Local spline embedding-based linear classification method

Abstract

The invention relates to a local spline embedding-based linear classification method. The method comprises the steps of inputting training data and test data; and performing supervised local spline embedding dimension reduction of the training data: constructing an intra-class graph and an inter-class graph, and selecting neighborhoods; constructing an intra-class local tangent space and an inter-class local tangent space of training data points; obtaining global low-dimensional coordinates of the training data points and obtaining corresponding optimal linear mapping; mapping the test data into a low-dimensional manifold; and classifying the test data subjected to dimension reduction by K-nearest neighbor classification to obtain category labels of the test data. According to the method, the defects that the intra-class nearest neighbor graph and the inter-class nearest neighbor graph of the data are not comprehensively analyzed and category information of the training data is not utilized in the past are overcome; and in addition, the data complexity is greatly lowered, the observability and distinguishability of the data are enhanced, and the classification accuracy of the data on a high-dimensional manifold is greatly improved.

Description

technical field [0001] The invention relates to classification and analysis of high-dimensional data, in particular to a linear classification method based on local spline embedding. Background technique [0002] The local spline embedding algorithm is an excellent manifold dimensionality reduction algorithm. For a low-dimensional manifold embedded in a high-dimensional input space, by obtaining the local coordinates of the sample point neighborhood projected on the tangent space, the spline function The embedding maps the local coordinates into global low-dimensional coordinates, and minimizes the mapping error of the sample data in the two mapping processes of local mapping to the tangent space and then mapping from the tangent space to the global, which can greatly maintain the local characteristics of the sample data. However, the local spline embedding algorithm is only a dimensionality reduction algorithm, and the data after dimensionality reduction is not necessarily ...

AI Technical Summary

Problems solved by technology

Compared with the orthogonal local spline discriminant projection algorithm, their method further considers the mapping relationship between the neighbors between classes, but still retains the most original orthogonal local spline dimensionality reduction algorithm, without deep analysis and modification. , and does not take into account the need to minimize the mapping distance of the nearest neighbors in the class

To sum up, the existing classification algorithms based on local spline embedding are limited by the original dimensionality reduction algorithm framework, and there is no comprehensive analysis of the intra-class neighbor graph (corresponding to intra-class compactness) and inter-class neighbor graph (corresponding to Discreteness between classes), so the category information of the training data cannot be fully utilized, and in-depth algorithm improvement and performance optimization are urgently needed

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