基于矩阵正态分布似然比测试的矩阵度量学习算法

Matrix metric learning algorithm based on likelihood ratio test with matrix normal distribution

本研究基于KISS(keep it simple and stupid)算法,利用似然比测试直接为矩阵模式定义度量,解决了现有大多数度量学习算法需要经过复杂优化过程的问题。通过在似然比测试中有目的地引入矩阵正态分布,该度量无需将矩阵模式通过向量化的方法变成向量模式,因而具有如下优点:(1)能够避免维数灾难;(2)比KISS更鲁棒;(3)无需计算大矩阵的逆和特征值分解,因此计算远快于KISS算法。最终的实验验证了该算法的优势。

Most metric learning algorithms involve tedious optimization procedure. In order to solve this problem, a metric for matrix data by using likelihood ratio test was defined based on the KISS algorithm （ keep it simple and stu- pid）. By introducing the matrix normal distribution into the likelihood ratio test, the proposed metric does not need to transform matrix pattern into vector pattern. The results showed that this algorithm could avoid the curse of dimension, could be more robust than KISS, and would not need to compute the inverse and eigen-decomposition of high dimen- sional matrix, which was faster than KISS. Experiments verified the advantages of the proposed algorithm.