Explore MATLAB source code curated for "降维" with clean implementations, documentation, and examples.
This implementation utilizes PCA for dimensionality reduction, preserving 90% of critical data variance through eigenvalue decomposition. The code includes comprehensive comments and comes with sample datasets, while allowing users to integrate custom data for flexible testing.
One challenge in applying statistical methods to pattern recognition is the dimensionality issue - classification problems are generally simpler in low-dimensional feature spaces than in high-dimensional ones. This leads to dimensionality reduction techniques, where a fundamental approach projects d-dimensional feature space onto a straight line to create one-dimensional space, which is mathematically straightforward. However, the key challenge is ensuring samples remain linearly separable after projection. While linearly separable samples can always find a projection direction maintaining linear separability after dimensionality reduction, Fisher Linear Discriminant specifically determines the optimal projection direction that maximizes separability by maximizing between-class distance while minimizing within-class variance.
Comprehensive machine learning source code authored by Zhejiang University professors Cai Deng and He Xiaofei, covering spectral regression, dimensionality reduction, feature selection, topic modeling, matrix factorization, sparse coding, hashing techniques, clustering methods, active learning, and matrix learning. This collection serves as an excellent resource for understanding algorithm implementations through practical code examples.
PCA algorithm for feature extraction in facial recognition, which is the most widely used traditional facial recognition technique. This method achieves dimensionality reduction by constructing feature subspaces through eigenvalue decomposition of covariance matrices.
MATLAB implementation for face image dimensionality reduction with PCA followed by neural network classifier training
JADE Dimensionality Reduction Technique with Algorithm and Implementation Insights
An improved piecewise linear representation approach incorporating four fundamental algorithms: top-down, bottom-up, sliding window, and hybrid sliding window bottom-up techniques. This widely-used dimensionality reduction and classification algorithm features continuous segment generation, overcoming limitations of discrete linear approximations through optimized implementation strategies.
Principal Component Analysis (PCA) is a dimensionality reduction technique based on the Karhunen-Loève (K-L) transform. The PCA algorithm identifies an optimal linear transformation matrix W according to specific performance criteria, enabling effective reduction of high-dimensional data while preserving maximum variance.
Dimensionality reduction using PCA algorithm to extract principal eigenvalues and reduce data dimensions, with MATLAB code implementation details.
KPCA is primarily applied for image denoising, with additional capabilities for feature extraction and dimensionality reduction in data preprocessing workflows.