多集典型相关分析松弛方法的比较及应用
A Comparison of Relaxations of Multiset Cannonical Correlation Analysis and Applications
摘要：
典型相关分析是一种统计技术，用于发现两组变量之间的关系。模式分析中的一个重要扩展是考虑两组以上的变量。这个问题可以表示为二次约束二次规划（QCQP），通常称为多集典型相关分析（MCCA）。这是一个非凸问题，因此贪心算法收敛到局部最优，而不能保证全局最优。在本文中，我们表明，尽管是高度结构化的，找到最佳的解决方案是NP-Hard。这促使我们放松的QCQP的半定规划（SDP）。SDP是凸的，可以合理有效地求解，并且具有绝对和输出敏感的近似质量。除了理论上的保证，我们做了广泛的比较QCQP方法和SDP松弛的各种合成和真实世界的数据。最后，我们提出了两个有用的扩展：我们将核方法和计算多组典型向量。
英文摘要：
Canonical correlation analysis is a statistical technique that is used to find relations between two sets of variables. An important extension in pattern analysis is to consider more than two sets of variables. This problem can be expressed as a quadratically constrained quadratic program (QCQP), commonly referred to Multi-set Canonical Correlation Analysis (MCCA). This is a non-convex problem and so greedy algorithms converge to local optima without any guarantees on global optimality. In this paper, we show that despite being highly structured, finding the optimal solution is NP-Hard. This motivates our relaxation of the QCQP to a semidefinite program (SDP). The SDP is convex, can be solved reasonably efficiently and comes with both absolute and output-sensitive approximation quality. In addition to theoretical guarantees, we do an extensive comparison of the QCQP method and the SDP relaxation on a variety of synthetic and real world data. Finally, we present two useful extensions: we incorporate kernel methods and computing multiple sets of canonical vectors.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
