文档介绍：该【权重随机正交化的极速非线性判别分析网络 】是由【niuww】上传分享，文档一共【3】页，该文档可以免费在线阅读，需要了解更多关于【权重随机正交化的极速非线性判别分析网络 】的内容，可以使用淘豆网的站内搜索功能，选择自己适合的文档，以下文字是截取该文章内的部分文字，如需要获得完整电子版，请下载此文档到您的设备，方便您编辑和打印。权重随机正交化的极速非线性判别分析网络
Title: Accelerated Non-linear Discriminant Analysis Network with Random Orthogonalization of Weights
Abstract:
Non-linear Discriminant Analysis (NDA) is a powerful technique used for dimensionality reduction and classification in pattern recognition and machine learning. The traditional NDA aims to extract relevant features from high-dimensional input data while maximizing the separation between different classes.
In this paper, we propose an Accelerated Non-linear Discriminant Analysis Network (ANDA-Net) with a novel approach of random orthogonalization of weights. The ANDA-Net enhances the discriminative power of NDA by exploiting non-linear relationships in the input data while preserving the orthogonality between weight vectors. This novel method not only improves classification accuracy but also facilitates interpretability and generalization of the learned features.
1. Introduction:
In recent years, deep learning techniques have achieved remarkable success in various domains, such as image recognition, speech processing, and natural language understanding. However, traditional shallow machine learning methods, including Linear Discriminant Analysis (LDA) and Support Vector Machines (SVM), still offer advantages in terms of interpretability and computational efficiency. Therefore, there is a growing need to develop powerful and efficient non-linear discriminant analysis techniques.
2. Related Work:
The traditional Non-linear Discriminant Analysis (NDA) involves mapping the input data into a higher-dimensional feature space to find a non-linear decision boundary for classification. However, NDA suffers from the curse of dimensionality and may lead to overfitting. Several approaches try to address these issues, such as Kernel Discriminant Analysis (KDA), Locality Preserving Projections (LPP), and Isometric Mapping (Isomap). Although successful to some extent, these methods still have limitations in terms of computation complexity and interpretability.
3. Methodology:
The ANDA-Net introduces a random orthogonalization step to the traditional NDA to improve both accuracy and interpretability. The main steps of the ANDA-Net are as follows:
Random Initialization:
We initialize the weight vectors randomly to ensure a diverse starting point for optimization. This randomness enables the network to explore various possible solutions and escape local optima.
Orthogonalization Procedure:
To preserve the orthogonality between weight vectors in the network, we propose a novel random orthogonalization procedure. In each training iteration, we randomly select a pair of weight vectors and apply a Givens rotation to make them orthogonal. This procedure ensures that the network discriminates between different classes based on independent and non-redundant features.
Network Training:
After the orthogonalization procedure, the ANDA-Net is trained using a gradient-based optimization algorithm, such as stochastic gradient descent. The network is optimized to minimize a cost function that incorporates both the classification loss and an orthogonality constraint. This constraint prevents weight vectors from becoming collinear and maintains the discriminative power of the network.
4. Experimental Results:
We conducted extensive experiments on several benchmark datasets to evaluate the performance of the proposed ANDA-Net compared to other state-of-the-art methods. The results demonstrate that the ANDA-Net achieves superior classification accuracy, improved generalization, and enhanced interpretability. Additionally, the computational complexity of the ANDA-Net is comparable to other non-linear discriminant analysis methods, making it practical for real-world applications.
5. Conclusion:
In this paper, we presented the Accelerated Non-linear Discriminant Analysis Network (ANDA-Net) with a novel approach of random orthogonalization of weights. The proposed method enhances the discriminative power of NDA by exploiting non-linear relationships in the input data while preserving the orthogonality between weight vectors. Extensive experiments demonstrate that ANDA-Net outperforms existing methods in terms of accuracy, interpretability, and generalization. Future work can focus on further optimizing the computational efficiency of the ANDA-Net and applying it to more complex tasks and datasets.