Single-cell data clustering based on sparse optimization and low-rank matrix factorization.
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ABSTRACT:
SUBMITTER: Hu Y
PROVIDER: S-EPMC8495739 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:BackgroundMatrix factorization methods are linear models, with limited capability to model complex relations. In our work, we use tropical semiring to introduce non-linearity into matrix factorization models. We propose a method called Sparse Tropical Matrix Factorization (STMF) for the estimation of missing (unknown) values in sparse data.ResultsWe evaluate the efficiency of the STMF method on both synthetic data and biological data in the form of gene expression measurements downloaded from The Cancer Genome Atlas (TCGA) database. Tests on unique synthetic data showed that STMF approximation achieves a higher correlation than non-negative matrix factorization (NMF), which is unable to recover patterns effectively. On real data, STMF outperforms NMF on six out of nine gene expression datasets. While NMF assumes normal distribution and tends toward the mean value, STMF can better fit to extreme values and distributions.ConclusionSTMF is the first work that uses tropical semiring on sparse data. We show that in certain cases semirings are useful because they consider the structure, which is different and simpler to understand than it is with standard linear algebra.
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Project description:Integrative analyses of high-throughput 'omic data, such as DNA methylation, DNA copy number alteration, mRNA and protein expression levels, have created unprecedented opportunities to understand the molecular basis of human disease. In particular, integrative analyses have been the cornerstone in the study of cancer to determine molecular subtypes within a given cancer. As malignant tumors with similar morphological characteristics have been shown to exhibit entirely different molecular profiles, there has been significant interest in using multiple 'omic data for the identification of novel molecular subtypes of disease, which could impact treatment decisions. Therefore, we have developed intNMF, an integrative approach for disease subtype classification based on non-negative matrix factorization. The proposed approach carries out integrative clustering of multiple high dimensional molecular data in a single comprehensive analysis utilizing the information across multiple biological levels assessed on the same individual. As intNMF does not assume any distributional form for the data, it has obvious advantages over other model based clustering methods which require specific distributional assumptions. Application of intNMF is illustrated using both simulated and real data from The Cancer Genome Atlas (TCGA).
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Project description:Due to occlusion or detached markers, information can often be lost while capturing human motion with optical tracking systems. Based on three natural properties of human gait movement, this study presents two different approaches to recover corrupted motion data. These properties are used to define a reconstruction model combining low-rank matrix completion of the measured data with a group-sparsity prior on the marker trajectories mapped in the frequency domain. Unlike most existing approaches, the proposed methodology is fully unsupervised and does not need training data or kinematic information of the user. We evaluated our methods on four different gait datasets with various gap lengths and compared their performance with a state-of-the-art approach using principal component analysis (PCA). Our results showed recovering missing data more precisely, with a reduction of at least 2 mm in mean reconstruction error compared to the literature method. When a small number of marker trajectories is available, our findings showed a reduction of more than 14 mm for the mean reconstruction error compared to the literature approach.
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Project description:Parsimony, including sparsity and low-rank, has shown great importance for data mining in social networks, particularly in tasks such as segmentation and recognition. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an objective function with convex l₁-norm or nuclear norm constraints. However, the obtained results by convex optimization are usually suboptimal to solutions of original sparse or low-rank problems. In this paper, a novel robust subspace segmentation algorithm has been proposed by integrating lp-norm and Schatten p-norm constraints. Our so-obtained affinity graph can better capture local geometrical structure and the global information of the data. As a consequence, our algorithm is more generative, discriminative and robust. An efficient linearized alternating direction method is derived to realize our model. Extensive segmentation experiments are conducted on public datasets. The proposed algorithm is revealed to be more effective and robust compared to five existing algorithms.
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Project description:BackgroundBayesian factorization methods, including Coordinated Gene Activity in Pattern Sets (CoGAPS), are emerging as powerful analysis tools for single cell data. However, these methods have greater computational costs than their gradient-based counterparts. These costs are often prohibitive for analysis of large single-cell datasets. Many such methods can be run in parallel which enables this limitation to be overcome by running on more powerful hardware. However, the constraints imposed by the prior distributions in CoGAPS limit the applicability of parallelization methods to enhance computational efficiency for single-cell analysis.ResultsWe developed a new software framework for parallel matrix factorization in Version 3 of the CoGAPS R/Bioconductor package to overcome the computational limitations of Bayesian matrix factorization for single cell data analysis. This parallelization framework provides asynchronous updates for sequential updating steps of the algorithm to enhance computational efficiency. These algorithmic advances were coupled with new software architecture and sparse data structures to reduce the memory overhead for single-cell data.ConclusionsAltogether our new software enhance the efficiency of the CoGAPS Bayesian matrix factorization algorithm so that it can analyze 1000 times more cells, enabling factorization of large single-cell data sets.
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