论文阅读 [TPAMI-2022] A Self-Consistent-Field Iteration for Orthogonal Canonical Correlation Analysis

论文搜索(studyai.com)

搜索论文: A Self-Consistent-Field Iteration for Orthogonal Canonical Correlation Analysis

搜索论文: http://www.studyai.com/search/whole-site/?q=A+Self-Consistent-Field+Iteration+for+Orthogonal+Canonical+Correlation+Analysis

关键字(Keywords)

Correlation; Feature extraction; Eigenvalues and eigenfunctions; Manifolds; Data visualization; Electronic mail; Optimization methods; Canonical correlation analysis; self-consistent-field iteration; orthogonal multiset canonical correlation analysis

摘要(Abstract)

We propose an efficient algorithm for solving orthogonal canonical correlation analysis (OCCA) in the form of trace-fractional structure and orthogonal linear projections.

我们提出了一种有效的算法，用于以迹分数结构和正交线性投影的形式求解正交典型相关分析（OCCA）。.

Even though orthogonality has been widely used and proved to be a useful criterion for visualization, pattern recognition and feature extraction, existing methods for solving OCCA problem are either numerically unstable by relying on a deflation scheme, or less efficient by directly using generic optimization methods.

尽管正交性已被广泛应用，并被证明是可视化、模式识别和特征提取的一个有用标准，但现有的OCCA问题求解方法要么依靠通缩方案在数值上不稳定，要么直接使用通用优化方法效率较低。.

In this paper, we propose an alternating numerical scheme whose core is the sub-maximization problem in the trace-fractional form with an orthogonality constraint.

本文提出了一种交替数值格式，其核心是带正交约束的迹分数形式的次最大化问题。.

A customized self-consistent-field (SCF) iteration for this sub-maximization problem is devised.

针对这个次最大化问题，设计了一个定制的自洽场（SCF）迭代。.

It is proved that the SCF iteration is globally convergent to a KKT point and that the alternating numerical scheme always converges.

证明了SCF迭代全局收敛于KKT点，交替数值格式始终收敛。.

We further formulate a new trace-fractional maximization problem for orthogonal multiset CCA and propose an efficient algorithm with an either Jacobi-style or Gauss-Seidel-style updating scheme based on the SCF iteration.

我们进一步建立了一个新的正交多集CCA跟踪分数最大化问题，并提出了一种基于SCF迭代的Jacobi或Gauss-Seidel更新方案。.

Extensive experiments are conducted to evaluate the proposed algorithms against existing methods, including real-world applications of multi-label classification and multi-view feature extraction.

我们进行了大量实验，以评估所提出的算法与现有方法的对比，包括多标签分类和多视图特征提取的实际应用。.

Experimental results show that our methods not only perform competitively to or better than the existing methods but also are more efficient…

实验结果表明，我们的方法不仅在性能上优于现有方法，而且效率更高。。.