Search

In the field of machine learning, it is a key issue to learn and represent similarity. This paper focuses on the problem of learning similarity with a multikernel method. Motivated by geometric intuition and computability, similarity between patterns is proposed to be measured by their included angle in a kernel-induced Hilbert space. Having noticed that the cosine of such an included angle can be represented by a normalized kernel, it can be said that the task of learning similarity is equivalent to learning an appropriate normalized kernel. In addition, an error bound is also established for learning similarity with the multikernel method. Based on this bound, a boosting-style algorithm is developed. The preliminary experiments validate the effectiveness of the algorithm for learning similarity. [ABSTRACT FROM AUTHOR]

The Gaussian process latent variable model (GP-LVM) has been identified to be an effective probabilistic approach for dimensionality reduction because it can obtain a low-dimensional manifold of a data set in an unsupervised fashion. Consequently, the GP-LVM is insufficient for supervised learning tasks (e.g., classification and regression) because it ignores the class label information for dimensionality reduction. In this paper, a supervised GP-LVM is developed for supervised learning tasks, and the maximum a posteriori algorithm is introduced to estimate positions of all samples in the latent variable space. We present experimental evidences suggesting that the supervised GP-LVM is able to use the class label information effectively, and thus, it outperforms the GP-LVM and the discriminative extension of the GP-LVM consistently. The comparison with some supervised classification methods, such as Gaussian process classification and support vector machines, is also given to illustrate the advantage of the proposed method. [ABSTRACT FROM AUTHOR]