Youdong Guo

Youdong Guo, Timothy E. Holy

Non-negative matrix factorization (NMF) is an important tool in signal processing and widely used to separate mixed sources into their components. Algorithms for NMF require that the user choose the number of components in advance, and if the results are unsatisfying one typically needs to start again with a different number of components. To make NMF more interactive and incremental, here we introduce GSVD-NMF, a method that proposes new components based on the generalized singular value decomposition (GSVD) to address discrepancies between the initial under-complete NMF results and the SVD of the original matrix. Simulation and experimental results demonstrate that GSVD-NMF often effectively recovers multiple missing components in under-complete NMF, with the recovered NMF solutions frequently reaching better local optima. The results further show that GSVD-NMF is compatible with various NMF algorithms and that directly augmenting components is more efficient than rerunning NMF from scratch with additional components. By deliberately starting from under-complete NMF, GSVD-NMF has the potential to be a recommended approach for a range of general NMF applications.

Youdong Guo, Timothy E. Holy

Non-negative matrix factorization (NMF) is a key technique for feature extraction and widely used in source separation. However, existing algorithms may converge to poor local minima, or to one of several minima with similar objective value but differing feature parametrizations. Here we show that some of these weaknesses may be mitigated by performing NMF in a higher-dimensional feature space and then iteratively combining components with an analytically-solvable pairwise merge strategy. Experimental results demonstrate our method helps non-ideal NMF solutions escape to better local optima and achieve greater consistency of the solutions. Despite these extra steps, our approach exhibits similar computational performance to established methods by reducing the occurrence of "plateau phenomenon" near saddle points. Moreover, the results also illustrate that our method is compatible with different NMF algorithms. Thus, this can be recommended as a preferred approach for most applications of NMF.

Ran Li, Pan Xiao, Kaushik Dutta et al.

Fluorescence Microcopy Calcium Imaging is a fundamental tool to in-vivo record and analyze large scale neuronal activities simultaneously at a single cell resolution. Automatic and precise detection of behaviorally relevant neuron activity from the recordings is critical to study the mapping of brain activity in organisms. However a perpetual bottleneck to this problem is the manual segmentation which is time and labor intensive and lacks generalizability. To this end, we present a Bayesian Deep Learning Framework to detect neuronal activities in 4D spatio-temporal data obtained by light sheet microscopy. Our approach accounts for the use of temporal information by calculating pixel wise correlation maps and combines it with spatial information given by the mean summary image. The Bayesian framework not only produces probability segmentation maps but also models the uncertainty pertaining to active neuron detection. To evaluate the accuracy of our framework we implemented the test of reproducibility to assert the generalization of the network to detect neuron activity. The network achieved a mean Dice Score of 0.81 relative to the synthetic Ground Truth obtained by Otsu's method and a mean Dice Score of 0.79 between the first and second run for test of reproducibility. Our method successfully deployed can be used for rapid detection of active neuronal activities for behavioural studies.