An Incremental Dimensionality Reduction Method for Visualizing Streaming Multidimensional Data

Incremental Classification for High-Dimensional EEG Manifold Representation Using Bidirectional Dimensionality Reduction and Prototype Learning

In brain-computer interface (BCI) systems, symmetric positive definite (SPD) manifold within Riemannian space has been frequently utilized to extract spatial features from electroencephalogram (EEG) signals. However, the intrinsic high dimensionality of SPD matrices introduces too much computational burden to hinder the real-time applications of such BCI, especially in handling dynamic tasks, like incremental learning. Directly reducing the dimensionality of SPD matrices with conventional dimensionality reduction (DR) methods will alter the fundamental properties of SPD matrices. Moreover, current DR methods for incremental learning always necessitate retaining old data to update their representations under new mapping. To this end, a bidirectional two-dimensional principal component analysis for SPD manifold (B2DPCA-SPD) is proposed to reduce the dimensionality of SPD matrices, in such way that the reduced matrices remain on SPD manifold. Afterwards, the B2DPCA-SPD is extended to adapt to incremental learning tasks without saving old data. The incremental B2DPCA-SPD can be seamlessly integrated with the matrix-formed growing neural gas network (MF-GNG) to achieve an incremental EEG classification, where the new low-dimensional representations of the prototypes in old classifiers can be easily recalculated with the updated projection matrix. Extensive experiments are conducted on two public datasets to perform the EEG classification. The results demonstrate that our method significantly reduces computation time by 38.53% and 35.96%, and outperforms conventional methods in classification accuracy by 4.21% to 19.59%.

A Large-Scale Sensitivity Analysis on Latent Embeddings and Dimensionality Reductions for Text Spatializations

The semantic similarity between documents of a text corpus can be visualized using map-like metaphors based on two-dimensional scatterplot layouts. These layouts result from a dimensionality reduction on the document-term matrix or a representation within a latent embedding, including topic models. Thereby, the resulting layout depends on the input data and hyperparameters of the dimensionality reduction and is therefore affected by changes in them. Furthermore, the resulting layout is affected by changes in the input data and hyperparameters of the dimensionality reduction. However, such changes to the layout require additional cognitive efforts from the user. In this work, we present a sensitivity study that analyzes the stability of these layouts concerning (1) changes in the text corpora, (2) changes in the hyperparameter, and (3) randomness in the initialization. Our approach has two stages: data measurement and data analysis. First, we derived layouts for the combination of three text corpora and six text embeddings and a grid-search-inspired hyperparameter selection of the dimensionality reductions. Afterward, we quantified the similarity of the layouts through ten metrics, concerning local and global structures and class separation. Second, we analyzed the resulting 42 817 tabular data points in a descriptive statistical analysis. From this, we derived guidelines for informed decisions on the layout algorithm and highlight specific hyperparameter settings. We provide our implementation as a Git repository at hpicgs/Topic-Models-and-Dimensionality-Reduction-Sensitivity-Study and results as Zenodo archive at DOI:10.5281/zenodo.12772898.

Mesoscopic structure graphs for interpreting uncertainty in non-linear embeddings

Probabilistic-based non-linear dimensionality reduction (PB-NL-DR) methods, such as t-SNE and UMAP, are effective in unfolding complex high-dimensional manifolds, allowing users to explore and understand the structural patterns of data. However, due to the trade-off between global and local structure preservation and the randomness during computation, these methods may introduce false neighborhood relationships, known as distortion errors and misleading visualizations. To address this issue, we first conduct a detailed survey to illustrate the design space of prior layout enrichment visualizations for interpreting DR results, and then propose a node-link visualization technique, ManiGraph. This technique rethinks the neighborhood fidelity between the high- and low-dimensional spaces by constructing dynamic mesoscopic structure graphs and measuring region-adapted trustworthiness. ManiGraph also addresses the overplotting issue in scatterplot visualization for large-scale datasets and supports examining in unsupervised scenarios. We demonstrate the effectiveness of ManiGraph in different analytical cases, including generic machine learning using 3D toy data illustrations and fashion-MNIST, a computational biology study using a single-cell RNA sequencing dataset, and a deep learning-enabled colorectal cancer study with histopathology-MNIST.

ASTF: Visual Abstractions of Time-Varying Patterns in Radio Signals

A time-frequency diagram is a commonly used visualization for observing the time-frequency distribution of radio signals and analyzing their time-varying patterns of communication states in radio monitoring and management. While it excels when performing short-term signal analyses, it becomes inadaptable for long-term signal analyses because it cannot adequately depict signal time-varying patterns in a large time span on a space-limited screen. This research thus presents an abstract signal time-frequency (ASTF) diagram to address this problem. In the diagram design, a visual abstraction method is proposed to visually encode signal communication state changes in time slices. A time segmentation algorithm is proposed to divide a large time span into time slices. Three new quantified metrics and a loss function are defined to ensure the preservation of important time-varying information in the time segmentation. An algorithm performance experiment and a user study are conducted to evaluate the effectiveness of the diagram for long-term signal analyses.

Incorporation of Human Knowledge into Data Embeddings to Improve Pattern Significance and Interpretability

Embedding is a common technique for analyzing multi-dimensional data. However, the embedding projection cannot always form significant and interpretable visual structures that foreshadow underlying data patterns. We propose an approach that incorporates human knowledge into data embeddings to improve pattern significance and interpretability. The core idea is (1) externalizing tacit human knowledge as explicit sample labels and (2) adding a classification loss in the embedding network to encode samples' classes. The approach pulls samples of the same class with similar data features closer in the projection, leading to more compact (significant) and class-consistent (interpretable) visual structures. We give an embedding network with a customized classification loss to implement the idea and integrate the network into a visualization system to form a workflow that supports flexible class creation and pattern exploration. Patterns found on open datasets in case studies, subjects' performance in a user study, and quantitative experiment results illustrate the general usability and effectiveness of the approach.

A Survey on ML4VIS: Applying Machine Learning Advances to Data Visualization

Inspired by the great success of machine learning (ML), researchers have applied ML techniques to visualizations to achieve a better design, development, and evaluation of visualizations. This branch of studies, known as ML4VIS, is gaining increasing research attention in recent years. To successfully adapt ML techniques for visualizations, a structured understanding of the integration of ML4VIS is needed. In this article, we systematically survey 88 ML4VIS studies, aiming to answer two motivating questions: "what visualization processes can be assisted by ML?" and "how ML techniques can be used to solve visualization problems? "This survey reveals seven main processes where the employment of ML techniques can benefit visualizations: Data Processing4VIS, Data-VIS Mapping, Insight Communication, Style Imitation, VIS Interaction, VIS Reading, and User Profiling. The seven processes are related to existing visualization theoretical models in an ML4VIS pipeline, aiming to illuminate the role of ML-assisted visualization in general visualizations. Meanwhile, the seven processes are mapped into main learning tasks in ML to align the capabilities of ML with the needs in visualization. Current practices and future opportunities of ML4VIS are discussed in the context of the ML4VIS pipeline and the ML-VIS mapping. While more studies are still needed in the area of ML4VIS, we hope this article can provide a stepping-stone for future exploration. A web-based interactive browser of this survey is available at https://ml4vis.github.io.

Getting over High-Dimensionality: How Multidimensional Projection Methods Can Assist Data Science

The exploration and analysis of multidimensional data can be pretty complex tasks, requiring sophisticated tools able to transform large amounts of data bearing multiple parameters into helpful information. Multidimensional projection techniques figure as powerful tools for transforming multidimensional data into visual information according to similarity features. Integrating this class of methods into a framework devoted to data sciences can contribute to generating more expressive means of visual analytics. Although the Principal Component Analysis (PCA) is a well-known method in this context, it is not the only one, and, sometimes, its abilities and limitations are not adequately discussed or taken into consideration by users. Therefore, knowing in-depth multidimensional projection techniques, their strengths, and the possible distortions they can create is of significant importance for researchers developing knowledge-discovery systems. This research presents a comprehensive overview of current state-of-the-art multidimensional projection techniques and shows example codes in Python and R languages, all available on the internet. The survey segment discusses the different types of techniques applied to multidimensional projection tasks from their background, application processes, capabilities, and limitations, opening the internal processes of the methods and demystifying their concepts. We also illustrate two problems, from a genetic experiment (supervised) and text mining (non-supervised), presenting solutions through multidimensional projection application. Finally, we brought elements that reverberate the competitiveness of multidimensional projection techniques towards high-dimension data visualization, commonly needed in data sciences solutions.

A Visual Analytics Approach for Hardware System Monitoring with Streaming Functional Data Analysis

Many real-world applications involve analyzing time-dependent phenomena, which are intrinsically functional, consisting of curves varying over a continuum (e.g., time). When analyzing continuous data, functional data analysis (FDA) provides substantial benefits, such as the ability to study the derivatives and to restrict the ordering of data. However, continuous data inherently has infinite dimensions, and for a long time series, FDA methods often suffer from high computational costs. The analysis problem becomes even more challenging when updating the FDA results for continuously arriving data. In this paper, we present a visual analytics approach for monitoring and reviewing time series data streamed from a hardware system with a focus on identifying outliers by using FDA. To perform FDA while addressing the computational problem, we introduce new incremental and progressive algorithms that promptly generate the magnitude-shape (MS) plot, which conveys both the functional magnitude and shape outlyingness of time series data. In addition, by using an MS plot in conjunction with an FDA version of principal component analysis, we enhance the analyst's ability to investigate the visually-identified outliers. We illustrate the effectiveness of our approach with two use scenarios using real-world datasets. The resulting tool is evaluated by industry experts using real-world streaming datasets.

ChartSeer: Interactive Steering Exploratory Visual Analysis With Machine Intelligence

During exploratory visual analysis (EVA), analysts need to continually determine which subsequent activities to perform, such as which data variables to explore or how to present data variables visually. Due to the vast combinations of data variables and visual encodings that are possible, it is often challenging to make such decisions. Further, while performing local explorations, analysts often fail to attend to the holistic picture that is emerging from their analysis, leading them to improperly steer their EVA. These issues become even more impactful in the real world analysis scenarios where EVA occurs in multiple asynchronous sessions that could be completed by one or more analysts. To address these challenges, this work proposes ChartSeer, a system that uses machine intelligence to enable analysts to visually monitor the current state of an EVA and effectively identify future activities to perform. ChartSeer utilizes deep learning techniques to characterize analyst-created data charts to generate visual summaries and recommend appropriate charts for further exploration based on user interactions. A case study was first conducted to demonstrate the usage of ChartSeer in practice, followed by a controlled study to compare ChartSeer's performance with a baseline during EVA tasks. The results demonstrated that ChartSeer enables analysts to adequately understand current EVA status and advance their analysis by creating charts with increased coverage and visual encoding diversity.

EVis: Visually Analyzing Environmentally Driven Events

Earth scientists are increasingly employing time series data with multiple dimensions and high temporal resolution to study the impacts of climate and environmental changes on Earth's atmosphere, biosphere, hydrosphere, and lithosphere. However, the large number of variables and varying time scales of antecedent conditions contributing to natural phenomena hinder scientists from completing more than the most basic analyses. In this paper, we present EVis (Environmental Visualization), a new visual analytics prototype to help scientists analyze and explore recurring environmental events (e.g. rock fracture, landslides, heat waves, floods) and their relationships with high dimensional time series of continuous numeric environmental variables, such as ambient temperature and precipitation. EVis provides coordinated scatterplots, heatmaps, histograms, and RadViz for foundational analyses. These features allow users to interactively examine relationships between events and one, two, three, or more environmental variables. EVis also provides a novel visual analytics approach to allowing users to discover temporally lagging relationships related to antecedent conditions between events and multiple variables, a critical task in Earth sciences. In particular, this latter approach projects multivariate time series onto trajectories in a 2D space using RadViz, and clusters the trajectories for temporal pattern discovery. Our case studies with rock cracking data and interviews with domain experts from a range of sub-disciplines within Earth sciences illustrate the extensive applicability and usefulness of EVis.

Pyramid-based Scatterplots Sampling for Progressive and Streaming Data Visualization

We present a pyramid-based scatterplot sampling technique to avoid overplotting and enable progressive and streaming visualization of large data. Our technique is based on a multiresolution pyramid-based decomposition of the underlying density map and makes use of the density values in the pyramid to guide the sampling at each scale for preserving the relative data densities and outliers. We show that our technique is competitive in quality with state-of-the-art methods and runs faster by about an order of magnitude. Also, we have adapted it to deliver progressive and streaming data visualization by processing the data in chunks and updating the scatterplot areas with visible changes in the density map. A quantitative evaluation shows that our approach generates stable and faithful progressive samples that are comparable to the state-of-the-art method in preserving relative densities and superior to it in keeping outliers and stability when switching frames. We present two case studies that demonstrate the effectiveness of our approach for exploring large data.

Interactive Dimensionality Reduction for Comparative Analysis

Finding the similarities and differences between groups of datasets is a fundamental analysis task. For high-dimensional data, dimensionality reduction (DR) methods are often used to find the characteristics of each group. However, existing DR methods provide limited capability and flexibility for such comparative analysis as each method is designed only for a narrow analysis target, such as identifying factors that most differentiate groups. This paper presents an interactive DR framework where we integrate our new DR method, called ULCA (unified linear comparative analysis), with an interactive visual interface. ULCA unifies two DR schemes, discriminant analysis and contrastive learning, to support various comparative analysis tasks. To provide flexibility for comparative analysis, we develop an optimization algorithm that enables analysts to interactively refine ULCA results. Additionally, the interactive visualization interface facilitates interpretation and refinement of the ULCA results. We evaluate ULCA and the optimization algorithm to show their efficiency as well as present multiple case studies using real-world datasets to demonstrate the usefulness of this framework.

Joint t-SNE for Comparable Projections of Multiple High-Dimensional Datasets

We present Joint t-Stochastic Neighbor Embedding (Joint t-SNE), a technique to generate comparable projections of multiple high-dimensional datasets. Although t-SNE has been widely employed to visualize high-dimensional datasets from various domains, it is limited to projecting a single dataset. When a series of high-dimensional datasets, such as datasets changing over time, is projected independently using t-SNE, misaligned layouts are obtained. Even items with identical features across datasets are projected to different locations, making the technique unsuitable for comparison tasks. To tackle this problem, we introduce edge similarity, which captures the similarities between two adjacent time frames based on the Graphlet Frequency Distribution (GFD). We then integrate a novel loss term into the t-SNE loss function, which we call vector constraints, to preserve the vectors between projected points across the projections, allowing these points to serve as visual landmarks for direct comparisons between projections. Using synthetic datasets whose ground-truth structures are known, we show that Joint t-SNE outperforms existing techniques, including Dynamic t-SNE, in terms of local coherence error, Kullback-Leibler divergence, and neighborhood preservation. We also showcase a real-world use case to visualize and compare the activation of different layers of a neural network.

A Visualization Approach for Monitoring Order Processing in E-Commerce Warehouse

The efficiency of warehouses is vital to e-commerce. Fast order processing at the warehouses ensures timely deliveries and improves customer satisfaction. However, monitoring, analyzing, and manipulating order processing in the warehouses in real time are challenging for traditional methods due to the sheer volume of incoming orders, the fuzzy definition of delayed order patterns, and the complex decision-making of order handling priorities. In this paper, we adopt a data-driven approach and propose OrderMonitor, a visual analytics system that assists warehouse managers in analyzing and improving order processing efficiency in real time based on streaming warehouse event data. Specifically, the order processing pipeline is visualized with a novel pipeline design based on the sedimentation metaphor to facilitate real-time order monitoring and suggest potentially abnormal orders. We also design a novel visualization that depicts order timelines based on the Gantt charts and Marey's graphs. Such a visualization helps the managers gain insights into the performance of order processing and find major blockers for delayed orders. Furthermore, an evaluating view is provided to assist users in inspecting order details and assigning priorities to improve the processing performance. The effectiveness of OrderMonitor is evaluated with two case studies on a real-world warehouse dataset.

Adaptive dimensionality reduction for neural network-based online principal component analysis

"Principal Component Analysis" (PCA) is an established linear technique for dimensionality reduction. It performs an orthonormal transformation to replace possibly correlated variables with a smaller set of linearly independent variables, the so-called principal components, which capture a large portion of the data variance. The problem of finding the optimal number of principal components has been widely studied for offline PCA. However, when working with streaming data, the optimal number changes continuously. This requires to update both the principal components and the dimensionality in every timestep. While the continuous update of the principal components is widely studied, the available algorithms for dimensionality adjustment are limited to an increment of one in neural network-based and incremental PCA. Therefore, existing approaches cannot account for abrupt changes in the presented data. The contribution of this work is to enable in neural network-based PCA the continuous dimensionality adjustment by an arbitrary number without the necessity to learn all principal components. A novel algorithm is presented that utilizes several PCA characteristics to adaptivly update the optimal number of principal components for neural network-based PCA. A precise estimation of the required dimensionality reduces the computational effort while ensuring that the desired amount of variance is kept. The computational complexity of the proposed algorithm is investigated and it is benchmarked in an experimental study against other neural network-based and incremental PCA approaches where it produces highly competitive results.

A Visual Analytics Framework for Reviewing Multivariate Time-Series Data with Dimensionality Reduction

Data-driven problem solving in many real-world applications involves analysis of time-dependent multivariate data, for which dimensionality reduction (DR) methods are often used to uncover the intrinsic structure and features of the data. However, DR is usually applied to a subset of data that is either single-time-point multivariate or univariate time-series, resulting in the need to manually examine and correlate the DR results out of different data subsets. When the number of dimensions is large either in terms of the number of time points or attributes, this manual task becomes too tedious and infeasible. In this paper, we present MulTiDR, a new DR framework that enables processing of time-dependent multivariate data as a whole to provide a comprehensive overview of the data. With the framework, we employ DR in two steps. When treating the instances, time points, and attributes of the data as a 3D array, the first DR step reduces the three axes of the array to two, and the second DR step visualizes the data in a lower-dimensional space. In addition, by coupling with a contrastive learning method and interactive visualizations, our framework enhances analysts' ability to interpret DR results. We demonstrate the effectiveness of our framework with four case studies using real-world datasets.

Temporal scatterplots

Visualizing high-dimensional data on a 2D canvas is generally challenging. It becomes significantly more difficult when multiple time-steps are to be presented, as the visual clutter quickly increases. Moreover, the challenge to perceive the significant temporal evolution is even greater. In this paper, we present a method to plot temporal high-dimensional data in a static scatterplot; it uses the established PCA technique to project data from multiple time-steps. The key idea is to extend each individual displacement prior to applying PCA, so as to skew the projection process, and to set a projection plane that balances the directions of temporal change and spatial variance. We present numerous examples and various visual cues to highlight the data trajectories, and demonstrate the effectiveness of the method for visualizing temporal data.

Visual Analytics for Dimension Reduction and Cluster Analysis of High Dimensional Electronic Health Records

Recent advancement in EHR-based (Electronic Health Record) systems has resulted in producing data at an unprecedented rate. The complex, growing, and high-dimensional data available in EHRs creates great opportunities for machine learning techniques such as clustering. Cluster analysis often requires dimension reduction to achieve efficient processing time and mitigate the curse of dimensionality. Given a wide range of techniques for dimension reduction and cluster analysis, it is not straightforward to identify which combination of techniques from both families leads to the desired result. The ability to derive useful and precise insights from EHRs requires a deeper understanding of the data, intermediary results, configuration parameters, and analysis processes. Although these tasks are often tackled separately in existing studies, we present a visual analytics (VA) system, called Visual Analytics for Cluster Analysis and Dimension Reduction of High Dimensional Electronic Health Records (VALENCIA), to address the challenges of high-dimensional EHRs in a single system. VALENCIA brings a wide range of cluster analysis and dimension reduction techniques, integrate them seamlessly, and make them accessible to users through interactive visualizations. It offers a balanced distribution of processing load between users and the system to facilitate the performance of high-level cognitive tasks in such a way that would be difficult without the aid of a VA system. Through a real case study, we have demonstrated how VALENCIA can be used to analyze the healthcare administrative dataset stored at ICES. This research also highlights what needs to be considered in the future when developing VA systems that are designed to derive deep and novel insights into EHRs.

An Approach for Streaming Data Feature Extraction Based on Discrete Cosine Transform and Particle Swarm Optimization

Incremental feature extraction algorithms are designed to analyze large-scale data streams. Many of them suffer from high computational cost, time complexity, and data dependency, which adversely affects the processing of the data stream. With this motivation, this paper presents a novel incremental feature extraction approach based on the Discrete Cosine Transform (DCT) for the data stream. The proposed approach is separated into initial and sequential phases, and each phase uses a fixed-size windowing technique for processing the current samples. The initial phase is performed only on the first window to construct the initial model as a baseline. In this phase, normalization and DCT are applied to each sample in the window. Subsequently, the efficient feature subset is determined by a particle swarm optimization-based method. With the construction of the initial model, the sequential phase begins. The normalization and DCT processes are likewise applied to each sample. Afterward, the feature subset is selected according to the initial model. Finally, the k-nearest neighbor classifier is employed for classification. The approach is tested on the well-known streaming data sets and compared with state-of-the-art incremental feature extraction algorithms. The experimental studies demonstrate the proposed approach’s success in terms of recognition accuracy and learning time.

Supporting Analysis of Dimensionality Reduction Results with Contrastive Learning

Dimensionality reduction (DR) is frequently used for analyzing and visualizing high-dimensional data as it provides a good first glance of the data. However, to interpret the DR result for gaining useful insights from the data, it would take additional analysis effort such as identifying clusters and understanding their characteristics. While there are many automatic methods (e.g., density-based clustering methods) to identify clusters, effective methods for understanding a cluster's characteristics are still lacking. A cluster can be mostly characterized by its distribution of feature values. Reviewing the original feature values is not a straightforward task when the number of features is large. To address this challenge, we present a visual analytics method that effectively highlights the essential features of a cluster in a DR result. To extract the essential features, we introduce an enhanced usage of contrastive principal component analysis (cPCA). Our method, called ccPCA (contrasting clusters in PCA), can calculate each feature's relative contribution to the contrast between one cluster and other clusters. With ccPCA, we have created an interactive system including a scalable visualization of clusters' feature contributions. We demonstrate the effectiveness of our method and system with case studies using several publicly available datasets.