Distance metric learning with local multiple kernel embedding

Distance metric learning aims to learn a data-dependent similarity measure, which is widely employed in machine learning. Recently, metric learning algorithms that incorporate multiple kernel learning have shown promising outcomes for classification tasks. However, the multiple kernel learning part of the existing metric learning with multiple kernel just uses a linear combination form of different kernel functions, where each kernel shares the same weight in the entire input space, thus the potential local structure of samples located at different locations in the input space is ignored. To address the aforementioned issues, in this paper, we propose a distance metric learning approach with local multiple kernel embedding (DMLLMK) for small datasets. The weight of each kernel function in DMLLMK is assigned locally, so that there are many different values of weight in each kernel space. This local weight method enables metric learning to capture more information in the data. Our proposed DMLLMK adjusts the kernel weight by using a gating function; moreover, the kernel weight locally depends on the input data. The metric of metric learning and the parameters of the gating function are optimized simultaneously by an alternating learning process. The DMLLMK makes metric learning applicable to small datasets by constructing constraints on the set of similar pairs and dissimilar pairs such that some data are reused, and they produce different constraints on the model. In addition, regularization techniques are used to keep DMLLMK more conservative and prevent overfitting on small data. The experimental results of our proposed method when compared with other metric learning methods on the benchmark dataset show that our proposed DMLLMK is effective.