Manifold-based linear regression learning method

Abstract

A manifold-based linear regression learning method comprises the steps of constructing a predictor Kn of an nth-type training sample; utilizing the nth-type training sample Kn for calculating an nth-type mapping matrix Hn, wherein Hn is obtained through the equation that Hn=Kn(Kn<T>Kn)<-1>Kn<T>; utilizing the nth-type mapping matrix Hn for calculating a linear regression image corresponding to each image y in the type n; constructing a similarity matrix Sij, wherein Sij is obtained in two modes, according to one mode, if 1(xi)=1(xj), Sij=1, if not, Sij=0, and i and j range from 1 to M, according to the other mode, if 1(xi)=1(xj), xi belongs to the k-nearest neighbor of xj or xj belongs to the k-nearest neighbor of xi, Sij meets the equation that Sij=exp(-||xi-xj||<2>/t), t meets the equation specified in the specification, xik represents the k-nearest neighbor of the xi sample, and if not, Sij=0; calculating a feature conversion matrix W. According to the manifold-based linear regression learning method, manifold learning and a linear regression classification model are combined, the nonlinear structure in the high-dimensional space can be kept, the sample can be mapped to the linear subspace easier to classify, the manifold-based linear regression learning method is high in practicability, easy to implement and feasible, and the classification purposes of human face recongnition, biometric feature recognition and the like can be achieved.

Description

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AI Technical Summary

Benefits of technology

This patented technology allows researchers to study how different types of patterns are formed by combining multiple variables into one equation called matrix equations (Ms). These MIs help predict or analyze new samples based on their characteristics like shape, size, coloration etc., which helps scientists make more accurate decisions about unknown objects. By doing this analysis over time, they may improve understanding of complex systems without having full knowledge from previous experiments. Overall, these techniques provide valuable tools for various applications related to object identification and biology science.

Problems solved by technology

Technics Problem: Existing techniques like Principal Component Analysis or Independent Component Analysis require significant amounts of memory resources due to their complexity and time required for training. Linear Discrimination Learning Protocols (LSDPS) has been developed but it requires expensive hardware devices with limited capabilities compared to existing approaches.

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