Quasi Cosine Similarity Metric Learning

Abstract

It is vital to select an appropriate distance metric for many learning algorithm. Cosine distance is an efficient metric for measuring the similarity of descriptors in classification task. However, the cosine similarity metric learning (CSML) [3] is not widely used due to the complexity of its formulation and time consuming. In this paper, a Quasi Cosine Similarity Metric Learning (QCSML) is proposed to make it easy. The normalization and Lagrange multipliers are employed to convert cosine distance into simple formulation, which is convex and its derivation is easy to calculate. The complexity of the QCSML algorithm is O($t\times p\times d$) (The parameters $t$, $p$, $d$ represent the number of iterations, the dimensionality of descriptors and the compressed features.), while the complexity of CSML is O($r\times b\times g\times s\times d\times m$) (From the paper [3], $r$ is the number of iterations used to optimize the projection matrix, $b$ is the number of values tested in cross validation process, $g$ is the number of steps in the Conjugate Gradient method, $s$ is the number of training data, $d$ and $m$ are the dimensions of projection matrix.). The experimental results of our method on UCI datasets for classification task and LFW dataset for face verification problem are better than the state-of-the-art methods. For classification task, the proposed approach is employed on Iris, Ionosphere and Wine dataset and the classification accuracy and the time consuming are much better than the compared methods. Moreover, our approach obtains $92.33\,\%$ accuracy for face verification on unrestricted setting of LFW dataset, which outperforms the state-of-the-art algorithms.