Flexible Multi-layer Sparse Approximations of Matrices and Applications

The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the complexity of applying linear operators in high dimension by approximately factorizing the corresponding matrix into few sparse factors. The approach relies on recent advances in non-convex optimization. It is first explained and analyzed in details and then demonstrated experimentally on various problems including dictionary learning for image denoising, and the approximation of large matrices arising in inverse problems

Decoding the Encoding of Functional Brain Networks: an fMRI Classification Comparison of Non-negative Matrix Factorization (NMF), Independent Component Analysis (ICA), and Sparse Coding Algorithms

Brain networks in fMRI are typically identified using spatial independent component analysis (ICA), yet mathematical constraints such as sparse coding and positivity both provide alternate biologically-plausible frameworks for generating brain networks. Non-negative Matrix Factorization (NMF) would suppress negative BOLD signal by enforcing positivity. Spatial sparse coding algorithms ($L1$ Regularized Learning and K-SVD) would impose local specialization and a discouragement of multitasking, where the total observed activity in a single voxel originates from a restricted number of possible brain networks. The assumptions of independence, positivity, and sparsity to encode task-related brain networks are compared; the resulting brain networks for different constraints are used as basis functions to encode the observed functional activity at a given time point. These encodings are decoded using machine learning to compare both the algorithms and their assumptions, using the time series weights to predict whether a subject is viewing a video, listening to an audio cue, or at rest, in 304 fMRI scans from 51 subjects. For classifying cognitive activity, the sparse coding algorithm of $L1$ Regularized Learning consistently outperformed 4 variations of ICA across different numbers of networks and noise levels (p$<$0.001). The NMF algorithms, which suppressed negative BOLD signal, had the poorest accuracy. Within each algorithm, encodings using sparser spatial networks (containing more zero-valued voxels) had higher classification accuracy (p$<$0.001). The success of sparse coding algorithms may suggest that algorithms which enforce sparse coding, discourage multitasking, and promote local specialization may capture better the underlying source processes than those which allow inexhaustible local processes such as ICA

Machine Learning and Integrative Analysis of Biomedical Big Data.

Recent developments in high-throughput technologies have accelerated the accumulation of massive amounts of omics data from multiple sources: genome, epigenome, transcriptome, proteome, metabolome, etc. Traditionally, data from each source (e.g., genome) is analyzed in isolation using statistical and machine learning (ML) methods. Integrative analysis of multi-omics and clinical data is key to new biomedical discoveries and advancements in precision medicine. However, data integration poses new computational challenges as well as exacerbates the ones associated with single-omics studies. Specialized computational approaches are required to effectively and efficiently perform integrative analysis of biomedical data acquired from diverse modalities. In this review, we discuss state-of-the-art ML-based approaches for tackling five specific computational challenges associated with integrative analysis: curse of dimensionality, data heterogeneity, missing data, class imbalance and scalability issues