Multiple kernel learning using composite kernel functions

Abstract

Multiple Kernel Learning (MKL) algorithms deals with learning the optimal kernel from training data along with learning the function that generates the data. Generally in MKL, the optimal kernel is defined as a combination of kernels under consideration (base kernels). In this paper, we formulated MKL using composite kernel functions (MKLCKF), in which the optimal kernel is represented as the linear combination of composite kernel functions. Corresponding to each data point a composite kernel function is designed whose domain is constructed as the direct product of the range space of base kernels, so that the composite kernels make use of the information of all the base kernels for finding their image. Thus MKLCKF has three layers in which the first layer consists of base kernels, the second layer consists of composite kernels and third layer is the optimal kernel which is a linear combination of the composite kernels. For making the algorithm more computationally effective, we formulated one more variation of the algorithm in which the coefficients of the linear combination are replaced with a similarity function that captures the local properties of the input data. We applied the proposed approach on a number of artificial intelligence applications and compared its performance with that of the other state-of-the-art techniques. Data compression techniques had been used for applying the models on large data, that is, for large scale classification, dictionary learning while for large scale regression pre-clustering approach had been applied. On the basis of the performance, rank was assigned to each model we used for analysis, The proposed models scored higher rank than the other models we used for comparison. We analyzed the performance of the MKLCKF model by incorporating with kernelized locally sensitive hashing (KLSH) also and the results were found to be promising.