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 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 Building Recognition on Subregion’s Multiscale Gist Feature Extraction and Corresponding Columns Information Based Dimensionality Reduction

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Bin Li ◽  
Wei Pang ◽  
Yuhao Liu ◽  
Xiangchun Yu ◽  
Anan Du ◽  
...  
Keyword(s):  
Dimensionality Reduction ◽  
Dimensional Subspace ◽  
Dimensional Manifold ◽  
Feature Maps ◽  
High Dimensions ◽  
Recognition Method ◽  
Second Stage ◽  
Building Recognition ◽  
Reduction Methods ◽  
Low Dimensional

In this paper, we proposed a new building recognition method named subregion’s multiscale gist feature (SM-gist) extraction and corresponding columns information based dimensionality reduction (CCI-DR). Our proposed building recognition method is presented as a two-stage model: in the first stage, a building image is divided into 4 × 5 subregions, and gist vectors are extracted from these regions individually. Then, we combine these gist vectors into a matrix with relatively high dimensions. In the second stage, we proposed CCI-DR to project the high dimensional manifold matrix to low dimensional subspace. Compared with the previous building recognition method the advantages of our proposed method are that (1) gist features extracted by SM-gist have the ability to adapt to nonuniform illumination and that (2) CCI-DR can address the limitation of traditional dimensionality reduction methods, which convert gist matrices into vectors and thus mix the corresponding gist vectors from different feature maps. Our building recognition method is evaluated on the Sheffield buildings database, and experiments show that our method can achieve satisfactory performance.

scholarly journals Multiclass spectral feature scaling method for dimensionality reduction

2020 ◽  
Vol 24 (6) ◽  
pp. 1273-1287
Author(s):  
Momo Matsuda ◽  
Keiichi Morikuni ◽  
Akira Imakura ◽  
Xiucai Ye ◽  
Tetsuya Sakurai
Keyword(s):  
Dimensionality Reduction ◽  
Spectral Clustering ◽  
Dimensional Space ◽  
Spectral Feature ◽  
Matrix Pencil ◽  
Linear Matrix ◽  
Scaling Factors ◽  
Label Information ◽  
Reduction Methods ◽  
Low Dimensional

Irregular features disrupt the desired classification. In this paper, we consider aggressively modifying scales of features in the original space according to the label information to form well-separated clusters in low-dimensional space. The proposed method exploits spectral clustering to derive scaling factors that are used to modify the features. Specifically, we reformulate the Laplacian eigenproblem of the spectral clustering as an eigenproblem of a linear matrix pencil whose eigenvector has the scaling factors. Numerical experiments show that the proposed method outperforms well-established supervised dimensionality reduction methods for toy problems with more samples than features and real-world problems with more features than samples.

scholarly journals Supervised dimensionality reduction for big data

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Joshua T. Vogelstein ◽  
Eric W. Bridgeford ◽  
Minh Tang ◽  
Da Zheng ◽  
Christopher Douville ◽  
...  
Keyword(s):  
Dimensionality Reduction ◽  
Data Science ◽  
Real Data ◽  
Low Rank ◽  
Conditional Moment ◽  
Desktop Computer ◽  
Reduction Techniques ◽  
Reduction Methods ◽  
The Individual ◽  
Low Dimensional

AbstractTo solve key biomedical problems, experimentalists now routinely measure millions or billions of features (dimensions) per sample, with the hope that data science techniques will be able to build accurate data-driven inferences. Because sample sizes are typically orders of magnitude smaller than the dimensionality of these data, valid inferences require finding a low-dimensional representation that preserves the discriminating information (e.g., whether the individual suffers from a particular disease). There is a lack of interpretable supervised dimensionality reduction methods that scale to millions of dimensions with strong statistical theoretical guarantees. We introduce an approach to extending principal components analysis by incorporating class-conditional moment estimates into the low-dimensional projection. The simplest version, Linear Optimal Low-rank projection, incorporates the class-conditional means. We prove, and substantiate with both synthetic and real data benchmarks, that Linear Optimal Low-Rank Projection and its generalizations lead to improved data representations for subsequent classification, while maintaining computational efficiency and scalability. Using multiple brain imaging datasets consisting of more than 150 million features, and several genomics datasets with more than 500,000 features, Linear Optimal Low-Rank Projection outperforms other scalable linear dimensionality reduction techniques in terms of accuracy, while only requiring a few minutes on a standard desktop computer.

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 A theory of multineuronal dimensionality, dynamics and measurement

2017 ◽  
Author(s):  
Peiran Gao ◽  
Eric Trautmann ◽  
Byron Yu ◽  
Gopal Santhanam ◽  
Stephen Ryu ◽  
...  
Keyword(s):  
Experimental Design ◽  
Large Scale ◽  
Task Complexity ◽  
Dimensional Space ◽  
Neural Dynamics ◽  
Firing Rates ◽  
Control Behavior ◽  
Reduction Methods ◽  
Low Dimensional

AbstractIn many experiments, neuroscientists tightly control behavior, record many trials, and obtain trial-averaged firing rates from hundreds of neurons in circuits containing billions of behaviorally relevant neurons. Di-mensionality reduction methods reveal a striking simplicity underlying such multi-neuronal data: they can be reduced to a low-dimensional space, and the resulting neural trajectories in this space yield a remarkably insightful dynamical portrait of circuit computation. This simplicity raises profound and timely conceptual questions. What are its origins and its implications for the complexity of neural dynamics? How would the situation change if we recorded more neurons? When, if at all, can we trust dynamical portraits obtained from measuring an infinitesimal fraction of task relevant neurons? We present a theory that answers these questions, and test it using physiological recordings from reaching monkeys. This theory reveals conceptual insights into how task complexity governs both neural dimensionality and accurate recovery of dynamic portraits, thereby providing quantitative guidelines for future large-scale experimental design.

scholarly journals Electromyography Classification during Reach-to-Grasp Motion using Manifold Learning

2020 ◽  
Author(s):  
Elnaz Lashgari ◽  
Uri Maoz
Keyword(s):  
Dimensionality Reduction ◽  
Cost Effective ◽  
Human Hand ◽  
Reach To Grasp ◽  
K Nearest Neighbors ◽  
Laplacian Eigenmaps ◽  
Non Invasive ◽  
Reduction Methods ◽  
Machine Interface ◽  
Low Dimensional

AbstractElectromyography (EMG) is a simple, non-invasive, and cost-effective technology for sensing muscle activity. However, EMG is also noisy, complex, and high-dimensional. It has nevertheless been widely used in a host of human-machine-interface applications (electrical wheelchairs, virtual computer mice, prosthesis, robotic fingers, etc.) and in particular to measure reaching and grasping motions of the human hand. Here, we developd a more automated pipeline to predict object weight in a reach-and-grasp task from an open dataset relying only on EMG data. In that we shifted the focus from manual feature-engineering to automated feature-extraction by using raw (filtered) EMG signals and thus letting the algorithms select the features. We further compared intrinsic EMG features, derived from several dimensionality-reduction methods, and then ran some classification algorithms on these low-dimensional representations. We found that the Laplacian Eigenmap algorithm generally outperformed other dimensionality-reduction methods. What is more, optimal classification accuracy was achieved using a combination of Laplacian Eigenmaps (simple-minded) and k-Nearest Neighbors (88% for 3-way classification). Our results, using EMG alone, are comparable to others in the literature that used EMG and EEG together. They also demonstrate the usefulness of dimensionality reduction when classifying movement based on EMG signals and more generally the usefulness of EMG for movement classification.

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 A quantitative framework for evaluating single-cell data structure preservation by dimensionality reduction techniques

2019 ◽  
Author(s):  
Cody N. Heiser ◽  
Ken S. Lau
Keyword(s):  
Data Structure ◽  
Dimensionality Reduction ◽  
Single Cell ◽  
Structure Preservation ◽  
Reduction Techniques ◽  
Reduction Methods ◽  
Biological Interpretation ◽  
Low Dimensional ◽  
Genome Scale ◽  
Global And Local

SummaryHigh-dimensional data, such as those generated using single-cell RNA sequencing, present challenges in interpretation and visualization. Numerical and computational methods for dimensionality reduction allow for low-dimensional representation of genome-scale expression data for downstream clustering, trajectory reconstruction, and biological interpretation. However, a comprehensive and quantitative evaluation of the performance of these techniques has not been established. We present an unbiased framework that defines metrics of global and local structure preservation in dimensionality reduction transformations. Using discrete and continuous scRNA-seq datasets, we find that input cell distribution and method parameters are largely determinant of global, local, and organizational data structure preservation by eleven published dimensionality reduction methods. Code available atgithub.com/KenLauLab/DR-structure-preservationallows for rapid evaluation of further datasets and methods.

scholarly journals Low Dimensional Representations along Intrinsic Reaction Coordinates and Molecular Dynamics Trajectories Using Interatomic Distance Matrices

2019 ◽  
Author(s):  
Stephanie Hare ◽  
Lars Bratholm ◽  
David Glowacki ◽  
Barry Carpenter
Keyword(s):  
Molecular Dynamics ◽  
Principal Component Analysis ◽  
Dimensionality Reduction ◽  
Physical Meaning ◽  
Interatomic Distance ◽  
Dimensional Space ◽  
Principal Component ◽  
Reaction Pathways ◽  
Reaction Coordinates ◽  
Low Dimensional

Low dimensional representations along reaction pathways were produced using newly created Python software that utilises Principal Component Analysis (PCA) to do dimensionality reduction. Plots of these pathways in reduced dimensional space, as well as the physical meaning of the reduced dimensional axes, are discussed.

Sign in / Sign up

Export Citation Format

Share Document