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Embedded topic models are able to learn interpretable topics even with large and heavy-tailed vocabularies. However, they generally hold the Euclidean embedding space assumption, leading to a basic limitation in capturing hierarchical…
In any other circumstance, it might make sense to define the extent of the terrain (Data Science) first, and then locate and describe the landmarks (Principles). But this data revolution we are experiencing defies a cadastral survey. Areas…
The large size and fast growth of data repositories, such as data lakes, has spurred the need for data discovery to help analysts find related data. The problem has become challenging as (i) a user typically does not know what datasets…
Here, the structural symmetries of a hypergraph are represented through equivalence relations on the vertex set of the hypergraph. A matrix associated with the hypergraph may not reflect a specific structural symmetry. In the context of a…
In this work, we study the correlation between attribute sets and the occurrence of dense subgraphs in large attributed graphs, a task we call structural correlation pattern mining. A structural correlation pattern is a dense subgraph…
Repetition is a basic indicator of musical structure. This study introduces new algorithms for identifying musical phrases based on repetition. Phrases combine to form sections yielding a two-level hierarchical structure. Automatically…
Unlike image or text domains that benefit from an abundance of large-scale datasets, point cloud learning techniques frequently encounter limitations due to the scarcity of extensive datasets. To overcome this limitation, we present…
We present an approach to statistical data modeling and exploratory data analysis called `LP Statistical Data Science.' It aims to generalize and unify traditional and novel statistical measures, methods, and exploratory tools. This article…
Topological Data Analysis is a recent and fast growing field providing a set of new topological and geometric tools to infer relevant features for possibly complex data. This paper is a brief introduction, through a few selected topics, to…
High-order phenomena play crucial roles in many systems of interest, but their analysis is often highly nontrivial. There is a rich literature providing a number of alternative information-theoretic quantities capturing high-order…
Despite the remarkable success of large large-scale neural networks, we still lack unified notation for thinking about and describing their representational spaces. We lack methods to reliably describe how their representations are…
Anomalies are occurrences in a dataset that are in some way unusual and do not fit the general patterns. The concept of the anomaly is typically ill-defined and perceived as vague and domain-dependent. Moreover, despite some 250 years of…
Hypergraphs provide a natural way to represent polyadic relationships in network data. For large hypergraphs, it is often difficult to visually detect structures within the data. Recently, a scalable polygon-based visualization approach was…
A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies…
A growing number of applications that generate massive streams of data need intelligent data processing and online analysis. Real-time surveillance systems, telecommunication systems, sensor networks and other dynamic environments are such…
The increasing power of computer technology does not dispense with the need to extract meaningful in- formation out of data sets of ever growing size, and indeed typically exacerbates the complexity of this task. To tackle this general…
Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that…
The data science revolution has led to an increased interest in the practice of data analysis. While much has been written about statistical thinking, a complementary form of thinking that appears in the practice of data analysis is design…
Structural analysis is a method for verifying equation-oriented models in the design of industrial systems. Existing structural analysis methods need flattening of the hierarchical models into an equation system for analysis. However, the…
A network is a typical expressive form of representing complex systems in terms of vertices and links, in which the pattern of interactions amongst components of the network is intricate. The network can be static that does not change over…