Informative Data Fusion: Beyond Canonical Correlation Analysis

Multi-modal data fusion is a challenging but common problem arising in fields such as economics, statistical signal processing, medical imaging, and machine learning. In such applications, we have access to multiple datasets that use different data modalities to describe some system feature. Canonical correlation analysis (CCA) is a multidimensional joint dimensionality reduction algorithm for exactly two datasets. CCA finds a linear transformation for each feature vector set such that the correlation between the two transformed feature sets is maximized. These linear transformations are easily found by solving the SVD of a matrix that only involves the covariance and cross-covariance matrices of the feature vector sets. When these covariance matrices are unknown, an empirical version of CCA substitutes sample covariance estimates formed from training data. However, when the number of training samples is less than the combined dimension of the datasets, CCA fails to reliably detect correlation between the datasets. This thesis explores the the problem of detecting correlations from data modeled by the ubiquitous signal-plus noise data model. We present a modification to CCA, which we call informative CCA (ICCA) that first projects each dataset onto a low-dimensional informative signal subspace. We verify the superior performance of ICCA on real-world datasets and argue the optimality of trim-then-fuse over fuse-then-trim correlation analysis strategies. We provide a significance test for the correlations returned by ICCA and derive improved estimates of the population canonical vectors using insights from random matrix theory. We then extend the analysis of CCA to regularized CCA (RCCA) and demonstrate that setting the regularization parameter to infinity results in the best performance and has the same solution as taking the SVD of the cross-covariance matrix of the two datasets. Finally, we apply the ideas learned from ICCA to multiset CCA (MCCA), which analyzes correlations for more than two datasets. There are multiple formulations of multiset CCA (MCCA), each using a different combination of objective function and constraint function to describe a notion of multiset correlation. We consider MAXVAR, provide an informative version of the algorithm, which we call informative MCCA (IMCCA), and demonstrate its superiority on a real-world dataset.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113419/1/asendorf_1.pd

Exercise-Induced Changes of Multimodal Interactions Within the Autonomic Nervous Network

Physical exercise has been shown to modulate activity within the autonomic nervous system (ANS). Considering physical exercise as a holistic stimulus on the nervous system and specifically the ANS, uni- and multimodal analysis tools were applied to characterize centrally driven interactions and control of ANS functions. Nineteen young and physically active participants performed treadmill tests at individually determined moderate and high intensities. Continuous electrodermal activity (EDA), heart rate (HR), and skin temperature at wrist (Temp) were recorded by wireless multisensor devices (Empatica® E4, Milan, Italy) before and 30 min after exercise. Artifact-free continuous 3 min intervals were analyzed. For unimodal analysis, mean values were calculated, for bimodal and multimodal analysis canonical correlation analysis (CCA) was performed. Unimodal results indicate that physical exercise affects ANS activity. More specifically, Temp increased due to physical activity (moderate intensity: from 34.15°C to 35.34°C and high intensity: from 34.11°C to 35.09°C). HR increased more for the high (from 60.76 bpm to 79.89 bpm) than for the moderate (from 64.81 bpm to 70.83 bpm) intensity. EDA was higher for the high (pre: 8.06 μS and post: 9.37 μS) than for the moderate (pre: 4.31 μS and post: 3.91 μS) intensity. Bimodal analyses revealed high variations in correlations before exercise. The overall correlation coefficient showed varying correlations in pretest measures for all modality pairs (EDA-HR, HR-Temp, Temp-EDA at moderate: 0.831, 0.998, 0.921 and high: 0.706, 0, 0.578). After exercising at moderate intensity coefficients changed little (0.828, 0.744, 0.994), but increased substantially for all modality pairs after exercising at high intensity (0.976, 0.898, 0.926). Multimodal analysis confirmed bimodal results. Exercise-induced changes in ANS activity can be found in multiple ANS modalities as well as in their interactions. Those changes are intensity-specific: with higher intensity the interactions increase. Canonical correlations between different ANS modalities may therefore offer a feasible approach to determine exercise induced modulations of ANS activity

Quadratic maximization under combinatorial constraints and related applications

Motivated primarily by restricted variants of Principal Component Analysis (PCA), we study quadratic maximization problems subject to sparsity, nonnegativity and other combinatorial constraints. Intuitively, a key technical challenge is determining the support of the optimal solution. We develop a method that can surprisingly solve the maximization exactly when the argument matrix of the quadratic objective is positive semidefinite and has constant rank. Our approach relies on a hyper-spherical transformation of the low-rank space and has complexity that scales exponentially in the rank of the input, but polynomially in the ambient dimension. Extending these observations, we describe a simpler {approximation} algorithm based on exploring the low-rank space with an [epsilon]-net, drastically improving the dependence on the ambient dimension, implying a Polynomial Time Approximation Scheme (PTAS) for inputs with rank scaling up to logarithmically in the dimension or sufficiently sharp spectral decay. We discuss extensions of our approach to jointly computing multiple principal components under combinatorial constraints, such as the problem of extracting multiple orthogonal nonnegative components, or sparse components with common or disjoint supports, and related approximate matrix factorization problems. We further extend our quadratic maximization framework to bilinear optimization problems and employ it in the context of specific applications, e.g., to develop a provable approximation algorithm for the NP-hard problem of Bipartite Correlation Clustering (BCC). Real datasets will typically produce covariance matrices that have full rank, rendering our algorithms not applicable. Our approach is to first obtain a low-rank approximation of the input data and subsequently solve the low-rank problem using our framework. Although this approach is not always suitable, from an optimization perspective it yields provable, data-dependent performance bounds that rely on the spectral decay of the input and the employed approximation technique. Interestingly, most real matrices can be well approximated by low-rank surrogates since the eigenvalues display a significant decay. Empirical evaluation shows that our algorithms have excellent performance and in many cases outperform the previous state of the art. Finally, utilizing our framework, we develop algorithms with interesting theoretical guarantees in the context of specific applications, such as approximate Orthogonal Nonnegative Matrix Factorization or Bipartite Correlation Clustering.Electrical and Computer Engineerin

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum

Neuroinformatics in Functional Neuroimaging

This Ph.D. thesis proposes methods for information retrieval in functional neuroimaging through automatic computerized authority identification, and searching and cleaning in a neuroscience database. Authorities are found through cocitation analysis of the citation pattern among scientific articles. Based on data from a single scientific journal it is shown that multivariate analyses are able to determine group structure that is interpretable as particular “known ” subgroups in functional neuroimaging. Methods for text analysis are suggested that use a combination of content and links, in the form of the terms in scientific documents and scientific citations, respectively. These included context sensitive author ranking and automatic labeling of axes and groups in connection with multivariate analyses of link data. Talairach foci from the BrainMap ™ database are modeled with conditional probability density models useful for exploratory functional volumes modeling. A further application is shown with conditional outlier detection where abnormal entries in the BrainMap ™ database are spotted using kernel density modeling and the redundancy between anatomical labels and spatial Talairach coordinates. This represents a combination of simple term and spatial modeling. The specific outliers that were found in the BrainMap ™ database constituted among others: Entry errors, errors in the article and unusual terminology

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum