Optimal Low Rank Factor Analysis for Multimodal Fusion
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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 talk, we shall be focussing our attention on the problem of multimodal data fusion with an interest in deriving associative structures from low rank factor analysis based on classical eigenvalue decomposition based algorithms. To that end, we introduce data driven algorithms: OptFuse, for optimal data level fusion and OptEigenFuse, for optimal feature level fusion, understand the performance of these algorithms in terms of phase transition boundaries and give sharp asymptotic bounds on their performance, by leveraging recent results from Random Matrix Theory. Throughout our study, we verify our theoretical predictions through numerical simulations.