This report concerns the problem of dimensionality reduction through information geometric methods on statistical manifolds. While there has been considerable work recently presented regarding dimensionality reduction for the purposes of learning tasks such as classification, clustering, and visualization, these methods have focused primarily on Riemannian manifolds in Euclidean space. While sufficient for many applications, there are many high-dimensional signals which have no straightforward and meaningful Euclidean representation. In these cases, signals may be more appropriately represented as a realization of some distribution lying on a statistical manifold, or a manifold of probability density functions (PDFs). We present a framework for dimensionality reduction that uses information geometry for both statistical manifold reconstruction as well as dimensionality reduction in the data domain.
Universitá di Pisa（比萨大学）；Universitá degli Studi di Cagliari（卡利亚里大学）
Deep neural networks are vulnerable to adversarial examples, i.e., carefully-perturbed inputs aimed to mislead classification. This work proposes a detection method based on combining non-linear dimensionality reduction and density estimation techniques. Our empirical findings show that the proposed approach is able to effectively detect adversarial examples crafted by non-adaptive attackers, i.e., not specifically tuned to bypass the detection method. Given our promising results, we plan to extend our analysis to adaptive attackers in future work.
An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few important features, but they are limited due to the lack of interpretability and connectivity to actual decision making associated with each physical variable. Variable selection techniques, as an alternative, can maintain the interpretability, but they often involve a greedy search that is susceptible to failure in capturing important interactions or a metaheuristi…
Dimensionality reduction methods are very common in the field of high dimensional data analysis. Typically, algorithms for dimensionality reduction are computationally expensive. Therefore, their applications for the analysis of massive amounts of data are impractical. For example, repeated computations due to accumulated data are computationally prohibitive. In this paper, an out-of-sample extension scheme, which is used as a complementary method for dimensionality reduction, is presented. We describe an algorithm which performs an out-of-sample extension to newly-arrived data points. Unlike …
Ensemble learning has had many successes in supervised learning, but it has been rare in unsupervised learning and dimensionality reduction. This study explores dimensionality reduction ensembles, using principal component analysis and manifold learning techniques to capture linear, nonlinear, local, and global features in the original dataset. Dimensionality reduction ensembles are tested first on simulation data and then on two real medical datasets using random forest classifiers; results suggest the efficacy of this approach, with accuracies approaching that of the full dataset. Limitation…
Nonlinear dimensionality reduction methods are a popular tool for data scientists and researchers to visualize complex, high dimensional data. However, while these methods continue to improve and grow in number, it is often difficult to evaluate the quality of a visualization due to a variety of factors such as lack of information about the intrinsic dimension of the data and additional tuning required for many evaluation metrics. In this paper, we seek to provide a systematic comparison of dimensionality reduction quality metrics using datasets where we know the ground truth manifold. We util…
Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have not been well studied. Our key contribution is to show that $2K$ projection vectors are sufficient for the independence preservation of any $K$ class data sampled from a union of independent subspaces. It is this non-trivial observation that we use for designing our dimensionality reduction technique. In this paper, we propose a novel dimensionality reductio…
Despite the fact that they do not consider the temporal nature of data, classic dimensionality reduction techniques, such as PCA, are widely applied to time series data. In this paper, we introduce a factor decomposition specific for time series that builds upon the Bayesian multivariate autoregressive model and hence evades the assumption that data points are mutually independent. The key is to find a low-rank estimation of the autoregressive matrices. As in the probabilistic version of other factor models, this induces a latent low-dimensional representation of the original data. We discuss …
We present a study on how to effectively reduce the dimensions of the $k$-means clustering problem, so that provably accurate approximations are obtained. Four algorithms are presented, two \textit{feature selection} and two \textit{feature extraction} based algorithms, all of which are randomized.
Dimensionality reduction is a topic of recent interest. In this paper, we present the classification constrained dimensionality reduction (CCDR) algorithm to account for label information. The algorithm can account for multiple classes as well as the semi-supervised setting. We present an out-of-sample expressions for both labeled and unlabeled data. For unlabeled data, we introduce a method of embedding a new point as preprocessing to a classifier. For labeled data, we introduce a method that improves the embedding during the training phase using the out-of-sample extension. We investigate cl…
In this era of data deluge, many signal processing and machine learning tasks are faced with high-dimensional datasets, including images, videos, as well as time series generated from social, commercial and brain network interactions. Their efficient processing calls for dimensionality reduction techniques capable of properly compressing the data while preserving task-related characteristics, going beyond pairwise data correlations. The present paper puts forth a nonlinear dimensionality reduction framework that accounts for data lying on known graphs. The novel framework encompasses most of t…
Adform ApS（Adform公司）；Technical University of Denmark（丹麦技术大学）
In online advertising, display ads are increasingly being placed based on real-time auctions where the advertiser who wins gets to serve the ad. This is called real-time bidding (RTB). In RTB, auctions have very tight time constraints on the order of 100ms. Therefore mechanisms for bidding intelligently such as clickthrough rate prediction need to be sufficiently fast. In this work, we propose to use dimensionality reduction of the user-website interaction graph in order to produce simplified features of users and websites that can be used as predictors of clickthrough rate. We demonstrate tha…
Thanks to their versatility, ease of deployment and high-performance, surrogate models have become staple tools in the arsenal of uncertainty quantification (UQ). From local interpolants to global spectral decompositions, surrogates are characterised by their ability to efficiently emulate complex computational models based on a small set of model runs used for training. An inherent limitation of many surrogate models is their susceptibility to the curse of dimensionality, which traditionally limits their applicability to a maximum of $\mathcal{O}(10^2)$ input dimensions. We present a novel ap…
We present local discriminative Gaussian (LDG) dimensionality reduction, a supervised dimensionality reduction technique for classification. The LDG objective function is an approximation to the leave-one-out training error of a local quadratic discriminant analysis classifier, and thus acts locally to each training point in order to find a mapping where similar data can be discriminated from dissimilar data. While other state-of-the-art linear dimensionality reduction methods require gradient descent or iterative solution approaches, LDG is solved with a single eigen-decomposition. Thus, it s…
University of Toyama（富山大学）；Institute of Natural Medicine, University of Toyama, Japan（富山大学自然医学研究所）
This paper proposes a new dimensionality reduction algorithm named branching embedding (BE). It converts a dendrogram to a two-dimensional scatter plot, and visualizes the inherent structures of the original high-dimensional data. Since the conversion part is not computationally demanding, the BE algorithm would be beneficial for the case where hierarchical clustering is already performed. Numerical experiments revealed that the outputs of the algorithm moderately preserve the original hierarchical structures.
The University of Electro-Communications（电气通信大学）；Microsoft（微软）
Dictionary leaning (DL) and dimensionality reduction (DR) are powerful tools to analyze high-dimensional noisy signals. This paper presents a proposal of a novel Riemannian joint dimensionality reduction and dictionary learning (R-JDRDL) on symmetric positive definite (SPD) manifolds for classification tasks. The joint learning considers the interaction between dimensionality reduction and dictionary learning procedures by connecting them into a unified framework. We exploit a Riemannian optimization framework for solving DL and DR problems jointly. Finally, we demonstrate that the proposed R-…
Wuhan University（武汉大学）；Huazhong University of Science and Technology（华中科技大学）
Affective computing has become a very important research area in human-machine interaction. However, affects are subjective, subtle, and uncertain. So, it is very difficult to obtain a large number of labeled training samples, compared with the number of possible features we could extract. Thus, dimensionality reduction is critical in affective computing. This paper presents our preliminary study on dimensionality reduction for affect classification. Five popular dimensionality reduction approaches are introduced and compared. Experiments on the DEAP dataset showed that no approach can univers…
We reframe linear dimensionality reduction as a problem of Bayesian inference on matrix manifolds. This natural paradigm extends the Bayesian framework to dimensionality reduction tasks in higher dimensions with simpler models at greater speeds. Here an orthogonal basis is treated as a single point on a manifold and is associated with a linear subspace on which observations vary maximally. Throughout this paper, we employ the Grassmann and Stiefel manifolds for various dimensionality reduction problems, explore the connection between the two manifolds, and use Hybrid Monte Carlo for posterior …
Dimensionality reduction is an important step in processing the hyperspectral images (HSI) to overcome the curse of dimensionality problem. Linear dimensionality reduction methods such as Independent component analysis (ICA) and Linear discriminant analysis (LDA) are commonly employed to reduce the dimensionality of HSI. These methods fail to capture non-linear dependency in the HSI data, as data lies in the nonlinear manifold. To handle this, nonlinear transformation techniques based on kernel methods were introduced for dimensionality reduction of HSI. However, the kernel methods involve cub…
Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of interest, such as covariance, dynamical structure, correlation between data sets, input-output relationships, and margin between data classes. Methods have been developed with a variety of names and motivations in many fields, and perhaps as a result the connections between all these methods have not been highlighted. Here we survey methods from this disparate li…
We demonstrate that almost all non-parametric dimensionality reduction methods can be expressed by a simple procedure: regularized loss minimization plus singular value truncation. By distinguishing the role of the loss and regularizer in such a process, we recover a factored perspective that reveals some gaps in the current literature. Beyond identifying a useful new loss for manifold unfolding, a key contribution is to derive new convex regularizers that combine distance maximization with rank reduction. These regularizers can be applied to any loss.
Technische Universität Darmstadt（达姆施塔特工业大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Movement primitives are an important policy class for real-world robotics. However, the high dimensionality of their parametrization makes the policy optimization expensive both in terms of samples and computation. Enabling an efficient representation of movement primitives facilitates the application of machine learning techniques such as reinforcement on robotics. Motions, especially in highly redundant kinematic structures, exhibit high correlation in the configuration space. For these reasons, prior work has mainly focused on the application of dimensionality reduction techniques in the co…
We present a theory for Euclidean dimensionality reduction with subgaussian matrices which unifies several restricted isometry property and Johnson-Lindenstrauss type results obtained earlier for specific data sets. In particular, we recover and, in several cases, improve results for sets of sparse and structured sparse vectors, low-rank matrices and tensors, and smooth manifolds. In addition, we establish a new Johnson-Lindenstrauss embedding for data sets taking the form of an infinite union of subspaces of a Hilbert space.
In our work, we propose a novel formulation for supervised dimensionality reduction based on a nonlinear dependency criterion called Statistical Distance Correlation, Szekely et. al. (2007). We propose an objective which is free of distributional assumptions on regression variables and regression model assumptions. Our proposed formulation is based on learning a low-dimensional feature representation $\mathbf{z}$, which maximizes the squared sum of Distance Correlations between low dimensional features $\mathbf{z}$ and response $y$, and also between features $\mathbf{z}$ and covariates $\mathb…
In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man ifold geometry using either local or global features of the data. Building on the Laplacian Eigenmap and Diffusionmaps framework, we propose a new paradigm that offers a guarantee, under reasonable assumptions, that any manifo ld learning algorithm will preserve the geometry of a data set. Our approach is based on augmenting the output of embedding algorith…
Institute of Medical Genetics, University Medical Centre Ljubljana（卢布尔雅那大学医学中心医学遗传学研究所）
Class prediction is an important application of microarray gene expression data analysis. The high-dimensionality of microarray data, where number of genes (variables) is very large compared to the number of samples (obser- vations), makes the application of many prediction techniques (e.g., logistic regression, discriminant analysis) difficult. An efficient way to solve this prob- lem is by using dimension reduction statistical techniques. Increasingly used in psychology-related applications, Rasch model (RM) provides an appealing framework for handling high-dimensional microarray data. In th…
Bogazici University（博阿齐奇大学）；Mississippi State University（密西西比州立大学）
This paper gives a review and synthesis of methods of evaluating dimensionality reduction techniques. Particular attention is paid to rank-order neighborhood evaluation metrics. A framework is created for exploring dimensionality reduction quality through visualization. An associated toolkit is implemented in R. The toolkit includes scatter plots, heat maps, loess smoothing, and performance lift diagrams. The overall rationale is to help researchers compare dimensionality reduction techniques and use visual insights to help select and improve techniques. Examples are given for dimensionality r…
Ariel University（阿里埃勒大学）；Ben-Gurion University of the Negev（内盖夫本-古里安大学）；Weizmann Institute of Science（魏茨曼科学研究所）
We study adaptive data-dependent dimensionality reduction in the context of supervised learning in general metric spaces. Our main statistical contribution is a generalization bound for Lipschitz functions in metric spaces that are doubling, or nearly doubling. On the algorithmic front, we describe an analogue of PCA for metric spaces: namely an efficient procedure that approximates the data's intrinsic dimension, which is often much lower than the ambient dimension. Our approach thus leverages the dual benefits of low dimensionality: (1) more efficient algorithms, e.g., for proximity search, …
In this project we further investigate the idea of reducing the dimensionality of datasets using a Borel isomorphism with the purpose of subsequently applying supervised learning algorithms, as originally suggested by my supervisor V. Pestov (in 2011 Dagstuhl preprint). Any consistent learning algorithm, for example kNN, retains universal consistency after a Borel isomorphism is applied. A series of concrete examples of Borel isomorphisms that reduce the number of dimensions in a dataset is provided, based on multiplying the data by orthogonal matrices before the dimensionality reducing Borel …
University of Waterloo（滑铁卢大学）；Vector Institute（向量研究所）
We consider the problem of sufficient dimensionality reduction (SDR), where the high-dimensional observation is transformed to a low-dimensional sub-space in which the information of the observations regarding the label variable is preserved. We propose DVSDR, a deep variational approach for sufficient dimensionality reduction. The deep structure in our model has a bottleneck that represent the low-dimensional embedding of the data. We explain the SDR problem using graphical models and use the framework of variational autoencoders to maximize the lower bound of the log-likelihood of the joint …
Huazhong University of Science and Technology（华中科技大学）；University of Technology Sydney（悉尼科技大学）
Dimensionality reduction is an important operation in information visualization, feature extraction, clustering, regression, and classification, especially for processing noisy high dimensional data. However, most existing approaches preserve either the global or the local structure of the data, but not both. Approaches that preserve only the global data structure, such as principal component analysis (PCA), are usually sensitive to outliers. Approaches that preserve only the local data structure, such as locality preserving projections, are usually unsupervised (and hence cannot use label inf…
We introduce "TriMap"; a dimensionality reduction technique based on triplet constraints, which preserves the global structure of the data better than the other commonly used methods such as t-SNE, LargeVis, and UMAP. To quantify the global accuracy of the embedding, we introduce a score that roughly reflects the relative placement of the clusters rather than the individual points. We empirically show the excellent performance of TriMap on a large variety of datasets in terms of the quality of the embedding as well as the runtime. On our performance benchmarks, TriMap easily scales to millions…
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-establis…
In this paper we introduce and analyze the learning scenario of \emph{coupled nonlinear dimensionality reduction}, which combines two major steps of machine learning pipeline: projection onto a manifold and subsequent supervised learning. First, we present new generalization bounds for this scenario and, second, we introduce an algorithm that follows from these bounds. The generalization error bound is based on a careful analysis of the empirical Rademacher complexity of the relevant hypothesis set. In particular, we show an upper bound on the Rademacher complexity that is in $\widetilde O(\sq…
A dimensionality reduction technique based on the Gromov-Wasserstein distance
Instituto Federal de Educação, Ciência e Tecnologia do Ceará（塞阿拉联邦教育、科学与技术研究所）；Federal University of Ceara（塞阿拉联邦大学）；Université Paris-Saclay, CEA, List（巴黎-萨克雷大学，CEA，List）
Graph Signal Processing (GSP) is a promising framework to analyze multi-dimensional neuroimaging datasets, while taking into account both the spatial and functional dependencies between brain signals. In the present work, we apply dimensionality reduction techniques based on graph representations of the brain to decode brain activity from real and simulated fMRI datasets. We introduce seven graphs obtained from a) geometric structure and/or b) functional connectivity between brain areas at rest, and compare them when performing dimension reduction for classification. We show that mixed graphs …
Mitsubishi Electric Research Laboratories（三菱电机研究实验室）
We propose a new concept of rateless auto-encoders (RL-AEs) that enable a flexible latent dimensionality, which can be seamlessly adjusted for varying distortion and dimensionality requirements. In the proposed RL-AEs, instead of a deterministic bottleneck architecture, we use an over-complete representation that is stochastically regularized with weighted dropouts, in a manner analogous to sparse AE (SAE). Unlike SAEs, our RL-AEs employ monotonically increasing dropout rates across the latent representation nodes such that the latent variables become sorted by importance like in principal com…
Stochastic kernel based dimensionality reduction approaches have become popular in the last decade. The central component of many of these methods is a symmetric kernel that quantifies the vicinity between pairs of data points and a kernel-induced Markov chain on the data. Typically, the Markov chain is fully specified by the kernel through row normalization. However, in many cases, it is desirable to impose user-specified stationary-state and dynamical constraints on the Markov chain. Unfortunately, no systematic framework exists to impose such user-defined constraints. Here, we introduce a p…
University of Electronic Science and Technology of China（电子科技大学）
Scientists in many fields have the common and basic need of dimensionality reduction: visualizing the underlying structure of the massive multivariate data in a low-dimensional space. However, many dimensionality reduction methods confront the so-called "crowding problem" that clusters tend to overlap with each other in the embedding. Previously, researchers expect to avoid that problem and seek to make clusters maximally separated in the embedding. However, the proposed in-tree (IT) based method, called IT-map, allows clusters in the embedding to be locally overlapped, while seeking to make t…
University of Tunis El Manar（突尼斯玛纳大学）；National Engineering School of Tunis（突尼斯国家工程学院）
In this study, we propose a new statical approach for high-dimensionality reduction of heterogenous data that limits the curse of dimensionality and deals with missing values. To handle these latter, we propose to use the Random Forest imputation's method. The main purpose here is to extract useful information and so reducing the search space to facilitate the data exploration process. Several illustrative numeric examples, using data coming from publicly available machine learning repositories are also included. The experimental component of the study shows the efficiency of the proposed anal…
Sparse random projection (RP) is a popular tool for dimensionality reduction that shows promising performance with low computational complexity. However, in the existing sparse RP matrices, the positions of non-zero entries are usually randomly selected. Although they adopt uniform sampling with replacement, due to large sampling variance, the number of non-zeros is uneven among rows of the projection matrix which is generated in one trial, and more data information may be lost after dimension reduction. To break this bottleneck, based on random sampling without replacement in statistics, this…
This paper introduces a new unsupervised method for dimensionality reduction via regression (DRR). The algorithm belongs to the family of invertible transforms that generalize Principal Component Analysis (PCA) by using curvilinear instead of linear features. DRR identifies the nonlinear features through multivariate regression to ensure the reduction in redundancy between he PCA coefficients, the reduction of the variance of the scores, and the reduction in the reconstruction error. More importantly, unlike other nonlinear dimensionality reduction methods, the invertibility, volume-preservati…
Dimensionality reduction is ubiquitous in analysis of complex dynamics. The conventional dimensionality reduction techniques, however, focus on reproducing the underlying configuration space, rather than the dynamics itself. The constructed low-dimensional space does not provide complete and accurate description of the dynamics. Here I describe how to perform dimensionality reduction while preserving the essential properties of the dynamics. The approach is illustrated by analyzing the chess game - the archetype of complex dynamics. A variable that provides complete and accurate description of…
Datasets with non-trivial large scale topology can be hard to embed in low-dimensional Euclidean space with existing dimensionality reduction algorithms. We propose to model topologically complex datasets using vector bundles, in such a way that the base space accounts for the large scale topology, while the fibers account for the local geometry. This allows one to reduce the dimensionality of the fibers, while preserving the large scale topology. We formalize this point of view, and, as an application, we describe an algorithm which takes as input a dataset together with an initial representa…
Natl. Centre for Biotechnology (CSIC)（国家生物技术中心（CSIC））
Experimental life sciences like biology or chemistry have seen in the recent decades an explosion of the data available from experiments. Laboratory instruments become more and more complex and report hundreds or thousands measurements for a single experiment and therefore the statistical methods face challenging tasks when dealing with such high dimensional data. However, much of the data is highly redundant and can be efficiently brought down to a much smaller number of variables without a significant loss of information. The mathematical procedures making possible this reduction are called …
Institute of Mathematical Sciences（数学科学研究所）；Claremont Graduate University（克莱蒙特研究生大学）
We propose a method for recognizing moving vehicles, using data from roadside audio sensors. This problem has applications ranging widely, from traffic analysis to surveillance. We extract a frequency signature from the audio signal using a short-time Fourier transform, and treat each time window as an individual data point to be classified. By applying a spectral embedding, we decrease the dimensionality of the data sufficiently for K-nearest neighbors to provide accurate vehicle identification.
College of Information and Communications University of South Carolina（南卡罗来纳大学信息与通信学院）；Arnold School of Public Health at the University of South Carolina（南卡罗来纳大学阿诺德公共卫生学院）
Large textual corpora are often represented by the document-term frequency matrix whose elements are the frequency of terms; however, this matrix has two problems: sparsity and high dimensionality. Four dimension reduction strategies are used to address these problems. Of the four strategies, unsupervised feature transformation (UFT) is a popular and efficient strategy to map the terms to a new basis in the document-term frequency matrix. Although several UFT-based methods have been developed, fuzzy clustering has not been considered for dimensionality reduction. This research explores fuzzy c…
Most dimensionality reduction methods employ frequency domain representations obtained from matrix diagonalization and may not be efficient for large datasets with relatively high intrinsic dimensions. To address this challenge, Correlated Clustering and Projection (CCP) offers a novel data domain strategy that does not need to solve any matrix. CCP partitions high-dimensional features into correlated clusters and then projects correlated features in each cluster into a one-dimensional representation based on sample correlations. Residue-Similarity (R-S) scores and indexes, the shape of data i…
Sun Yat-sen University（中山大学）；RIKEN Center for Brain Science（理化学研究所脑科学中心）
Deep neural networks are widely used in various domains. However, the nature of computations at each layer of the deep networks is far from being well understood. Increasing the interpretability of deep neural networks is thus important. Here, we construct a mean-field framework to understand how compact representations are developed across layers, not only in deterministic deep networks with random weights but also in generative deep networks where an unsupervised learning is carried out. Our theory shows that the deep computation implements a dimensionality reduction while maintaining a fini…
Normalizing flows are diffeomorphic, typically dimension-preserving, models trained using the likelihood of the model. We use the SurVAE framework to construct dimension reducing surjective flows via a new layer, known as the funnel. We demonstrate its efficacy on a variety of datasets, and show it improves upon or matches the performance of existing flows while having a reduced latent space size. The funnel layer can be constructed from a wide range of transformations including restricted convolution and feed forward layers.
The Ohio State University（俄亥俄州立大学）；New York University（纽约大学）
Given labeled points in a high-dimensional vector space, we seek a low-dimensional subspace such that projecting onto this subspace maintains some prescribed distance between points of differing labels. Intended applications include compressive classification. Taking inspiration from large margin nearest neighbor classification, this paper introduces a semidefinite relaxation of this problem. Unlike its predecessors, this relaxation is amenable to theoretical analysis, allowing us to provably recover a planted projection operator from the data.
Manifold learning-based encoders have been playing important roles in nonlinear dimensionality reduction (NLDR) for data exploration. However, existing methods can often fail to preserve geometric, topological and/or distributional structures of data. In this paper, we propose a deep manifold learning framework, called deep manifold transformation (DMT) for unsupervised NLDR and embedding learning. DMT enhances deep neural networks by using cross-layer local geometry-preserving (LGP) constraints. The LGP constraints constitute the loss for deep manifold learning and serve as geometric regulari…
Molecular simulations produce very high-dimensional data-sets with millions of data points. As analysis methods are often unable to cope with so many dimensions, it is common to use dimensionality reduction and clustering methods to reach a reduced representation of the data. Yet these methods often fail to capture the most important features necessary for the construction of a Markov model. Here we demonstrate the results of various dimensionality reduction methods on two simulation data-sets, one of protein folding and another of protein-ligand binding. The methods tested include a k-means c…
The University of Sydney（悉尼大学）；China University of Geosciences（中国地质大学）
Locality preserving projections (LPP) are a classical dimensionality reduction method based on data graph information. However, LPP is still responsive to extreme outliers. LPP aiming for vectorial data may undermine data structural information when it is applied to multidimensional data. Besides, it assumes the dimension of data to be smaller than the number of instances, which is not suitable for high-dimensional data. For high-dimensional data analysis, the tensor-train decomposition is proved to be able to efficiently and effectively capture the spatial relations. Thus, we propose a tensor…
Faculty of Mathematics and Physics of Charles University（查理大学数学与物理学院）；Luxembourg Centre for Systems Biomedicine, University of Luxembourg（卢森堡大学卢森堡系统生物医学中心）；Institute of Haematology and Blood Transfusion（血液学与输血研究所）；Institute of Organic Chemistry and Biochemistry（有机化学与生物化学研究所）
Dimensionality reduction methods have found vast application as visualization tools in diverse areas of science. Although many different methods exist, their performance is often insufficient for providing quick insight into many contemporary datasets, and the unsupervised mode of use prevents the users from utilizing the methods for dataset exploration and fine-tuning the details for improved visualization quality. We present BlosSOM, a high-performance semi-supervised dimensionality reduction software for interactive user-steerable visualization of high-dimensional datasets with millions of …
