Related papers: A Primer on the Signature Method in Machine Learni…
We introduce a new feature map for barcodes that arise in persistent homology computation. The main idea is to first realize each barcode as a path in a convenient vector space, and to then compute its path signature which takes values in…
Splines are central objects for the interpolation of discrete data via piecewise smooth paths. Their iterated-integral signature is an infinite collection of tensors which characterizes paths almost uniquely. We study truncations of this…
Over the past decade, the importance of the 1D signature which can be seen as a functional defined along a path, has been pivotal in both path-wise stochastic calculus and the analysis of time series data. By considering an image as a…
We develop two methods to reconstruct a path of bounded variation from its signature. The first method gives a simple and explicit expression of any axis path in terms of its signature, but it does not apply directlty to more general ones.…
The expected signature maps a collection of data streams to a lower dimensional representation, with a remarkable property: the resulting feature tensor can fully characterize the data generating distribution. This "model-free" embedding…
Signature verification has been one of the major researched areas in the field of computer vision. Many financial and legal organizations use signature verification as access control and authentication. Signature images are not rich in…
Deep hedging is a promising direction in quantitative finance, incorporating models and techniques from deep learning research. While giving excellent hedging strategies, models inherently requires careful treatment in designing…
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.…
Understanding protein dynamics are essential for deciphering protein functional mechanisms and developing molecular therapies. However, the complex high-dimensional dynamics and interatomic interactions of biological processes pose…
Matrix congruence extends naturally to the setting of tensors. We apply methods from tensor decomposition, algebraic geometry and numerical optimization to this group action. Given a tensor in the orbit of another tensor, we compute a…
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…
Handwritten signature verification poses a formidable challenge in biometrics and document authenticity. The objective is to ascertain the authenticity of a provided handwritten signature, distinguishing between genuine and forged ones.…
Machine learning on graphs is an important and ubiquitous task with applications ranging from drug design to friendship recommendation in social networks. The primary challenge in this domain is finding a way to represent, or encode, graph…
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…
Signature verification is an authentication technique that considers handwritten signature as a biometric. From a biometric perspective this project made use of automatic means through an integration of intelligent algorithms to perform…
Channel charting, an unsupervised learning method that learns a low-dimensional representation from channel information to preserve geometrical property of physical space of user equipments (UEs), has drawn many attentions from both…
In this paper, we present an algorithm that computes the topological signature for a given periodic motion sequence. Such signature consists of a vector obtained by persistent homology which captures the topological and geometric changes of…
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…
We are in the era of data analytics and data science which is on full bloom. There is abundance of all kinds of data for example biometrics based data, satellite images data, chip-seq data, social network data, sensor based data etc. from a…
Visual localization is a useful alternative to standard localization techniques. It works by utilizing cameras. In a typical scenario, features are extracted from captured images and compared with geo-referenced databases. Location…