Multiple Kernel Geometric Mean Metric Learning for Heterogeneous Data

How to choose a proper distance metric is vital to many machine learning and pattern recognition tasks. Metric learning mainly uses discriminant information to learn a Mahalanobis distance or similarity metric. However, most existing metric learning methods are for numerical data, and it is unreasonable to calculate the similarity between two heterogeneous objects (e.g., categorical data) using traditional distance metrics. Besides, they suffer from curse of dimensionality, resulting in poor efficiency and scalability when the feature dimension is very high. In this paper, a geometric mean metric learning method is proposed for heterogeneous data. The numerical data and categorical data are mapped to a reproducing kernel Hilbert space by using different kernel functions, thus avoiding the negative influence of the high dimensionality of the feature. At the same time, a multiple kernel metric learning model based on geometric mean is introduced to transform the metric learning problem of heterogeneous data into solving the midpoint between two points on the Riemannian manifold. Experiments on benchmark UCI datasets show that the presented method shows promising performances in terms of accuracy in comparison with the state-of-the-art metric learning methods.