scholarly journals SCDRHA: A scRNA-Seq Data Dimensionality Reduction Algorithm Based on Hierarchical Autoencoder

2021 ◽  
Vol 12 ◽  
Author(s):  
Jianping Zhao ◽  
Na Wang ◽  
Haiyun Wang ◽  
Chunhou Zheng ◽  
Yansen Su
Keyword(s):  
Dimensionality Reduction ◽  
Data Visualization ◽  
State Of The Art ◽  
Dimensional Space ◽  
High Dimensional ◽  
Reduction Algorithm ◽  
Cell Clustering ◽  
Data Dimensionality Reduction ◽  
Single Cell Rna Sequencing ◽  
Low Dimensional

Dimensionality reduction of high-dimensional data is crucial for single-cell RNA sequencing (scRNA-seq) visualization and clustering. One prominent challenge in scRNA-seq studies comes from the dropout events, which lead to zero-inflated data. To address this issue, in this paper, we propose a scRNA-seq data dimensionality reduction algorithm based on a hierarchical autoencoder, termed SCDRHA. The proposed SCDRHA consists of two core modules, where the first module is a deep count autoencoder (DCA) that is used to denoise data, and the second module is a graph autoencoder that projects the data into a low-dimensional space. Experimental results demonstrate that SCDRHA has better performance than existing state-of-the-art algorithms on dimension reduction and noise reduction in five real scRNA-seq datasets. Besides, SCDRHA can also dramatically improve the performance of data visualization and cell clustering.

scholarly journals Unsupervised Text Feature Learning via Deep Variational Auto-encoder

2020 ◽  
Vol 49 (3) ◽  
pp. 421-437
Author(s):  
Genggeng Liu ◽  
Lin Xie ◽  
Chi-Hua Chen
Keyword(s):  
Dimensionality Reduction ◽  
High Dimensional Data ◽  
Image Data ◽  
Original Data ◽  
Feature Representation ◽  
High Dimensional ◽  
Learning To Learn ◽  
Text Feature ◽  
Reduction Methods ◽  
Low Dimensional

Dimensionality reduction plays an important role in the data processing of machine learning and data mining, which makes the processing of high-dimensional data more efficient. Dimensionality reduction can extract the low-dimensional feature representation of high-dimensional data, and an effective dimensionality reduction method can not only extract most of the useful information of the original data, but also realize the function of removing useless noise. The dimensionality reduction methods can be applied to all types of data, especially image data. Although the supervised learning method has achieved good results in the application of dimensionality reduction, its performance depends on the number of labeled training samples. With the growing of information from internet, marking the data requires more resources and is more difficult. Therefore, using unsupervised learning to learn the feature of data has extremely important research value. In this paper, an unsupervised multilayered variational auto-encoder model is studied in the text data, so that the high-dimensional feature to the low-dimensional feature becomes efficient and the low-dimensional feature can retain mainly information as much as possible. Low-dimensional feature obtained by different dimensionality reduction methods are used to compare with the dimensionality reduction results of variational auto-encoder (VAE), and the method can be significantly improved over other comparison methods.

scholarly journals Season- and Trend-aware Symbolic Approximation for Accurate and Efficient Time Series Matching

2021 ◽  
Author(s):  
Lars Kegel ◽  
Claudio Hartmann ◽  
Maik Thiele ◽  
Wolfgang Lehner
Keyword(s):  
Time Series ◽  
State Of The Art ◽  
Dimensional Space ◽  
Symbolic Aggregate Approximation ◽  
Current State ◽  
Optimal Representation ◽  
Symbolic Approximation ◽  
Low Dimensional ◽  
Deterministic Behavior ◽  
Support Time

AbstractProcessing and analyzing time series datasets have become a central issue in many domains requiring data management systems to support time series as a native data type. A core access primitive of time series is matching, which requires efficient algorithms on-top of appropriate representations like the symbolic aggregate approximation (SAX) representing the current state of the art. This technique reduces a time series to a low-dimensional space by segmenting it and discretizing each segment into a small symbolic alphabet. Unfortunately, SAX ignores the deterministic behavior of time series such as cyclical repeating patterns or a trend component affecting all segments, which may lead to a sub-optimal representation accuracy. We therefore introduce a novel season- and a trend-aware symbolic approximation and demonstrate an improved representation accuracy without increasing the memory footprint. Most importantly, our techniques also enable a more efficient time series matching by providing a match up to three orders of magnitude faster than SAX.

Capturing discrete latent structures: choose LDs over PCs

Biostatistics ◽  
2021 ◽  
Author(s):  
Theresa A Alexander ◽  
Rafael A Irizarry ◽  
Héctor Corrada Bravo
Keyword(s):  
Dimensionality Reduction ◽  
Biological Data ◽  
Reduction Technique ◽  
Latent Structure ◽  
High Dimensional ◽  
Underlying Structure ◽  
Linear Transformations ◽  
Latent Structures ◽  
Low Dimensional ◽  
Discriminatory Information

Summary High-dimensional biological data collection across heterogeneous groups of samples has become increasingly common, creating high demand for dimensionality reduction techniques that capture underlying structure of the data. Discovering low-dimensional embeddings that describe the separation of any underlying discrete latent structure in data is an important motivation for applying these techniques since these latent classes can represent important sources of unwanted variability, such as batch effects, or interesting sources of signal such as unknown cell types. The features that define this discrete latent structure are often hard to identify in high-dimensional data. Principal component analysis (PCA) is one of the most widely used methods as an unsupervised step for dimensionality reduction. This reduction technique finds linear transformations of the data which explain total variance. When the goal is detecting discrete structure, PCA is applied with the assumption that classes will be separated in directions of maximum variance. However, PCA will fail to accurately find discrete latent structure if this assumption does not hold. Visualization techniques, such as t-Distributed Stochastic Neighbor Embedding (t-SNE) and Uniform Manifold Approximation and Projection (UMAP), attempt to mitigate these problems with PCA by creating a low-dimensional space where similar objects are modeled by nearby points in the low-dimensional embedding and dissimilar objects are modeled by distant points with high probability. However, since t-SNE and UMAP are computationally expensive, often a PCA reduction is done before applying them which makes it sensitive to PCAs downfalls. Also, tSNE is limited to only two or three dimensions as a visualization tool, which may not be adequate for retaining discriminatory information. The linear transformations of PCA are preferable to non-linear transformations provided by methods like t-SNE and UMAP for interpretable feature weights. Here, we propose iterative discriminant analysis (iDA), a dimensionality reduction technique designed to mitigate these limitations. iDA produces an embedding that carries discriminatory information which optimally separates latent clusters using linear transformations that permit post hoc analysis to determine features that define these latent structures.

scholarly journals Discovering a sparse set of pairwise discriminating features in high-dimensional data

2020 ◽  
Author(s):  
Samuel Melton ◽  
Sharad Ramanathan
Keyword(s):  
Single Cell ◽  
Dimensional Space ◽  
Cell Types ◽  
Dimensional Subspace ◽  
Supplementary Information ◽  
High Dimensional ◽  
Technological Advances ◽  
Data Points ◽  
Low Dimensional ◽  
Sparse Set

Abstract Motivation Recent technological advances produce a wealth of high-dimensional descriptions of biological processes, yet extracting meaningful insight and mechanistic understanding from these data remains challenging. For example, in developmental biology, the dynamics of differentiation can now be mapped quantitatively using single-cell RNA sequencing, yet it is difficult to infer molecular regulators of developmental transitions. Here, we show that discovering informative features in the data is crucial for statistical analysis as well as making experimental predictions. Results We identify features based on their ability to discriminate between clusters of the data points. We define a class of problems in which linear separability of clusters is hidden in a low-dimensional space. We propose an unsupervised method to identify the subset of features that define a low-dimensional subspace in which clustering can be conducted. This is achieved by averaging over discriminators trained on an ensemble of proposed cluster configurations. We then apply our method to single-cell RNA-seq data from mouse gastrulation, and identify 27 key transcription factors (out of 409 total), 18 of which are known to define cell states through their expression levels. In this inferred subspace, we find clear signatures of known cell types that eluded classification prior to discovery of the correct low-dimensional subspace. Availability and implementation https://github.com/smelton/SMD. Supplementary information Supplementary data are available at Bioinformatics online.

scholarly journals Complex Moment-Based Supervised Eigenmap for Dimensionality Reduction

2019 ◽  
Vol 33 ◽  
pp. 3910-3918 ◽  
Author(s):  
Akira Imakura ◽  
Momo Matsuda ◽  
Xiucai Ye ◽  
Tetsuya Sakurai
Keyword(s):  
Dimensionality Reduction ◽  
Parallel Implementation ◽  
Dimensional Space ◽  
Recognition Performance ◽  
Optimization Methods ◽  
Original Data ◽  
Dimensional Subspace ◽  
Reduction Methods ◽  
Low Dimensional ◽  
Matrix Trace

Dimensionality reduction methods that project highdimensional data to a low-dimensional space by matrix trace optimization are widely used for clustering and classification. The matrix trace optimization problem leads to an eigenvalue problem for a low-dimensional subspace construction, preserving certain properties of the original data. However, most of the existing methods use only a few eigenvectors to construct the low-dimensional space, which may lead to a loss of useful information for achieving successful classification. Herein, to overcome the deficiency of the information loss, we propose a novel complex moment-based supervised eigenmap including multiple eigenvectors for dimensionality reduction. Furthermore, the proposed method provides a general formulation for matrix trace optimization methods to incorporate with ridge regression, which models the linear dependency between covariate variables and univariate labels. To reduce the computational complexity, we also propose an efficient and parallel implementation of the proposed method. Numerical experiments indicate that the proposed method is competitive compared with the existing dimensionality reduction methods for the recognition performance. Additionally, the proposed method exhibits high parallel efficiency.

scholarly journals Subspace Clustering with Sparsity and Grouping Effect

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Binbin Zhang ◽  
Weiwei Wang ◽  
Xiangchu Feng
Keyword(s):  
State Of The Art ◽  
Subspace Clustering ◽  
The Self ◽  
Dimensional Structure ◽  
High Dimensional ◽  
Affinity Matrix ◽  
Grouping Effect ◽  
Art Methods ◽  
Data Points ◽  
Low Dimensional

Subspace clustering aims to group a set of data from a union of subspaces into the subspace from which it was drawn. It has become a popular method for recovering the low-dimensional structure underlying high-dimensional dataset. The state-of-the-art methods construct an affinity matrix based on the self-representation of the dataset and then use a spectral clustering method to obtain the final clustering result. These methods show that sparsity and grouping effect of the affinity matrix are important in recovering the low-dimensional structure. In this work, we propose a weighted sparse penalty and a weighted grouping effect penalty in modeling the self-representation of data points. The experimental results on Extended Yale B, USPS, and Berkeley 500 image segmentation datasets show that the proposed model is more effective than state-of-the-art methods in revealing the subspace structure underlying high-dimensional dataset.

scholarly journals Extracting Low-Dimensional Latent Structure from Time Series in the Presence of Delays

2015 ◽  
Vol 27 (9) ◽  
pp. 1825-1856 ◽  
Author(s):  
Karthik C. Lakshmanan ◽  
Patrick T. Sadtler ◽  
Elizabeth C. Tyler-Kabara ◽  
Aaron P. Batista ◽  
Byron M. Yu
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Motor Cortex ◽  
Dimensionality Reduction ◽  
Gaussian Process ◽  
Latent Variables ◽  
Time Delays ◽  
High Dimensional ◽  
Latent Space ◽  
Low Dimensional

Noisy, high-dimensional time series observations can often be described by a set of low-dimensional latent variables. Commonly used methods to extract these latent variables typically assume instantaneous relationships between the latent and observed variables. In many physical systems, changes in the latent variables manifest as changes in the observed variables after time delays. Techniques that do not account for these delays can recover a larger number of latent variables than are present in the system, thereby making the latent representation more difficult to interpret. In this work, we introduce a novel probabilistic technique, time-delay gaussian-process factor analysis (TD-GPFA), that performs dimensionality reduction in the presence of a different time delay between each pair of latent and observed variables. We demonstrate how using a gaussian process to model the evolution of each latent variable allows us to tractably learn these delays over a continuous domain. Additionally, we show how TD-GPFA combines temporal smoothing and dimensionality reduction into a common probabilistic framework. We present an expectation/conditional maximization either (ECME) algorithm to learn the model parameters. Our simulations demonstrate that when time delays are present, TD-GPFA is able to correctly identify these delays and recover the latent space. We then applied TD-GPFA to the activity of tens of neurons recorded simultaneously in the macaque motor cortex during a reaching task. TD-GPFA is able to better describe the neural activity using a more parsimonious latent space than GPFA, a method that has been used to interpret motor cortex data but does not account for time delays. More broadly, TD-GPFA can help to unravel the mechanisms underlying high-dimensional time series data by taking into account physical delays in the system.

scholarly journals Dimensionality Reduction by Weighted Connections between Neighborhoods

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Fuding Xie ◽  
Yutao Fan ◽  
Ming Zhou
Keyword(s):  
Dimensionality Reduction ◽  
Dimensional Space ◽  
High Dimensional Data ◽  
Reduction Technique ◽  
Experimental Results ◽  
High Dimensional ◽  
Reduced Dimensionality ◽  
Dimensionality Reduction Technique ◽  
Low Dimensionality ◽  
Local Topology

Dimensionality reduction is the transformation of high-dimensional data into a meaningful representation of reduced dimensionality. This paper introduces a dimensionality reduction technique by weighted connections between neighborhoods to improveK-Isomap method, attempting to preserve perfectly the relationships between neighborhoods in the process of dimensionality reduction. The validity of the proposal is tested by three typical examples which are widely employed in the algorithms based on manifold. The experimental results show that the local topology nature of dataset is preserved well while transforming dataset in high-dimensional space into a new dataset in low-dimensionality by the proposed method.

Extracting principal parameters of complex networks

2015 ◽  
Vol 26 (09) ◽  
pp. 1550103
Author(s):  
Yifang Ma ◽  
Zhiming Zheng
Keyword(s):  
Dynamic Systems ◽  
Growth Process ◽  
Dimensional Space ◽  
High Dimensional ◽  
Scale Function ◽  
Control Parameters ◽  
Diffusion Matrix ◽  
Similarity Relations ◽  
Low Dimensional ◽  
Network Ensembles

The evolution of networks or dynamic systems is controlled by many parameters in high-dimensional space, and it is crucial to extract the reduced and dominant ones in low-dimensional space. Here we consider the network ensemble, introduce a matrix resolvent scale function and apply it to a spectral approach to get the similarity relations between each pair of networks. The concept of Diffusion Maps is used to get the principal parameters, and we point out that the reduced dimensional principal parameters are captured by the low order eigenvectors of the diffusion matrix of the network ensemble. We validate our results by using two classical network ensembles and one dynamical network sequence via a cooperative Achlioptas growth process where an abrupt transition of the structures has been captured by our method. Our method provides a potential access to the pursuit of invisible control parameters of complex systems.

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