Related papers: Path Signatures on Lie Groups
In this paper, we propose a novel space-time geometric representation of human landmark configurations and derive tools for comparison and classification. We model the temporal evolution of landmarks as parametrized trajectories on the…
The continued digitization of societal processes translates into a proliferation of time series data that cover applications such as fraud detection, intrusion detection, and energy management, where anomaly detection is often essential to…
Signed graphs are graphs with signed edges. They are commonly used to represent positive and negative relationships in social networks. While balance theory and clusterizable graphs deal with signed graphs to represent social interactions,…
Permutations on a set, endowed with function composition, build a group called a symmetric group. In addition to their algebraic structure, symmetric groups have two metrics that are of particular interest to us here: the Cayley distance…
Motion is an important signal for agents in dynamic environments, but learning to represent motion from unlabeled video is a difficult and underconstrained problem. We propose a model of motion based on elementary group properties of…
The characterization of the Hamiltonian parameters defining a quantum walk is of paramount importance when performing a variety of tasks, from quantum communication to computation. When dealing with physical implementations of quantum…
Parallel transport, or path development, provides a rich characterization of paths which preserves the underlying algebraic structure of concatenation. The path signature is universal among such maps: any (translation-invariant) parallel…
Analyzing the temporal behavior of nodes in time-varying graphs is useful for many applications such as targeted advertising, community evolution and outlier detection. In this paper, we present a novel approach, STWalk, for learning…
We present an overview of characteristic identities for Lie algebras and superalgebras. We outline methods that employ these characteristic identities to deduce matrix elements of finite dimensional representations. To demonstrate the…
We present an algorithm to compute path homology for simple digraphs, and use it to topologically analyze various small digraphs en route to an analysis of complex temporal networks which exhibit such digraphs as underlying motifs. The…
Unsupervised clustering of temporal data is both challenging and crucial in machine learning. In this paper, we show that neither traditional clustering methods, time series specific or even deep learning-based alternatives generalise well…
In this paper we put the visibility transformation on a clear theoretical footing and show that this transform is able to embed the effect of the absolute position of the data stream into signature features in a unified and efficient way.…
We present Euler Characteristic Surfaces as a multiscale spatiotemporal topological summary of time series data encapsulating the topology of the system at different time instants and length scales. Euler Characteristic Surfaces with an…
Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such…
It is confirmed in this work that the graph isomorphism can be tested in polynomial time, which resolves a longstanding problem in the theory of computation. The contributions are in three phases as follows. 1. A description graph…
The growing popularity of wearable sensors has generated large quantities of temporal physiological and activity data. Ability to analyze this data offers new opportunities for real-time health monitoring and forecasting. However, temporal…
Deep time series metric learning is challenging due to the difficult trade-off between temporal invariance to nonlinear distortion and discriminative power in identifying non-matching sequences. This paper proposes a novel neural…
A profile from the Argo ocean observation array is a sequence of three-dimensional vectors composed of pressure, salinity, and temperature, appearing as a continuous curve in three-dimensional space. The shape of this curve is faithfully…
Traditionally stationarity refers to shift invariance of the distribution of a stochastic process. In this paper, we rediscover stationarity as a path property instead of a distributional property. More precisely, we characterize a set of…
We propose Path Signatures Logistic Regression (PSLR), a semi-parametric framework for classifying vector-valued functional data with scalar covariates. Classical functional logistic regression models rely on linear assumptions and fixed…