Supervised dimension reduction method based on robust l1, 2 norm constraints

Abstract

The invention provides a supervised dimension reduction method based on robust l1, 2 norm constraints. Firstly, a robust dimensionality reduction optimization model based on l1 and l2 norm constraintsis constructed, l1 norms are used between data points, l2 norms are used for data features, and through the l1 norms, the influence of the model on data abnormal values can be greatly reduced, and the robustness of the model is improved; and then, a corresponding optimization algorithm is designed for model solving, thus obtaining an optimal projection matrix through supervised learning, and further applying the projection matrix to a high-dimensional data set without a sample label to realize effective dimension reduction of high-dimensional data. According to the invention, the problem thatthe LDA method is sensitive to abnormal values is essentially solved by utilizing l1 and l2 norms, and the method is an effective and robust dimension reduction method.

Description

technical field [0001] The invention belongs to the technical field of machine learning, and specifically relates to a 1,2 Norm-Constrained Supervised Dimensionality Reduction Methods. Background technique [0002] As an important supervised dimensionality reduction technique in the field of machine learning, Fisher linear discriminant analysis (LDA) has been successfully applied in many scientific fields in recent years. As a subspace analysis method for learning the low-dimensional structure of high-dimensional data, LDA is mainly to find a set of vectors that maximize Fisher's criterion, and then use these vectors to perform dimensionality reduction on the original data. [0003] The traditional LDA method uses an objective function based on the trace ratio, which is transformed into an eigenvalue problem to obtain the closed-form solution of the model. However, the solution to this problem requires the inversion of the within-class scatter matrix. Therefore, when the ...

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Problems solved by technology

But also because l 1 The introduction of norms makes the model difficult to optimize

Because all LDA methods (including those based on ratio and difference) need to minimize the intra-class divergence and maximize the inter-class divergence at the same time, existing sparse learning optimization algorithms such as gradient projection method (GradientProjection), homotopy algorithm (Homotopy ), iterative shrinkage threshold method (Iterative ShrinkageThresholding), augmented Lagrange method (Augmented Lagrange Multiplier methods), etc., cannot solve the problem based on l 1 Norm of the LDA objective function

[0005] In summary, it is difficult for existing models to improve their robustness to outliers and noise in the data.

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