Related papers: A multi-dimensional stream and its signature repre…
The signature of a path is a sequence of tensors which allows to uniquely reconstruct the path. By employing the geometric theory of nonlinear systems of ordinary differential equations, we find necessary and sufficient algebraic conditions…
Random walks are powerful tools to analyze spatial-temporal patterns produced by living organisms ranging from cells to humans. At the same time, it is evident that these patterns are not completely random but are results of a convolution…
This work is devoted to a certain class of probabilistic snapshots for elements of the observed data stream. We show you how one can control their probabilistic properties and we show some potential applications. Our solution can be used to…
Typically, for analysing and modelling social phenomena, networks are a convenient framework that allows for the representation of the interconnectivity of individuals. These networks are often considered transmission structures for…
The concept of signatures and expected signatures is vital in data science, especially for sequential data analysis. The signature transform, a Cartan type development, translates paths into high-dimensional feature vectors, capturing their…
We introduce features for massive data streams. These stream features can be thought of as "ordered moments" and generalize stream sketches from "moments of order one" to "ordered moments of arbitrary order". In analogy to classic moments,…
Anomaly detection is the process of identifying abnormal instances or events in data sets which deviate from the norm significantly. In this study, we propose a signatures based machine learning algorithm to detect rare or unexpected items…
In the context of controlled differential equations, the signature is the exponential function on paths. B. Hambly and T. Lyons proved that the signature of a bounded variation path is trivial if and only if the path is tree-like. We extend…
Recently it was proved that the group of rough paths modulo tree-like equivalence is isomorphic to the corresponding signature group through the signature map S (a generalized notion of taking iterated path integrals). However, the proof of…
The signature kernel is a positive definite kernel for sequential data. It inherits theoretical guarantees from stochastic analysis, has efficient algorithms for computation, and shows strong empirical performance. In this short survey…
We introduce a new technique to visualize complex flowing phenomena by using concepts from shape analysis. Our approach uses techniques that examine the intrinsic geometry of manifolds through their heat kernel, to obtain representations of…
The 'signature method' refers to a collection of feature extraction techniques for multivariate time series, derived from the theory of controlled differential equations. There is a great deal of flexibility as to how this method can be…
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…
Stream ciphers play important role in cryptography. In this paper we do a survey on stream ciphers.Various possible attacks are analyzed.
Stochastic line integrals provide a useful tool for quantitatively characterizing irreversibility and detailed balance violation in noise-driven dynamical systems. A particular realization is the stochastic area, recently studied in coupled…
In this article we introduce the insertion method for reconstructing the path from its signature, i.e. inverting the signature of a path. For this purpose, we prove that a converging upper bound exists for the difference between the…
Machine learning from data streams is an active and growing research area. Research on learning from streaming data typically makes strict assumptions linked to computational resource constraints, including requirements for stream mining…
The path signature, having enjoyed recent success in the machine learning community, is a theoretically-driven method for engineering features from irregular paths. On the other hand, graph neural networks (GNN), neural architectures for…
The aim of this article is to develop an explicit procedure that enables one to reconstruct any $C^1$ path (at natural parametrization) from its signature. We also explicitly quantify the distance between the reconstructed path and the…
In real-world contexts, sometimes data are available in form of Natural Data Streams, i.e. data characterized by a streaming nature, unbalanced distribution, data drift over a long time frame and strong correlation of samples in short time…