Related papers: On a New Method of Storing a Variable Size Array
This paper derives new results for the analysis of nonlinear systems by extending contraction theory in the framework of vector distances. A new tool, vector contraction analysis utilizing a notion of the vector-valued norm which evidently…
In this paper, we distinguish between two kinds of compositional data sets: elementary and aggregate. This fact will help us to decide the choice of the weights to use in log interaction analysis of aggregate compositional vectors. We show…
Persistent Homology (PH) is a useful tool to study the underlying structure of a data set. Persistence Diagrams (PDs), which are 2D multisets of points, are a concise summary of the information found by studying the PH of a data set.…
Learning in the latent variable model is challenging in the presence of the complex data structure or the intractable latent variable. Previous variational autoencoders can be low effective due to the straightforward encoder-decoder…
Data Integration of heterogeneous data sources relies either on periodically transferring large amounts of data to a physical Data Warehouse or retrieving data from the sources on request only. The latter results in the creation of what is…
Agglomerative hierarchical clustering can be implemented with several strategies that differ in the way elements of a collection are grouped together to build a hierarchy of clusters. Here we introduce versatile linkage, a new infinite…
Modern data analysis increasingly requires identifying shared latent structure across multiple high-dimensional datasets. A commonly used model assumes that the data matrices are noisy observations of low-rank matrices with a shared…
Modern databases typically makes use of the Log Structured Merge-Tree for organizing data in indexes, which is a kind of disk-based data structure. It was proposed to efficiently handle frequent update queries (also called update intensive…
We present a data-structure for orthogonal range searching for random points in the plane. The new data-structure uses (in expectation) $O\bigl(n \log n ( \log \log n)^2 \bigr)$ space, and answers emptiness queries in constant time. As a…
A storage code is an assignment of symbols to the vertices of a connected graph $G(V,E)$ with the property that the value of each vertex is a function of the values of its neighbors, or more generally, of a certain neighborhood of the…
Feature selection is among the most important components because it not only helps enhance the classification accuracy, but also or even more important provides potential biomarker discovery. However, traditional multivariate methods is…
We present a new algorithm for clustering longitudinal data. Data of this type can be conceptualized as consisting of individuals and, for each such individual, observations of a time-dependent variable made at various times. Generically,…
Temporal graphs model relationships among entities over time. Recent studies applied temporal graphs to abstract complex systems such as continuous communication among participants of social networks. Often, the amount of data is larger…
Logs are essential for diagnosing failures and conducting retrospective studies, leading many software organizations to retain log messages for a long time. Nevertheless, the volume of generated log data grows rapidly as software systems…
In this paper, we introduce a study of prolongations of homogeneous vector bundles. We give an alternative approach for the prolongation. For a given homogeneous vector bundle E, we obtain a new homogeneous vector bundle. The homogeneous…
We propose a clustering-based approach for identifying coherent flow structures in continuous dynamical systems. We first treat a particle trajectory over a finite time interval as a high-dimensional data point and then cluster these data…
A novel unsupervised learning method is proposed in this paper for biclustering large-dimensional matrix-valued time series based on an entirely new latent two-way factor structure. Each block cluster is characterized by its own row and…
The simultaneous grouping of rows and columns is an important technique that is increasingly used in large-scale data analysis. In this paper, we present a novel co-clustering method using co-variables in its construction. It is based on a…
Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their $0$-dimensional homology. While this area has been substantially studied, we present a new approach to…
Matrix valued data has become increasingly prevalent in many applications. Most of the existing clustering methods for this type of data are tailored to the mean model and do not account for the dependence structure of the features, which…