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Register a new userA Manifold Proximal Linear Method for Sparse Spectral Clustering with Application to Single-Cell RNA Sequencing Data Analysis
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Spectral clustering is one of the fundamental unsupervised learning methods widely used in data analysis. Sparse spectral clustering (SSC) imposes sparsity to the spectral clustering and it improves the interpretability of the model. This paper considers a widely adopted model for SSC, which can be formulated as an optimization problem over the Stiefel manifold with nonsmooth and nonconvex objective. Such an optimization problem is very challenging to solve. Existing methods usually solve its convex relaxation or need to smooth its nonsmooth part using certain smoothing techniques. In this paper, we propose a manifold proximal linear method (ManPL) that solves the original SSC formulation. We also extend the algorithm to solve the multiple-kernel SSC problems, for which an alternating ManPL algorithm is proposed. Convergence and iteration complexity results of the proposed methods are established. We demonstrate the advantage of our proposed methods over existing methods via the single-cell RNA sequencing data analysis.
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Sparse principal component analysis (PCA) and sparse canonical correlation analysis (CCA) are two essential techniques from high-dimensional statistics and machine learning for analyzing large-scale data. Both problems can be formulated as an optimization problem with nonsmooth objective and nonconvex constraints. Since non-smoothness and nonconvexity bring numerical difficulties, most algorithms suggested in the literature either solve some relaxations or are heuristic and lack convergence guarantees. In this paper, we propose a new alternating manifold proximal gradient method to solve these two high-dimensional problems and provide a unified convergence analysis. Numerical experiment results are reported to demonstrate the advantages of our algorithm.
The recent advances in single-cell technologies have enabled us to profile genomic features at unprecedented resolution and datasets from multiple domains are available, including datasets that profile different types of genomic features and datasets that profile the same type of genomic features across different species. These datasets typically have different powers in identifying the unknown cell types through clustering, and data integration can potentially lead to a better performance of clustering algorithms. In this work, we formulate the problem in an unsupervised transfer learning framework, which utilizes knowledge learned from auxiliary dataset to improve the clustering performance of target dataset. The degree of shared information among the target and auxiliary datasets can vary, and their distributions can also be different. To address these challenges, we propose an elastic coupled co-clustering based transfer learning algorithm, by elastically propagating clustering knowledge obtained from the auxiliary dataset to the target dataset. Implementation on single-cell genomic datasets shows that our algorithm greatly improves clustering performance over the traditional learning algorithms. The source code and data sets are available at https://github.com/cuhklinlab/elasticC3.
According to the National Cancer Institute, there were 9.5 million cancer-related deaths in 2018. A challenge in improving treatment is resistance in genetically unstable cells. The purpose of this study is to evaluate unsupervised machine learning on classifying treatment-resistant phenotypes in heterogeneous tumors through analysis of single cell RNA sequencing(scRNAseq) data with a pipeline and evaluation metrics. scRNAseq quantifies mRNA in cells and characterizes cell phenotypes. One scRNAseq dataset was analyzed (tumor/non-tumor cells of different molecular subtypes and patient identifications). The pipeline consisted of data filtering, dimensionality reduction with Principal Component Analysis, projection with Uniform Manifold Approximation and Projection, clustering with nine approaches (Ward, BIRCH, Gaussian Mixture Model, DBSCAN, Spectral, Affinity Propagation, Agglomerative Clustering, Mean Shift, and K-Means), and evaluation. Seven models divided tumor versus non-tumor cells and molecular subtype while six models classified different patient identification (13 of which were presented in the dataset); K-Means, Ward, and BIRCH often ranked highest with ~80% accuracy on the tumor versus non-tumor task and ~60% for molecular subtype and patient ID. An optimized classification pipeline using K-Means, Ward, and BIRCH models was evaluated to be most effective for further analysis. In clinical research where there is currently no standard protocol for scRNAseq analysis, clusters generated from this pipeline can be used to understand cancer cell behavior and malignant growth, directly affecting the success of treatment.
Given a large data matrix, sparsifying, quantizing, and/or performing other entry-wise nonlinear operations can have numerous benefits, ranging from speeding up iterative algorithms for core numerical linear algebra problems to providing nonlinear filters to design state-of-the-art neural network models. Here, we exploit tools from random matrix theory to make precise statements about how the eigenspectrum of a matrix changes under such nonlinear transformations. In particular, we show that very little change occurs in the informative eigenstructure even under drastic sparsification/quantization, and consequently that very little downstream performance loss occurs with very aggressively sparsified or quantized spectral clustering. We illustrate how these results depend on the nonlinearity, we characterize a phase transition beyond which spectral clustering becomes possible, and we show when such nonlinear transformations can introduce spurious non-informative eigenvectors.
We describe a new library named picasso, which implements a unified framework of pathwise coordinate optimization for a variety of sparse learning problems (e.g., sparse linear regression, sparse logistic regression, sparse Poisson regression and scaled sparse linear regression) combined with efficient active set selection strategies. Besides, the library allows users to choose different sparsity-inducing regularizers, including the convex $ell_1$, nonconvex MCP and SCAD regularizers. The library is coded in C++ and has user-friendly R and Python wrappers. Numerical experiments demonstrate that picasso can scale up to large problems efficiently.
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