Matrix-based Representations Research Articles

Accurate Offline Asynchronous Detection of Individual Finger Movement From Intracranial Brain Signals Using a Novel Multiway Approach.

Asynchronous motor Brain Computer Interfacing (BCI) is characterized by the continuous decoding of intended muscular activity from brain signals. Such applications have gained widespread interest for enabling users to issue commands volitionally. In conventional motor BCIs features extracted from brain signals are concatenated into vector- or matrix-based (or one-/two-way) representations. Nevertheless, when accounting for the original multimodal or multiway signal structure, decoding performance has been shown to improve jointly with result interpretability. However, as multiway decoders are notorious for the extensive computational cost to train them, conventional ones are still preferred. To curb this limitation, we introduce a novel multiway classifier, called Block-Term Tensor Classifier that inherits the improved accuracy of multiway methods while providing fast training. We show that it can outperform state-of-the-art multiway and two-way Linear Discriminant Analysis classifiers in asynchronous detection of individual finger movements from intracranial recordings, an essential feature to achieve a sense of dexterity with hand prosthetics and exoskeletons.

Hybrid Graph Visualizations With ChordLink: Algorithms, Experiments, and Applications.

Many real-world networks are globally sparse but locally dense. Typical examples are social networks, biological networks, and information networks. This double structural nature makes it difficult to adopt a homogeneous visualization model that clearly conveys both an overview of the network and the internal structure of its communities at the same time. As a consequence, the use of hybrid visualizations has been proposed. For instance, NodeTrix combines node-link and matrix-based representations (Henry et al., 2007). In this article we describe ChordLink, a hybrid visualization model that embeds chord diagrams, used to represent dense subgraphs, into a node-link diagram, which shows the global network structure. The visualization makes it possible to interactively highlight the structure of a community while keeping the rest of the layout stable. We discuss the intriguing algorithmic challenges behind the ChordLink model, present a prototype system that implements it, and illustrate case studies on real-world networks.

Cross-covariance matrix: Time-shifted correlations for 3D action recognition

In this paper, we introduce cross-covariance to form Symmetric Positive Definite (SPD) matrix-based representations for 3D action recognition. The cross-covariance is generated by the correlational statistics between the time-shifted poses, which brings more informative features and time-order structure to improve the discriminative power on actions. Due to the special manifold structure, the cross-covariance is a totally different SPD matrix representation compared to covariance. In order to utilize such cross-covariance statistics while holding the covariance statistics, we devise a fashion of expression to mix them together as a larger SPD matrix benefiting from the Riemannian geometry. Further, we extend the symmetric cross-covariance into the non-symmetric versions, where the time-order information can be embodied in the related matrix structures. Thus, the derived SPD representations are able to improve the discriminative power of actions. In addition, our representations are easy to implement and to be extended by other prevalent techniques, such as kernel methods, metric learning, etc. Experimental results show that our proposed method efficiently promotes the performance of 3D action recognition tasks. In some public databases, our method outperforms the state-of-the-art methods which are based on other feature representations, kernel matrices, temporal hierarchical features, etc.

Knowledge Fusion via Joint Tensor and Matrix Factorization

We consider the task of knowledge fusion, an important aspect of cognitive intelligence, with the goal of combining part-of knowledge drawn from different sources. For this, entities and relations are cast into matrix-based representations. Unlike previous work on relation prediction, we consider the challenging setting of graphs with large amounts of completely separate connected components and no overlap between the training and test set entities. In order to address these challenges, we propose a novel cognitively inspired factorization method that jointly factorizes a subject–predicate–object tensor via RESCAL and a similarity matrix via matrix factorization. Our experimental results show that our method significantly outperforms several strong baseline models, including RESCAL and several TransE-style models. The proposed joint factorization of a subject–predicate–object tensor while applying matrix factorization to a similarity matrix obtains substantially higher average accuracy rates than previous approaches. This shows that it can successfully address the challenge of knowledge fusion of disconnected data.

Tensor Maps for Synchronizing Heterogeneous Shape Collections.

Establishing high-quality correspondence maps between geometric shapes has been shown to be the fundamental problem in managing geometric shape collections. Prior work has focused on computing efficient maps between pairs of shapes, and has shown a quantifiable benefit of joint map synchronization, where a collection of shapes are used to improve (denoise) the pairwise maps for consistency and correctness. However, these existing map synchronization techniques place very strong assumptions on the input shapes collection such as all the input shapes fall into the same category and/or the majority of the input pairwise maps are correct. In this paper, we present a multiple map synchronization approach that takes a heterogeneous shape collection as input and simultaneously outputs consistent dense pairwise shape maps. We achieve our goal by using a novel tensor-based representation for map synchronization, which is efficient and robust than all prior matrix-based representations. We demonstrate the usefulness of this approach across a wide range of geometric shape datasets and the applications in shape clustering and shape co-segmentation.

Implicitizing rational curves by the method of moving quadrics

A new technique for finding implicit matrix-based representations of rational curves in arbitrary dimension is introduced. It relies on the use of moving quadrics following curve parameterizations, providing a high-order extension of the implicit matrix representations built from their linear counterparts, the moving planes. The matrices we obtain offer new, more compact, implicit representations of rational curves. Their entries are filled by linear and quadratic forms in the space variables and their ranks drop exactly on the curve. Typically, for a general rational curve of degree d we obtain a matrix whose size is half of the size of the corresponding matrix obtained with the moving planes method. We illustrate the advantages of these new matrices with some examples, including the computation of the singularities of a rational curve.

Visual Analysis of Large Graphs Using (X,Y)-Clustering and Hybrid Visualizations

Many different approaches have been proposed for the challenging problem of visually analyzing large networks. Clustering is one of the most promising. In this paper, we propose a new clustering technique whose goal is that of producing both intracluster graphs and intercluster graph with desired topological properties. We formalize this concept in the (X,Y) -clustering framework, where Y is the class that defines the desired topological properties of intracluster graphs and X is the class that defines the desired topological properties of the intercluster graph. By exploiting this approach, hybrid visualization tools can effectively combine different node-link and matrix-based representations, allowing users to interactively explore the graph by expansion/contraction of clusters without loosing their mental map. As a proof of concept, we describe the system Visual Hybrid (X,Y)-clustering (VHYXY) that implements our approach and we present the results of case studies to the visual analysis of social networks.

MatrixExplorer: a Dual-Representation System to Explore Social Networks

MatrixExplorer is a network visualization system that uses two representations: node-link diagrams and matrices. Its design comes from a list of requirements formalized after several interviews and a participatory design session conducted with social science researchers. Although matrices are commonly used in social networks analysis, very few systems support the matrix-based representations to visualize and analyze networks. MatrixExplorer provides several novel features to support the exploration of social networks with a matrix-based representation, in addition to the standard interactive filtering and clustering functions. It provides tools to reorder (layout) matrices, to annotate and compare findings across different layouts and find consensus among several clusterings. MatrixExplorer also supports Node-link diagram views which are familiar to most users and remain a convenient way to publish or communicate exploration results. Matrix and node-link representations are kept synchronized at all stages of the exploration process.

Matrices or Node-Link Diagrams: Which Visual Representation is Better for Visualising Connectivity Models?

Adjacency matrices or DSMs (design structure matrices) and node-link diagrams are both visual representations of graphs, which are a common form of data in many disciplines. DSMs are used throughout the engineering community for various applications, such as process modelling or change prediction. However, outside this community, DSMs (and other matrix-based representations of graphs) are rarely applied and node-link diagrams are very popular. This paper will examine, which representation is more suitable for visualising graphs. For this purpose, several user experiments were conducted that aimed to answer this research question in the context of product models used, for example in engineering, but the results can be generalised to other applications. These experiments identify key factors on the readability of graph visualisations and confirm work on comparisons of different representations. This study widens the scope of readability comparisons between node-link and matrix-based representations by introducing new user tasks and replacing simulated, undirected graphs with directed ones employing real-world semantics.

On the Readability of Graphs Using Node-Link and Matrix-Based Representations: A Controlled Experiment and Statistical Analysis

In this article, we describe a taxonomy of generic graph related tasks along with a computer-based evaluation designed to assess the readability of two representations of graphs: matrix-based representations and node-link diagrams. This evaluation encompasses seven generic tasks and leads to insightful recommendations for the representation of graphs according to their size and density. Typically, we show that when graphs are bigger than twenty vertices, the matrix-based visualization outperforms node-link diagrams on most tasks. Only path finding is consistently in favor of node-link diagrams throughout the evaluation.