Diffusion map for clustering fMRI spatial maps extracted by independent component analysis

Functional magnetic resonance imaging (fMRI) produces data about activity inside the brain, from which spatial maps can be extracted by independent component analysis (ICA). In datasets, there are n spatial maps that contain p voxels. The number of voxels is very high compared to the number of analyzed spatial maps. Clustering of the spatial maps is usually based on correlation matrices. This usually works well, although such a similarity matrix inherently can explain only a certain amount of the total variance contained in the high-dimensional data where n is relatively small but p is large. For high-dimensional space, it is reasonable to perform dimensionality reduction before clustering. In this research, we used the recently developed diffusion map for dimensionality reduction in conjunction with spectral clustering. This research revealed that the diffusion map based clustering worked as well as the more traditional methods, and produced more compact clusters when needed.Comment: 6 pages. 8 figures. Copyright (c) 2013 IEEE. Published at 2013 IEEE International Workshop on Machine Learning for Signal Processin

Fast Robust PCA on Graphs

Mining useful clusters from high dimensional data has received significant attention of the computer vision and pattern recognition community in the recent years. Linear and non-linear dimensionality reduction has played an important role to overcome the curse of dimensionality. However, often such methods are accompanied with three different problems: high computational complexity (usually associated with the nuclear norm minimization), non-convexity (for matrix factorization methods) and susceptibility to gross corruptions in the data. In this paper we propose a principal component analysis (PCA) based solution that overcomes these three issues and approximates a low-rank recovery method for high dimensional datasets. We target the low-rank recovery by enforcing two types of graph smoothness assumptions, one on the data samples and the other on the features by designing a convex optimization problem. The resulting algorithm is fast, efficient and scalable for huge datasets with O(nlog(n)) computational complexity in the number of data samples. It is also robust to gross corruptions in the dataset as well as to the model parameters. Clustering experiments on 7 benchmark datasets with different types of corruptions and background separation experiments on 3 video datasets show that our proposed model outperforms 10 state-of-the-art dimensionality reduction models. Our theoretical analysis proves that the proposed model is able to recover approximate low-rank representations with a bounded error for clusterable data

Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs

Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and finite mixture modeling methods, they provide probabilistic or fuzzy dimensionality reductions or domain decompositions for a variety of input data types, including mixture distributions, feature vectors, and graphs or networks. Provable optimal recovery using the algorithm is analytically shown for a nontrivial class of cluster graphs. Heuristic approximations for scalable high-performance implementations are described and empirically tested. Connections to PageRank and community detection in network analysis demonstrate the wide applicability of this approach. The origins of fuzzy spectral methods, beginning with generalized heat or diffusion equations in physics, are reviewed and summarized. Comparisons to other dimensionality reduction and clustering methods for challenging unsupervised machine learning problems are also discussed.Comment: 13 figures, 35 reference

Identification of Cell Types in scRNA-seq Data via Enhanced Local Embedding and Clustering

Identifying specific cell types is a significant step for studying diseases and potentially leading to better diagnosis, drug discovery, and prognosis. High-throughput single-cell RNA-Seq (scRNA-seq) technologies have advanced in recent years, enabling researchers to investigate cells individually and understand their biological mechanisms. Computational techniques such as clustering, which are categorized in the form of unsupervised learning methods, are the most suitable approach in scRNA-seq data analysis when the cell types have not been characterized. These techniques can be used to identify a group of genes that belong to a specific cell type based on their similar gene expression patterns. However, due to the sparsity and high-dimensional nature of scRNA-seq data, classical clustering methods are not efficient. Therefore, the use of non-linear dimensionality reduction techniques to improve clustering results is crucial. We introduce a pipeline to identify representative clusters of different cell types by combining non-linear dimensionality reduction techniques such as modified locally linear embedding (MLLE) and clustering algorithms. We assess the impact of different dimensionality reduction techniques combined with the clustering of thirteen publicly available scRNA-seq datasets of different tissues, sizes, and technologies. We evaluate the intra- and inter-cluster performance based on the Silhouette score before performing a biological assessment. We further performed gene enrichment analysis across biological databases to evaluate the proposed method\u27s performance. As such, our results show that MLLE combined with independent component analysis yields overall the best performance relative to the existing unsupervised methods across different experiments

Unsupervised Adaptation for High-Dimensional with Limited-Sample Data Classification Using Variational Autoencoder

High-dimensional with limited-sample size (HDLSS) datasets exhibit two critical problems: (1) Due to the insufficiently small-sample size, there is a lack of enough samples to build classification models. Classification models with a limited-sample may lead to overfitting and produce erroneous or meaningless results. (2) The 'curse of dimensionality' phenomena is often an obstacle to the use of many methods for solving the high-dimensional with limited-sample size problem and reduces classification accuracy. This study proposes an unsupervised framework for high-dimensional limited-sample size data classification using dimension reduction based on variational autoencoder (VAE). First, the deep learning method variational autoencoder is applied to project high-dimensional data onto lower-dimensional space. Then, clustering is applied to the obtained latent-space of VAE to find the data groups and classify input data. The method is validated by comparing the clustering results with actual labels using purity, rand index, and normalized mutual information. Moreover, to evaluate the proposed model strength, we analyzed 14 datasets from the Arizona State University Digital Repository. Also, an empirical comparison of dimensionality reduction techniques shown to conclude their applicability in the high-dimensional with limited-sample size data settings. Experimental results demonstrate that variational autoencoder can achieve more accuracy than traditional dimensionality reduction techniques in high-dimensional with limited-sample-size data analysis

SCALE method for single-cell ATAC-seq analysis via latent feature extraction.

Single-cell ATAC-seq (scATAC-seq) profiles the chromatin accessibility landscape at single cell level, thus revealing cell-to-cell variability in gene regulation. However, the high dimensionality and sparsity of scATAC-seq data often complicate the analysis. Here, we introduce a method for analyzing scATAC-seq data, called Single-Cell ATAC-seq analysis via Latent feature Extraction (SCALE). SCALE combines a deep generative framework and a probabilistic Gaussian Mixture Model to learn latent features that accurately characterize scATAC-seq data. We validate SCALE on datasets generated on different platforms with different protocols, and having different overall data qualities. SCALE substantially outperforms the other tools in all aspects of scATAC-seq data analysis, including visualization, clustering, and denoising and imputation. Importantly, SCALE also generates interpretable features that directly link to cell populations, and can potentially reveal batch effects in scATAC-seq experiments