# Computational Methods for Neuron Segmentation in Two-Photon Calcium Imaging Data: A Survey
## 5 Matrix Factorization-Based Methods
### Independent Component Analysis-Based Approaches  
Independent component analysis is a computational approach which separates a multivariate signal into additive sub-components. It defines a generative model for the observed multivariate data. The data variables are assumed to be weighted linear combinations of some unknown latent variables. It also assumes that the combination weights for each latent variable are also unknown. The latent variables are assumed to be non-Gaussian and mutually independent. Therefore, the end goal of ICA is to find a new representation of observed data defined by latent variables which are statistically independent of each other. In the context of calcium imaging, the ICA tries to separate the observed fluorescent stack in independent sources which will (hopefully) represent the fluorescence activity of individual neurons. The underlying assumption is that the fluorescence activities of individual neurons are statistically independent. [PERSON] et al. proposed an ICA framework aided by image segmentation to isolate neurons in calcium image data at scale [56]. Individual frames of a calcium imaging stack are first converted into a column vector by rearranging the frame. Then, principal component analysis (PCA) is used to reduce the dimensionality of the image vector which can be of order \(10^{5}\). After PCA, the ICA algorithm is used to extract independent components in the spatio-temporal domain by maximizing the non-Gaussian distribution in the temporal domain. Then the extracted independent components are checked for spatial and temporal sparsity. To increase the independence of found components, the filters for all independent components are first smoothed and then applied to the image data. Local regions with strong response to a filter are thresholded and if one filter results in more than one binarized regions, new filters are created which make sure that one filter results in only one binarized response region. This process verifies that regions with correlated neural activity are disentangled. The performance of the proposed approach was quantified by comparing it to ground truth produced by a human annotator. The authors report an F1 score of 75%. The authors also tested their approach on calcium imaging data acquired from the molecular layer of cerebellar lobules V and VI of anesthetized and awake head-fixed mice. They have not reported comparative performance for this dataset but they did report that the shape of filters extracted by ICA was same as of the Purkinje cells they were targeting. The proposed ICA+image segmentation framework offers an advantage in the form of iterative fine tuning by targeting regions with correlated neural activity but it also carries the inherent weakness of the ICA frameworks, i.e., the ICA framework is built upon the assumption that the signal sources (neurons) are independent, which might not always be the case. It also cannot detect cells that do not spike or differentiate cells that fire synchronously. It also identifies neuronal projections that may not be of interest to the user for network-level analysis. [PERSON] et al. proposed a semi-automated ICA-based neuron segmentation framework for neuronal networks quantification and single cell dynamics analysis in calcium imaging data [57]. Under this framework, initial estimates for neurons' ROI are generated using the ICA framework proposed by [PERSON] et al. [56]. The authors then assume that the generated ROIs might not be a correct approximation of the actual neurons ROIs since they might contain merged ROIs or some ROIs might be missed. Therefore, those ROIs are displayed and the user is then first presented with the option to change the ICA parameters to get a better initial estimate of the ROIs. Then, the user can modify the ROIs, delete the ROIs or manually add more ROIs. The authors have neither provided any quantitative figures for their neuron segmentation framework when compared to manual annotation, nor have they tested the segmentation framework against public benchmarks.