相关论文: Path Signatures for Feature Extraction. An Introdu…

In this paper, we propose a novel set of features for offline writer identification based on the path signature approach, which provides a principled way to express information contained in a path. By extracting local pathlets from…

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…

The signature is a representation of a path as an infinite sequence of its iterated integrals. Under certain assumptions, the signature characterizes the path, up to translation and reparameterization. Therefore, a crucial question of…

The signature of a path is a sequence of tensors whose entries are iterated integrals, playing a key role in stochastic analysis and applications. The set of all signature tensors at a particular level gives rise to the universal signature…

Rough path theory is focused on capturing and making precise the interactions between highly oscillatory and non-linear systems. It draws on the analysis of LC Young and the geometric algebra of KT Chen. The concepts and the uniform…

Path signatures have been proposed as a powerful representation of paths that efficiently captures the path's analytic and geometric characteristics, having useful algebraic properties including fast concatenation of paths through tensor…

We introduce a proper notion of 2-dimensional signature for images. This object is inspired by the so-called rough paths theory, and it captures many essential features of a 2-dimensional object such as an image. It thus serves as a…

Central to rough path theory is the signature transform of a path, an infinite series of tensors given by the iterated integrals of the underlying path. The signature poses an effective way to capture sequentially ordered information,…

This paper explores the automated analysis of palmar features using machine learning techniques. We present a computer vision pipeline that extracts key characteristics from palm images, such as principal line structures, texture, and shape…

The signature is a fundamental object that describes paths (that is, continuous functions from an interval to a Euclidean space). Likewise, the expected signature provides a statistical description of the law of stochastic processes. We…

Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…

In Machine Learning, feature selection entails selecting a subset of the available features in a dataset to use for model development. There are many motivations for feature selection, it may result in better models, it may provide insight…

Iterated-integral signatures and log signatures are vectors calculated from a path that characterise its shape. They come from the theory of differential equations driven by rough paths, and also have applications in statistics and machine…

In graph theory and its practical networking applications, e.g., telecommunications and transportation, the problem of finding paths has particular importance. Selecting paths requires giving scores to the alternative solutions to drive a…

This paper establishes a comprehensive concentration theory for truncated signatures of Gaussian rough paths. The signature of a path, defined as the collection of all iterated integrals, provides a complete description of its geometric…

The aim of this article is to provide a simple sampling procedure to reconstruct any monotone path from its signature. For every N, we sample a lattice path of N steps with weights given by the coefficient of the corresponding word in the…

We bring the theory of rough paths to the study of non-parametric statistics on streamed data. We discuss the problem of regression where the input variable is a stream of information, and the dependent response is also (potentially) a…

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…

Pattern analysis often requires a pre-processing stage for extracting or selecting features in order to help the classification, prediction, or clustering stage discriminate or represent the data in a better way. The reason for this…

In the last decade, the concept of path signature has achieved significant success in data science applications. It offers a powerful set of features that effectively capture and describe the characteristics of paths or sequential data.…