Related papers: Constructing Time Series Shape Association Measure…
High dimensional time series datasets are becoming increasingly common in various fields such as economics, finance, meteorology, and neuroscience. Given this ubiquity of time series data, it is surprising that very few works on variable…
It is demonstrated how to generate time series with tailored nonlinearities by inducing well- defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of…
This work is focused on constructing space-time covariance functions through a hierarchical mixture approach that can serve as building blocks for capturing complex dependency structures. This hierarchical mixture approach provides a…
Studies on various facets of pattern classification is often imperative while working with multi-dimensional samples pertaining to diverse application scenarios. In this notion, weighted dimension-based distance measure has been one of 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…
Time series clustering is the process of grouping time series with respect to their similarity or characteristics. Previous approaches usually combine a specific distance measure for time series and a standard clustering method. However,…
Systems are commonly monitored for health and security through collection and streaming of multivariate time series. Advances in time series forecasting due to adoption of multilayer recurrent neural network architectures make it possible…
To the families of geometric measures of convex bodies (the area measures of Aleksandrov-Fenchel-Jessen, the curvature measures of Federer, and the recently discovered dual curvature measures) a new family is added. The new family of…
In the realm of time series analysis, accurately measuring similarity is crucial for applications such as forecasting, anomaly detection, and clustering. However, existing metrics often fail to capture the complex, multidimensional nature…
We propose a new class of measures for shaping time-dependent trajectories in dynamic optimization (DO). The proposed measures are analogous to risk measures used in stochastic optimization (SO) and are inspired by a recently-proposed…
Properties of weighted averages are studied for the general case that the individual measurements are subject to hidden correlations and have asymmetric statistical as well as systematic errors. Explicit expressions are derived for an…
Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…
We study the problem of similarity detection by sequence alignment with gaps, using a recently established theoretical framework based on the morphology of alignment paths. Alignments of sequences without mutual correlations are found to…
We consider a Markov chain on $\mathbb{R}^d$ with invariant measure $\mu$. We are interested in the rate of convergence of the empirical measures towards the invariant measure with respect to various dual distances, including in particular…
We present a new method for embedding a causal set into an interval of Minkowski spacetime. The method uses spacetime volumes for causally related elements to define causal set analogs of Minkowski inner products. These are used to…
Modeling heterogeneous correlated time series requires the ability to learn hidden dynamic relationships between component time series with possibly varying periodicities and generative processes. To address this challenge, we formulate and…
Statistically simulated time series of wave parameters are required for many coastal and offshore engineering applications, often at the resolution of approximately one hour. Various studies have relied on autoregressive moving-average…
A time series is a sequence of data items; typical examples are streams of temperature measurements, stock ticker data, or gestures recorded with modern virtual reality motion controllers. Quite some research has been devoted to comparing…
We investigate the limitations of length measurements by accelerated observers in Minkowski spacetime brought about via the hypothesis of locality, namely, the assumption that an accelerated observer at each instant is equivalent to an…
Network theory and inverse modeling are two standard tools of applied physics, whose combination is needed when studying the dynamical organization of spatially distributed systems from indirect measurements. However, the associated…