumption that its initial coherence is not large, and we use this bound to derive a fast algorithm for feature extraction.
منابع مشابه
Improving Chernoff criterion for classification by using the filled function
Linear discriminant analysis is a well-known matrix-based dimensionality reduction method. It is a supervised feature extraction method used in two-class classification problems. However, it is incapable of dealing with data in which classes have unequal covariance matrices. Taking this issue, the Chernoff distance is an appropriate criterion to measure distances between distributions. In the p...
متن کاملWeak log-majorization inequalities of singular values between normal matrices and their absolute values
This paper presents two main results that the singular values of the Hadamard product of normal matrices $A_i$ are weakly log-majorized by the singular values of the Hadamard product of $|A_{i}|$ and the singular values of the sum of normal matrices $A_i$ are weakly log-majorized by the singular values of the sum of $|A_{i}|$. Some applications to these inequalities are also given. In addi...
متن کاملبررسی اثر ناسازگاری ماتریس های واریانس- کواریانس در شاخص انتخاب
In selection index procedure, phenotype and genetic (co)variance matrices of traits are used for calculating different genetic parameters like index coefficients, index variance, genetic gain in selection goal and selection accuracy. Sometimes, it is possible that these matrices become inconsistent or they are not positive, nor definite. In the current study, for investigation of the effect of ...
متن کاملA Survey on Evolutionary Co-Clustering Formulations for Mining Time-Varying Data Using Sparsity Learning
The data matrix is considered as static in Traditional clustering and feature selection methods. However, the data matrices evolve smoothly over time in many applications. A simple approach to learn from these time-evolving data matrices is to analyze them separately. Such strategy ignores the time-dependent nature of the underlying data. Two formulations are proposed for evolutionary co-cluste...
متن کاملبررسی اثر ناسازگاری ماتریس های واریانس- کواریانس در شاخص انتخاب
In selection index procedure, phenotype and genetic (co)variance matrices of traits are used for calculating different genetic parameters like index coefficients, index variance, genetic gain in selection goal and selection accuracy. Sometimes, it is possible that these matrices become inconsistent or they are not positive, nor definite. In the current study, for investigation of the effect of ...
متن کامل