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Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…
Data aggregation in Geographic Information Systems (GIS) is only marginally present in commercial systems nowadays, mostly through ad-hoc solutions. In this paper, we first present a formal model for representing spatial data. This model…
We present a generative model for representing and reasoning about the relationships among events in continuous time. We apply the model to the domain of networked and distributed computing environments where we fit the parameters of the…
We address the problem of comparing and aligning spatial point configurations in $\mathbb{R}^3$ arising from structured geometric patterns. Each pattern is decomposed into arms along which we define a normalized finite-difference operator…
Time series are ubiquitous in our data rich world. In what follows I will describe how ideas from dynamical systems and topological data analysis can be combined to gain insights from time-varying data. We will see several applications to…
In the paper, we consider the problem of discovering sequential patterns from event-based spatio-temporal data. The problem is defined as follows: for a set of event types $F$ and for a dataset of events instances $D$ (where each instance…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
Event data is present in a variety of domains such as electronic health records, daily living activities and web clickstream records. Current visualization methods to explore event data focus on discovering sequential patterns but present…
The kinetic data structure (KDS) framework is a powerful tool for maintaining various geometric configurations of continuously moving objects. In this work, we introduce the kinetic hourglass, a novel KDS implementation designed to compute…
We introduce and discuss (local) symmetries of geometric structures. These symmetries generalize the classical (locally) symmetric spaces to various other geometries. Our main tools are homogeneous Cartan geometries and their explicit…
Point cloud has drawn more and more research attention as well as real-world applications. However, many of these applications (e.g. autonomous driving and robotic manipulation) are actually based on sequential point clouds (i.e. four…
Noisy 3D point clouds arise in many applications. They may be due to errors when constructing a 3D model from images or simply to imprecise depth sensors. Point clouds can be given geometrical structure using graphs created from the…
We study the notion of geometric structures for toposes: This generalizes the notion of (X,G) manifolds. We give some applications to algebraic geometry
Data exchange is the problem of transforming data that is structured under a source schema into data structured under another schema, called the target schema, so that both the source and target data satisfy the relationship between the…
We explore geometric and topological properties of 3d surfaces swept by Poncelet triangles, as well as tangles formed by associated points.
We introduce a new technique for the efficient management of large sequences of multidimensional data, which takes advantage of regularities that arise in real-world datasets and supports different types of aggregation queries. More…
At present, state-of-the-art forecasting models are short of the ability to capture spatio-temporal dependency and synthesize global information at the stage of learning. To address this issue, in this paper, through the adaptive fuzzified…
We perform experimental studies on data structures that answer path median, path counting, and path reporting queries in weighted trees. These query problems generalize the well-known range median query problem in arrays, as well as the…
Recent advances in data collection and storage have allowed both researchers and industry alike to collect data in real time. Much of this data comes in the form of 'events', or timestamped interactions, such as email and social media…
Inspired by the classical fractional cascading technique, we introduce new techniques to speed up the following type of iterated search in 3D: The input is a graph $\mathbf{G}$ with bounded degree together with a set $H_v$ of 3D hyperplanes…