| Multimodal data fusion is an interesting problem and its applications can be seen in image processing, signal processing and machine learning. In applications where we are given matrix data samples, for instance, adjacency matrices of networks or preference matrices from recommender matrices, it is desirable to extract trends from the data by using low rank representations of the matrices and finding low dimensional representations of the underlying entities.;In this thesis, we shall be focussing our attention on the problem of multimodal data fusion with an interest in eigen value decomposition based algorithms. The contribution of this thesis is to introduce algorithms, that in a principled sense combine the samples to generate inferences about the underlying signal components by leveraging recent results from Random Matrix Theory. The focus of our study would be to understand these algorithms in terms of phase transition boundaries, give sharp asymptotic bounds on the performance. To that end, we discuss data driven algorithms at the data level fusion, OptFuse and feature level fusion OptEigenFuse that give optimal inference about the latent eigen-space.;We will then focus on the planted quasi clique recovery problem and discuss how could multiple independent network samples be used to generate an optimal inference about the clique structure in large networks. We develop an optimal linear fusion rule in such a setting by using ideas from OptFuse and demonstrate the performance of this scheme. We also revisit a popular algorithm for tensor decomposition HOSVD to understand its performance limitations in the missing data setting. |
