Related papers: Path Signatures on Lie Groups

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…

Time-series data exists in every corner of real-world systems and services, ranging from satellites in the sky to wearable devices on human bodies. Learning representations by extracting and inferring valuable information from these time…

A key overall goal of biomolecular simulations is the characterization of "mechanism" -- the pathways through configuration space of processes such as conformational transitions and binding. Some amount of heterogeneity is intrinsic to the…

Community detection for time series without prior knowledge poses an open challenge within complex networks theory. Traditional approaches begin by assessing time series correlations and maximizing modularity under diverse null models.…

The signature of a path, introduced by K.T. Chen [5] in $1954$, has been extensively studied in recent years. The $2010$ paper [12] of Hambly and Lyons showed that the signature is injective on the space of continuous finite-variation paths…

We provide a data-driven algorithm to classify market regimes for time series. We utilise the path signature, encoding time series into easy-to-describe objects, and provide a metric structure which establishes a connection between…

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…

We propose a novel generative model for multivariate discrete-time time series data. Drawing inspiration from the construction of neural spline flows, our algorithm incorporates linear transformations and the signature transform as a…

Online goal recognition in continuous domains poses two central challenges: efficiently encoding large trajectories and effectively comparing them. Recent work addresses these challenges by using custom state-space representations and…

The selection of algorithms is a crucial step in designing AI services for real-world time series classification use cases. Traditional methods such as neural architecture search, automated machine learning, combined algorithm selection,…

Paths of persistence diagrams provide a summary of the dynamic topological structure of a one-parameter family of metric spaces. These summaries can be used to study and characterize the dynamic shape of data such as swarming behavior in…

Coupled dynamical systems are frequently observed in nature, but often not well understood in terms of their causal structure without additional domain knowledge about the system. Especially when analyzing observational time series data of…

We introduce an approach based on moving frames for polygon recognition and symmetry detection. We present detailed algorithms for recognition of polygons modulo the special Euclidean, Euclidean, equi-affine, skewed-affine and similarity…

In stochastic analysis, a standard method to study a path is to work with its signature. This is a sequence of tensors of different order that encode information of the path in a compact form. When the path varies, such signatures…

We introduce the notions of tree-like path and tree-like equivalence between paths and prove that the latter is an equivalence relation for paths of finite length. We show that the equivalence classes form a group with some similarity to a…

Periodic and semi periodic patterns are very common in nature. In this paper we introduce a topological toolbox aiming in detecting and quantifying periodicity. The presented technique is of a general nature and may be employed wherever…

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…

The problem of detecting and quantifying the presence of symmetries in datasets is useful for model selection, generative modeling, and data analysis, amongst others. While existing methods for hard-coding transformations in neural networks…

Rough path theory provides one with the notion of signature, a graded family of tensors which characterise, up to a negligible equivalence class, and ordered stream of vector-valued data. In the last few years, use of the signature has…

Time series constitute a challenging data type for machine learning algorithms, due to their highly variable lengths and sparse labeling in practice. In this paper, we tackle this challenge by proposing an unsupervised method to learn…