scholarly journals Metric Multidimensional Scaling for Large Single-Cell Data Sets using Neural Networks

2021 ◽  
Author(s):  
Stefan Canzar ◽  
Van Hoan Do ◽  
Slobodan Jelic ◽  
Soeren Laue ◽  
Domagoj Matijevic ◽  
...  
Keyword(s):  
Multidimensional Scaling ◽  
Single Cell ◽  
State Of The Art ◽  
Dimensional Space ◽  
Linear Mapping ◽  
Alternative Methods ◽  
Dimensional Euclidean Space ◽  
Data Sets ◽  
Metric Multidimensional Scaling ◽  
Low Dimensional

Metric multidimensional scaling is one of the classical methods for embedding data into low-dimensional Euclidean space. It creates the low-dimensional embedding by approximately preserving the pairwise distances between the input points. However, current state-of-the-art approaches only scale to a few thousand data points. For larger data sets such as those occurring in single-cell RNA sequencing experiments, the running time becomes prohibitively large and thus alternative methods such as PCA are widely used instead. Here, we propose a neural network based approach for solving the metric multidimensional scaling problem that is orders of magnitude faster than previous state-of-the-art approaches, and hence scales to data sets with up to a few million cells. At the same time, it provides a non-linear mapping between high- and low-dimensional space that can place previously unseen cells in the same embedding.

scholarly journals Fast Multidimensional Scaling Through Sampling, Springs and Interpolation

2003 ◽  
Vol 2 (1) ◽  
pp. 68-77 ◽  
Author(s):  
Alistair Morrison ◽  
Greg Ross ◽  
Matthew Chalmers
Keyword(s):  
Multidimensional Scaling ◽  
Dimensional Space ◽  
Hybrid Approach ◽  
Real Data ◽  
Visual Exploration ◽  
Data Sets ◽  
Proximity Data ◽  
Stochastic Sampling ◽  
Similarity Relations ◽  
Low Dimensional

The term ‘proximity data’ refers to data sets within which it is possible to assess the similarity of pairs of objects. Multidimensional scaling (MDS) is applied to such data and attempts to map high-dimensional objects onto low-dimensional space through the preservation of these similarity relations. Standard MDS techniques have in the past suffered from high computational complexity and, as such, could not feasibly be applied to data sets over a few thousand objects in size. Through a novel hybrid approach based upon stochastic sampling, interpolation and spring models, we have designed an algorithm running in O( N√N). Using Chalmers’ 1996 O( N2) spring model as a benchmark for the evaluation of our technique, we compare layout quality and run times using sets of synthetic and real data. Our algorithm executes significantly faster than Chalmers’ 1996 algorithm, while producing superior layouts. In reducing complexity and run time, we allow the visualisation of data sets of previously infeasible size. Our results indicate that our method is a solid foundation for interactive and visual exploration of data.

scholarly journals ON MULTIDIMENSIONAL SCALING WITH EUCLIDEAN AND CITY BLOCK METRICS

2006 ◽  
Vol 12 (1) ◽  
pp. 69-75 ◽  
Author(s):  
Antanas Žilinskas ◽  
Julius Žilinskas
Keyword(s):  
Multidimensional Scaling ◽  
Search Algorithm ◽  
Dimensional Space ◽  
Optimization Method ◽  
Data Sets ◽  
Proximity Data ◽  
Information Elicitation ◽  
Evolutionary Metaheuristic ◽  
Unknown Structure ◽  
Low Dimensional

Experimental sciences collect large amounts of data. Different techniques are available for information elicitation from data. Frequently statistical analysis should be combined with the experience and intuition of researchers. Human heuristic abilities are developed and oriented to patterns in space of dimensionality up to 3. Multidimensional scaling (MDS) addresses the problem how objects represented by proximity data can be represented by points in low dimensional space. MDS methods are implemented as the optimization of a stress function measuring fit of the proximity data by the distances between the respective points. Since the optimization problem is multimodal, a global optimization method should be used. In the present paper a combination of an evolutionary metaheuristic algorithm with a local search algorithm is used. The experimental results show the influence of metrics defining distances in the considered spaces on the results of multidimensional scaling. Data sets with known and unknown structure and different dimensionality (up to 512 variables) have been visualized.

scholarly journals Fast and precise single-cell data analysis using a hierarchical autoencoder

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Duc Tran ◽  
Hung Nguyen ◽  
Bang Tran ◽  
Carlo La Vecchia ◽  
Hung N. Luu ◽  
...  
Keyword(s):  
Single Cell ◽  
State Of The Art ◽  
Dimensional Space ◽  
Cell Decomposition ◽  
Excess Noise ◽  
Analysis Framework ◽  
Extensive Analysis ◽  
Low Dimensional ◽  
Cell Segregation ◽  
Cell Data

AbstractA primary challenge in single-cell RNA sequencing (scRNA-seq) studies comes from the massive amount of data and the excess noise level. To address this challenge, we introduce an analysis framework, named single-cell Decomposition using Hierarchical Autoencoder (scDHA), that reliably extracts representative information of each cell. The scDHA pipeline consists of two core modules. The first module is a non-negative kernel autoencoder able to remove genes or components that have insignificant contributions to the part-based representation of the data. The second module is a stacked Bayesian autoencoder that projects the data onto a low-dimensional space (compressed). To diminish the tendency to overfit of neural networks, we repeatedly perturb the compressed space to learn a more generalized representation of the data. In an extensive analysis, we demonstrate that scDHA outperforms state-of-the-art techniques in many research sub-fields of scRNA-seq analysis, including cell segregation through unsupervised learning, visualization of transcriptome landscape, cell classification, and pseudo-time inference.

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.

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.

Learning representations of Web entities for entity resolution

2019 ◽  
Vol 15 (3) ◽  
pp. 346-358
Author(s):  
Luciano Barbosa
Keyword(s):  
Deep Learning ◽  
Dimensional Space ◽  
Entity Resolution ◽  
Data Sets ◽  
Content Type ◽  
Learning Framework ◽  
Document Frequency ◽  
Deep Learning Network ◽  
Low Dimensional ◽  
Vector Representations

Purpose Matching instances of the same entity, a task known as entity resolution, is a key step in the process of data integration. This paper aims to propose a deep learning network that learns different representations of Web entities for entity resolution. Design/methodology/approach To match Web entities, the proposed network learns the following representations of entities: embeddings, which are vector representations of the words in the entities in a low-dimensional space; convolutional vectors from a convolutional layer, which capture short-distance patterns in word sequences in the entities; and bag-of-word vectors, created by a bow layer that learns weights for words in the vocabulary based on the task at hand. Given a pair of entities, the similarity between their learned representations is used as a feature to a binary classifier that identifies a possible match. In addition to those features, the classifier also uses a modification of inverse document frequency for pairs, which identifies discriminative words in pairs of entities. Findings The proposed approach was evaluated in two commercial and two academic entity resolution benchmarking data sets. The results have shown that the proposed strategy outperforms previous approaches in the commercial data sets, which are more challenging, and have similar results to its competitors in the academic data sets. Originality/value No previous work has used a single deep learning framework to learn different representations of Web entities for entity resolution.

scholarly journals Unsupervised Deep Video Hashing with Balanced Rotation

2017 ◽  
Author(s):  
Gengshen Wu ◽  
Li Liu ◽  
Yuchen Guo ◽  
Guiguang Ding ◽  
Jungong Han ◽  
...  
Keyword(s):  
State Of The Art ◽  
Dimensional Space ◽  
Image Hashing ◽  
Neighborhood Structure ◽  
Function Learning ◽  
Video Hashing ◽  
Real World Datasets ◽  
Low Dimensional ◽  
Balanced Code ◽  
Hash Codes

Recently, hashing video contents for fast retrieval has received increasing attention due to the enormous growth of online videos. As the extension of image hashing techniques, traditional video hashing methods mainly focus on seeking the appropriate video features but pay little attention to how the video-specific features can be leveraged to achieve optimal binarization. In this paper, an end-to-end hashing framework, namely Unsupervised Deep Video Hashing (UDVH), is proposed, where feature extraction, balanced code learning and hash function learning are integrated and optimized in a self-taught manner. Particularly, distinguished from previous work, our framework enjoys two novelties: 1) an unsupervised hashing method that integrates the feature clustering and feature binarization, enabling the neighborhood structure to be preserved in the binary space; 2) a smart rotation applied to the video-specific features that are widely spread in the low-dimensional space such that the variance of dimensions can be balanced, thus generating more effective hash codes. Extensive experiments have been performed on two real-world datasets and the results demonstrate its superiority, compared to the state-of-the-art video hashing methods. To bootstrap further developments, the source code will be made publically available.

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 cell functional annotation for single-cell RNA-Seq

2021 ◽  
Author(s):  
Dongshunyi Li ◽  
Jun Ding ◽  
Ziv Bar-Joseph
Keyword(s):  
Single Cell ◽  
Dimensional Space ◽  
Cell Types ◽  
Specific Gene ◽  
Rna Seq ◽  
Cell Type ◽  
Sequencing Data ◽  
Gene Sets ◽  
Supervised Methods ◽  
Low Dimensional

One of the first steps in the analysis of single cell RNA-Sequencing data (scRNA-Seq) is the assignment of cell types. While a number of supervised methods have been developed for this, in most cases such assignment is performed by first clustering cells in low-dimensional space and then assigning cell types to different clusters. To overcome noise and to improve cell type assignments we developed UNIFAN, a neural network method that simultaneously clusters and annotates cells using known gene sets. UNIFAN combines both, low dimension representation for all genes and cell specific gene set activity scores to determine the clustering. We applied UNIFAN to human and mouse scRNA-Seq datasets from several different organs. As we show, by using knowledge on gene sets, UNIFAN greatly outperforms prior methods developed for clustering scRNA-Seq data. The gene sets assigned by UNIFAN to different clusters provide strong evidence for the cell type that is represented by this cluster making annotations easier.

scholarly journals Prediction of Disease-related microRNAs through Integrating Attributes of microRNA Nodes and Multiple Kinds of Connecting Edges

Molecules ◽  
2019 ◽  
Vol 24 (17) ◽  
pp. 3099 ◽  
Author(s):  
Xuan ◽  
Li ◽  
Zhang ◽  
Zhang ◽  
Song
Keyword(s):  
State Of The Art ◽  
Dimensional Space ◽  
Nonnegative Matrix ◽  
Superior Performance ◽  
Pancreatic Cancers ◽  
Node Attribute ◽  
Disease Associations ◽  
Node Attributes ◽  
Novel Method ◽  
Low Dimensional

Identifying disease-associated microRNAs (disease miRNAs) contributes to the understanding of disease pathogenesis. Most previous computational biology studies focused on multiple kinds of connecting edges of miRNAs and diseases, including miRNA–miRNA similarities, disease–disease similarities, and miRNA–disease associations. Few methods exploited the node attribute information related to miRNA family and cluster. The previous methods do not completely consider the sparsity of node attributes. Additionally, it is challenging to deeply integrate the node attributes of miRNAs and the similarities and associations related to miRNAs and diseases. In the present study, we propose a novel method, known as MDAPred, based on nonnegative matrix factorization to predict candidate disease miRNAs. MDAPred integrates the node attributes of miRNAs and the related similarities and associations of miRNAs and diseases. Since a miRNA is typically subordinate to a family or a cluster, the node attributes of miRNAs are sparse. Similarly, the data for miRNA and disease similarities are sparse. Projecting the miRNA and disease similarities and miRNA node attributes into a common low-dimensional space contributes to estimating miRNA-disease associations. Simultaneously, the possibility that a miRNA is associated with a disease depends on the miRNA’s neighbour information. Therefore, MDAPred deeply integrates projections of multiple kinds of connecting edges, projections of miRNAs node attributes, and neighbour information of miRNAs. The cross-validation results showed that MDAPred achieved superior performance compared to other state-of-the-art methods for predicting disease-miRNA associations. MDAPred can also retrieve more actual miRNA-disease associations at the top of prediction results, which is very important for biologists. Additionally, case studies of breast, lung, and pancreatic cancers further confirmed the ability of MDAPred to discover potential miRNA–disease associations.

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