Mutual-energy inner product optimization method for constructing feature coordinates and image classification in Machine Learning

• URL: http://arxiv.org/abs/2411.06100v1
• Date: Sat, 09 Nov 2024 07:26:03 GMT
• Title: Mutual-energy inner product optimization method for constructing feature coordinates and image classification in Machine Learning
• Authors: Yuanxiu Wang,
• Abstract summary: This paper proposes the mutual-energy inner product optimization method for constructing a feature coordinate system. By expressing the mutual-energy inner product as a series of eigenfunctions, it shows a significant advantage of enhancing low-frequency features. A stable and efficient sequential linearization algorithm is constructed to solve the optimization model.
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• Abstract: As a key task in machine learning, data classification is essentially to find a suitable coordinate system to represent data features of different classes of samples. This paper proposes the mutual-energy inner product optimization method for constructing a feature coordinate system. First, by analyzing the solution space and eigenfunctions of partial differential equations describing a non-uniform membrane, the mutual-energy inner product is defined. Second, by expressing the mutual-energy inner product as a series of eigenfunctions, it shows a significant advantage of enhancing low-frequency features and suppressing high-frequency noise, compared with the Euclidean inner product. And then, a mutual-energy inner product optimization model is built to extract data features, and convexity and concavity properties of its objective function are discussed. Next, by combining the finite element method, a stable and efficient sequential linearization algorithm is constructed to solve the optimization model. This algorithm only solves equations including positive definite symmetric matrix and linear programming with a few constraints, and its vectorized implementation is discussed. Finally, the mutual-energy inner product optimization method is used to construct feature coordinates, and multi-class Gaussian classifiers are trained on the MINST training set. Good prediction results of Gaussian classifiers are achieved on the MINST test set.

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