In this paper, we develop structure assisted nonnegative matrix factorization
(NMF) methods for blind source separation of degenerate data. The motivation
originates from nuclear magnetic resonance (NMR) spectroscopy, where a multiple mixture NMR spectra are recorded to identify chemical compounds with similar
structures. Consider the linear mixing model (LMM), we aim to identify the chemical compounds involved when the mixing process is known to be nearly singular. We first consider a class of data with dominant interval(s) (DI) where each of
source signals has dominant peaks over others. Besides, a nearly singular mixing process produces degenerate mixtures. The DI condition implies clustering
structures in the data points. Hence, the estimation of the mixing matrix could be
achieved by data clustering. Due to the presence of the noise and the degeneracy
of the data, a small deviation in the estimation may introduce errors in the output.
To resolve this problem and improve robustness of the separation, methods are
developed in two aspects. One is to find better estimation of the mixing matrix by
allowing a constrained perturbation to the clustering output, and it can be achieved
by a quadratic programming. The other is to seek sparse source signals by exploiting the DI condition, and it solves an 1 optimization. If no source information is
available, we propose to adopt the nonnegative matrix factorization approach by
incorporating the matrix structure (parallel columns of the mixing matrix) into the
cost function and develop multiplicative iteration rules for the numerical solutions.
We present experimental results of NMR data to show the performance and reliability of the method in the applications arising in NMR spectroscopy.
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Efficient and accurate extraction of in vivo calcium signals from microendoscopic video data
In vivo calcium imaging through microendoscopic lenses enables imaging of previously inaccessible neuronal populations deep within the brains of freely moving animals. However, it is computationally challenging to extract single-neuronal activity from microendoscopic data, because of the very large background fluctuations and high spatial overlaps intrinsic to this recording modality. Here, we describe a new constrained matrix factorization approach to accurately separate the background and then demix and denoise the neuronal signals of interest. We compared the proposed method against previous independent components analysis and constrained nonnegative matrix factorization approaches. On both simulated and experimental data recorded from mice, our method substantially improved the quality of extracted cellular signals and detected more well-isolated neural signals, especially in noisy data regimes. These advances can in turn significantly enhance the statistical power of downstream analyses, and ultimately improve scientific conclusions derived from microendoscopic data.
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- Award ID(s):
- 1707398
- NSF-PAR ID:
- 10061810
- Date Published:
- Journal Name:
- eLife
- Volume:
- 7
- ISSN:
- 2050-084X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Fluorescence microscopy and genetically encoded calcium indicators help understand brain function by recording large-scale
in vivo videos in assorted animal models. Extracting the fluorescent transients that represent active periods of individual neurons is a key step when analyzing imaging videos. Non-specific calcium sources and background adjacent to segmented neurons contaminate the neurons’ temporal traces with false transients. We developed and characterized a novel method, temporal unmixing of calcium traces (TUnCaT), to quickly and accurately unmix the calcium signals of neighboring neurons and background. Our algorithm used background subtraction to remove the false transients caused by background fluctuations, and then applied targeted non-negative matrix factorization to remove the false transients caused by neighboring calcium sources. TUnCaT was more accurate than existing algorithms when processing multiple experimental and simulated datasets. TUnCaT’s speed was faster than or comparable to existing algorithms. -
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Abstract Automated experimentation has yielded data acquisition rates that supersede human processing capabilities. Artificial Intelligence offers new possibilities for automating data interpretation to generate large, high-quality datasets. Background subtraction is a long-standing challenge, particularly in settings where multiple sources of the background signal coexist, and automatic extraction of signals of interest from measured signals accelerates data interpretation. Herein, we present an unsupervised probabilistic learning approach that analyzes large data collections to identify multiple background sources and establish the probability that any given data point contains a signal of interest. The approach is demonstrated on X-ray diffraction and Raman spectroscopy data and is suitable to any type of data where the signal of interest is a positive addition to the background signals. While the model can incorporate prior knowledge, it does not require knowledge of the signals since the shapes of the background signals, the noise levels, and the signal of interest are simultaneously learned via a probabilistic matrix factorization framework. Automated identification of interpretable signals by unsupervised probabilistic learning avoids the injection of human bias and expedites signal extraction in large datasets, a transformative capability with many applications in the physical sciences and beyond.
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Techniques of matrix completion aim to impute a large portion of missing entries in a data matrix through a small portion of observed ones. In practice, prior information and special structures are usually employed in order to improve the accuracy of matrix completion. In this paper, we propose a unified nonconvex optimization framework for matrix completion with linearly parameterized factors. In particular, by introducing a condition referred to as Correlated Parametric Factorization, we conduct a unified geometric analysis for the nonconvex objective by establishing uniform upper bounds for low-rank estimation resulting from any local minimizer. Perhaps surprisingly, the condition of Correlated Parametric Factorization holds for important examples including subspace-constrained matrix completion and skew-symmetric matrix completion. The effectiveness of our unified nonconvex optimization method is also empirically illustrated by extensive numerical simulations.more » « less
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Anandkumar Animashree (Ed.)Techniques of matrix completion aim to impute a large portion of missing entries in a data matrix through a small portion of observed ones. In practice, prior information and special structures are usually employed in order to improve the accuracy of matrix completion. In this paper, we propose a unified nonconvex optimization framework for matrix completion with linearly parameterized factors. In particular, by introducing a condition referred to as Correlated Parametric Factorization, we conduct a unified geometric analysis for the nonconvex objective by establishing uniform upper bounds for low-rank estimation resulting from any local minimizer. Perhaps surprisingly, the condition of Correlated Parametric Factorization holds for important examples including subspace-constrained matrix completion and skew-symmetric matrix completion. The effectiveness of our unified nonconvex optimization method is also empirically illustrated by extensive numerical simulations.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.7554/eLife.28728
