We present ShapeVis, a scalable visualization technique for point cloud data inspired from topological data analysis. Our method captures the underlying geometric and topological structure of the data in a compressed graphical representation. Much success has been reported by the data visualization technique Mapper, that discreetly approximates the Reeb graph of a filter function on the data. However, when using standard dimensionality reduction algorithms as the filter function, Mapper suffers from considerable computational cost. This makes it difficult to scale to high-dimensional data. Our proposed technique relies on finding a subset of points called landmarks along the data manifold to construct a weighted witness-graph over it. This graph captures the structural characteristics of the point cloud, and its weights are determined using a Finite Markov Chain. We further compress this graph by applying induced maps from standard community detection algorithms. Using techniques borrowed from manifold tearing, we prune and reinstate edges in the induced graph based on their modularity to summarize the shape of data. We empirically demonstrate how our technique captures the structural characteristics of real and synthetic data sets. Further, we compare our approach with Mapper using various filter functions like t-SNE, UMAP, LargeVis and show that our algorithm scales to millions of data points while preserving the quality of data visualization.
We provide a rigorous mathematical treatment to the crowding issue in data visualization when high dimensional data sets are projected down to low dimensions for visualization. By properly adjusting the capacity of high dimensional balls, our method makes right enough room to prepare for the embedding. A key component of the proposed method is an estimation of the correlation dimension at various scales which reflects the data density variation. The proposed adjustment to the capacity applies to any distance (Euclidean, geodesic, diffusion) and can potentially be used in many existing methods …
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…
We propose a visualization technique that utilizes neural network embeddings and a generative network to reconstruct original data. This method allows for independent manipulation of individual image embeddings through its non-parametric structure, providing more flexibility than traditional autoencoder approaches. We have evaluated the effectiveness of this technique in data visualization and compared it to t-SNE and VAE methods. Furthermore, we have demonstrated the scalability of our method through visualizations on the ImageNet dataset. Our technique has potential applications in human-in-…
Here, we propose an unsupervised fuzzy rule-based dimensionality reduction method primarily for data visualization. It considers the following important issues relevant to dimensionality reduction-based data visualization: (i) preservation of neighborhood relationships, (ii) handling data on a non-linear manifold, (iii) the capability of predicting projections for new test data points, (iv) interpretability of the system, and (v) the ability to reject test points if required. For this, we use a first-order Takagi-Sugeno type model. We generate rule antecedents using clusters in the input data.…
This paper describes the method of visualization of periodic constituents and instability areas in series of measurements, being based on the algorithm of smoothing out and concept of one-dimensional cellular automata. A method can be used at the analysis of temporal series, related to the volumes of thematic publications in web-space.
Utah State University（犹他州立大学）；Université de Montréal（蒙特利尔大学）
Dimensionality reduction is often used as an initial step in data exploration, either as preprocessing for classification or regression or for visualization. Most dimensionality reduction techniques to date are unsupervised; they do not take class labels into account (e.g., PCA, MDS, t-SNE, Isomap). Such methods require large amounts of data and are often sensitive to noise that may obfuscate important patterns in the data. Various attempts at supervised dimensionality reduction methods that take into account auxiliary annotations (e.g., class labels) have been successfully implemented with go…
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…
In this short paper, a neural network that is able to form a low dimensional topological hidden representation is explained. The neural network can be trained as an autoencoder, a classifier or mix of both, and produces different low dimensional topological map for each of them. When it is trained as an autoencoder, the inherent topological structure of the data can be visualized, while when it is trained as a classifier, the topological structure is further constrained by the concept, for example the labels the data, hence the visualization is not only structural but also conceptual. The prop…
Hyperbolic space can naturally embed hierarchies that often exist in real-world data and semantics. While high-dimensional hyperbolic embeddings lead to better representations, most hyperbolic models utilize low-dimensional embeddings, due to non-trivial optimization and visualization of high-dimensional hyperbolic data. We propose CO-SNE, which extends the Euclidean space visualization tool, t-SNE, to hyperbolic space. Like t-SNE, it converts distances between data points to joint probabilities and tries to minimize the Kullback-Leibler divergence between the joint probabilities of high-dimen…
Dimension reduction and data visualization aim to project a high-dimensional dataset to a low-dimensional space while capturing the intrinsic structures in the data. It is an indispensable part of modern data science, and many dimensional reduction and visualization algorithms have been developed. However, different algorithms have their own strengths and weaknesses, making it critically important to evaluate their relative performance for a given dataset, and to leverage and combine their individual strengths. In this paper, we propose an efficient spectral method for assessing and combining …
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究所）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）
Modern methods for data visualization via dimensionality reduction, such as t-SNE, usually have performance issues that prohibit their application to large amounts of high-dimensional data. In this work, we propose NCVis -- a high-performance dimensionality reduction method built on a sound statistical basis of noise contrastive estimation. We show that NCVis outperforms state-of-the-art techniques in terms of speed while preserving the representation quality of other methods. In particular, the proposed approach successfully proceeds a large dataset of more than 1 million news headlines in se…
In recent years, machine learning (ML) has gained significant popularity in the field of chemical informatics and electronic structure theory. These techniques often require researchers to engineer abstract "features" that encode chemical concepts into a mathematical form compatible with the input to machine-learning models. However, there is no existing tool to connect these abstract features back to the actual chemical system, making it difficult to diagnose failures and to build intuition about the meaning of the features. We present ElectroLens, a new visualization tool for high-dimensiona…
Institute for Ophthalmic Research, University of Tübingen（蒂宾根大学眼科研究所）；International Max Planck Research School for Intelligent Systems（国际马克斯·普朗克智能系统研究学院）；Tübingen AI Center, University of Tübingen（蒂宾根大学蒂宾根人工智能中心）
Patch-seq, a recently developed experimental technique, allows neuroscientists to obtain transcriptomic and electrophysiological information from the same neurons. Efficiently analyzing and visualizing such paired multivariate data in order to extract biologically meaningful interpretations has, however, remained a challenge. Here, we use sparse deep neural networks with and without a two-dimensional bottleneck to predict electrophysiological features from the transcriptomic ones using a group lasso penalty, yielding concise and biologically interpretable two-dimensional visualizations. In two…
Visualizing high-dimensional data is an essential task in Data Science and Machine Learning. The Centroid-Encoder (CE) method is similar to the autoencoder but incorporates label information to keep objects of a class close together in the reduced visualization space. CE exploits nonlinearity and labels to encode high variance in low dimensions while capturing the global structure of the data. We present a detailed analysis of the method using a wide variety of data sets and compare it with other supervised dimension reduction techniques, including NCA, nonlinear NCA, t-distributed NCA, t-dist…
Stanford University（斯坦福大学）；University of Wyoming（怀俄明大学）
Employee theft and dishonesty is a major contributor to loss in the retail industry. Retailers have reported the need for more automated analytic tools to assess the liability of their employees. In this work, we train and optimize several machine learning models for regression prediction and analysis on this data, which will help retailers identify and manage risky employees. Since the data we use is very high dimensional, we use feature selection techniques to identify the most contributing factors to an employee's assessed risk. We also use dimension reduction and data embedding techniques …
Westlake University（西湖大学）；Westlake Institute for Advanced Study（西湖高等研究院）
High dimensional data analysis for exploration and discovery includes three fundamental tasks: dimensionality reduction, clustering, and visualization. When the three associated tasks are done separately, as is often the case thus far, inconsistencies can occur among the tasks in terms of data geometry and others. This can lead to confusing or misleading data interpretation. In this paper, we propose a novel neural network-based method, called Consistent Representation Learning (CRL), to accomplish the three associated tasks end-to-end and improve the consistencies. The CRL network consists of…
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 …
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
Dimensionality reduction techniques aim at representing high-dimensional data in low-dimensional spaces to extract hidden and useful information or facilitate visual understanding and interpretation of the data. However, few of them take into consideration the potential cluster information contained implicitly in the high-dimensional data. In this paper, we propose LaptSNE, a new graph-layout nonlinear dimensionality reduction method based on t-SNE, one of the best techniques for visualizing high-dimensional data as 2D scatter plots. Specifically, LaptSNE leverages the eigenvalue information o…
Interactive exploration of large, multidimensional datasets plays a very important role in various scientific fields. It makes it possible not only to identify important structural features and forms, such as clusters of vertices and their connection patterns, but also to evaluate their interrelationships in terms of position, distance, shape and connection density. We argue that the visualization of multidimensional data is well approximated by the problem of two-dimensional embedding of undirected nearest-neighbor graphs. The size of complex networks is a major challenge for today's computer…
Princeton University（普林斯顿大学）；Institute for Advanced Study（高等研究院）
A first line of attack in exploratory data analysis is data visualization, i.e., generating a 2-dimensional representation of data that makes clusters of similar points visually identifiable. Standard Johnson-Lindenstrauss dimensionality reduction does not produce data visualizations. The t-SNE heuristic of van der Maaten and Hinton, which is based on non-convex optimization, has become the de facto standard for visualization in a wide range of applications. This work gives a formal framework for the problem of data visualization - finding a 2-dimensional embedding of clusterable data that cor…
Central South University（中南大学）；Zhejiang University（浙江大学）；I4 data；Pennsylvania State University（宾夕法尼亚州立大学）；Facebook；Graz University of Technology（格拉茨技术大学）
Nowadays, as data becomes increasingly complex and distributed, data analyses often involve several related datasets that are stored on different servers and probably owned by different stakeholders. While there is an emerging need to provide these stakeholders with a full picture of their data under a global context, conventional visual analytical methods, such as dimensionality reduction, could expose data privacy when multi-party datasets are fused into a single site to build point-level relationships. In this paper, we reformulate the conventional t-SNE method from the single-site mode int…
Clustering and visualizing high-dimensional (HD) data are important tasks in a variety of fields. For example, in bioinformatics, they are crucial for analyses of single-cell data such as mass cytometry (CyTOF) data. Some of the most effective algorithms for clustering HD data are based on representing the data by nodes in a graph, with edges connecting neighbouring nodes according to some measure of similarity or distance. However, users of graph-based algorithms are typically faced with the critical but challenging task of choosing the value of an input parameter that sets the size of neighb…
Kyoto University（京都大学）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）；NAVER Corporation（NAVER公司）
Multimodal relational data analysis has become of increasing importance in recent years, for exploring across different domains of data, such as images and their text tags obtained from social networking services (e.g., Flickr). A variety of data analysis methods have been developed for visualization; to give an example, t-Stochastic Neighbor Embedding (t-SNE) computes low-dimensional feature vectors so that their similarities keep those of the observed data vectors. However, t-SNE is designed only for a single domain of data but not for multimodal data; this paper aims at visualizing multimod…
University of Melbourne（墨尔本大学）；Walter and Eliza Hall Institute for Medical Research（沃尔特与伊丽莎·霍尔医学研究所）
Non-parametric dimensionality reduction techniques, such as t-SNE and UMAP, are proficient in providing visualizations for datasets of fixed sizes. However, they cannot incrementally map and insert new data points into an already provided data visualization. We present Self-Organizing Nebulous Growths (SONG), a parametric nonlinear dimensionality reduction technique that supports incremental data visualization, i.e., incremental addition of new data while preserving the structure of the existing visualization. In addition, SONG is capable of handling new data increments, no matter whether they…
School of Computer Engineering, Nanyang Technological University（南洋理工大学计算机工程学院）；& Dept. of Informatics, Nicolaus Copernicus University（哥白尼大学信息学系）
Neural networks are commonly regarded as black boxes performing incomprehensible functions. For classification problems networks provide maps from high dimensional feature space to K-dimensional image space. Images of training vector are projected on polygon vertices, providing visualization of network function. Such visualization may show the dynamics of learning, allow for comparison of different networks, display training vectors around which potential problems may arise, show differences due to regularization and optimization procedures, investigate stability of network classification unde…
We propose the topic grids to detect anomaly and analyze the behavior based on the access log content. Content-based behavioral risk is quantified in the high dimensional space where the topics are generated from the log. The topics are being projected homogeneously into a space that is perception- and interaction-friendly to the human experts.
cGAP: Generalized Association Plots with HOMALS-Guided Heatmaps for Visualization of High-Dimensional Categorical Data
Institute of Statistical Science, Academia Sinica（学术院统计研究所）；Department of Statistics, National Taipei University（台北国立大学统计系）；Holistic Education Center, Mackay Medical University（Mackay医学院整体教育中心）；Department of Statistics and Data Science, Tamkang University（淡江大学统计与数据科学系）；Institute for Information Industry（资讯产业研究院）；Department of Applied Mathematical and Graduate Institute of Statistics, National Chung Hsing University（中正大学应用数学及统计研究所）；Department of Statistics, National Chengchi University（中正大学统计系）
University of Massachusetts Lowell（马萨诸塞大学洛厄尔分校）；University of Colorado Boulder（科罗拉多大学博尔德分校）
A fundamental task in machine learning involves visualizing high-dimensional data sets that arise in high-impact application domains. When considering the context of large imbalanced data, this problem becomes much more challenging. In this paper, the t-Distributed Stochastic Neighbor Embedding (t-SNE) algorithm is used to reduce the dimensions of an earthquake engineering related data set for visualization purposes. Since imbalanced data sets greatly affect the accuracy of classifiers, we employ Synthetic Minority Oversampling Technique (SMOTE) to tackle the imbalanced nature of such data set…
Georgia Institute of Technology（佐治亚理工学院）；Northwestern University（西北大学）；Ansys Inc.（Ansys公司）；Temple University（天普大学）
The optimization of electric machines at multiple operating points is crucial for applications that require frequent changes on speeds and loads, such as the electric vehicles, to strive for the machine optimal performance across the entire driving cycle. However, the number of objectives that would need to be optimized would significantly increase with the number of operating points considered in the optimization, thus posting a potential problem in regards to the visualization techniques currently in use, such as in the scatter plots of Pareto fronts, the parallel coordinates, and in the pri…
Mercedes-Benz Research and Development India Pvt. Ltd.（梅赛德斯-奔驰印度私人有限公司研发中心）；Centre of Studies in Resources Engineering, Indian Institute of Technology Bombay（印度理工学院孟买分校资源工程研究中心）
Hyperspectral Imagery (and Remote Sensing in general) captured from UAVs or satellites are highly voluminous in nature due to the large spatial extent and wavelengths captured by them. Since analyzing these images requires a huge amount of computational time and power, various dimensionality reduction techniques have been used for feature reduction. Some popular techniques among these falter when applied to Hyperspectral Imagery due to the famed curse of dimensionality. In this paper, we propose a novel approach, LEt-SNE, which combines graph based algorithms like t-SNE and Laplacian Eigenmaps…
Mayachitra, Inc.（玛雅奇特拉公司）；U.S. Naval Research Laboratory（美国海军研究实验室）；UC Santa Barbara（加州大学圣巴巴拉分校）
The number of malware is constantly on the rise. Though most new malware are modifications of existing ones, their sheer number is quite overwhelming. In this paper, we present a novel system to visualize and map millions of malware to points in a 2-dimensional (2D) spatial grid. This enables visualizing relationships within large malware datasets that can be used to develop triage solutions to screen different malware rapidly and provide situational awareness. Our approach links two visualizations within an interactive display. Our first view is a spatial point-based visualization of similari…
School of Computing, National University of Singapore（新加坡国立大学计算机学院）；Key Lab of High-Confidence Software Technology, MoE (Peking University)（高可信软件技术教育部重点实验室（北京大学））
Understanding how the predictions of deep learning models are formed during the training process is crucial to improve model performance and fix model defects, especially when we need to investigate nontrivial training strategies such as active learning, and track the root cause of unexpected training results such as performance degeneration. In this work, we propose a time-travelling visual solution DeepVisualInsight (DVI), aiming to manifest the spatio-temporal causality while training a deep learning image classifier. The spatio-temporal causality demonstrates how the gradient-descent algor…
Spatially resolved transcriptomics (ST) measures gene expression along with the spatial coordinates of the measurements. The analysis of ST data involves significant computation complexity. In this work, we propose gene expression dimensionality reduction algorithm that retains spatial structure. We combine the wavelet transformation with matrix factorization to select spatially-varying genes. We extract a low-dimensional representation of these genes. We consider Empirical Bayes setting, imposing regularization through the prior distribution of factor genes. Additionally, We provide visualiza…
Dimensionality reduction techniques are powerful tools for data preprocessing and visualization which typically come with few guarantees concerning the topological correctness of an embedding. The interleaving distance between the persistent homology of Vietoris-Rips filtrations can be used to identify a scale at which topological features such as clusters or holes in an embedding and original data set are in correspondence. We show how optimization seeking to minimize the interleaving distance can be incorporated into dimensionality reduction algorithms, and explicitly demonstrate its use in …
