Related papers: Topological time-series analysis with delay-varian…
Topological data analysis (TDA) offers novel mathematical tools for deep learning. Inspired by Carlsson et al., this study designs topology-aware convolutional kernels that significantly improve speech recognition networks. Theoretically,…
We use tools from applied topology for feature selection on time series data. We develop a method for scoring the variables in a multivariate time series that reflects their contributions to the topological features of the corresponding…
Many complex networks, ranging from social to biological systems, exhibit structural patterns consistent with an underlying hyperbolic geometry. Revealing the dimensionality of this latent space can disentangle the structural complexity of…
We introduce a general framework for leveraging graph stream data for temporal prediction-based applications. Our proposed framework includes novel methods for learning an appropriate graph time-series representation, modeling and weighting…
In this paper, we investigate dynamic feature selection within multivariate time-series scenario, a common occurrence in clinical prediction monitoring where each feature corresponds to a bio-test result. Many existing feature selection…
A common problem in time series analysis is to predict dynamics with only scalar or partial observations of the underlying dynamical system. For data on a smooth compact manifold, Takens theorem proves a time delayed embedding of the…
Recent studies have actively employed persistent homology (PH), a topological data analysis technique, to analyze the topological information in time series data. Many successful studies have utilized graph representations of time series…
Analyzing large-scale time-series network data, such as social media and email communications, poses a significant challenge in understanding social dynamics, detecting anomalies, and predicting trends. In particular, the scalability of…
Machine learning algorithms are designed to capture complex relationships between features. In this context, the high dimensionality of data often results in poor model performance, with the risk of overfitting. Feature selection, the…
Topological phase of matter is now a mainstream of research in condensed matter physics, of which the classification, synthesis, and detection of topological states have brought excitements over the recent decade while remain incomplete…
We introduce a new framework to analyze shape descriptors that capture the geometric features of an ensemble of point clouds. At the core of our approach is the point of view that the data arises as sampled recordings from a metric…
Network embedding has recently emerged as a promising technique to embed nodes of a network into low-dimensional vectors. While fairly successful, most existing works focus on the embedding techniques for static networks. But in practice,…
We provide a method to identify system parameters of dynamical systems, called ID-ODE -- Inference by Differentiation and Observing Delay Embeddings. In this setting, we are given a dataset of trajectories from a dynamical system with…
Feature selection aims to identify the most pattern-discriminative feature subset. In prior literature, filter (e.g., backward elimination) and embedded (e.g., Lasso) methods have hyperparameters (e.g., top-K, score thresholding) and tie to…
Data quality is crucial for the successful training, generalization and performance of machine learning models. We propose to measure the quality of a subset concerning the dataset it represents, using topological data analysis techniques.…
This paper proposes a novel approach for detecting the topology of distribution networks based on the analysis of time series measurements. The time-based analysis approach draws on data from high-precision phasor measurement units (PMUs or…
Nowadays, the deployment of deep learning models on edge devices for addressing real-world classification problems is becoming more prevalent. Moreover, there is a growing popularity in the approach of early classification, a technique that…
Dynamic graphs refer to graphs whose structure dynamically changes over time. Despite the benefits of learning vertex representations (i.e., embeddings) for dynamic graphs, existing works merely view a dynamic graph as a sequence of changes…
In forecasting multiple time series, accounting for the individual features of each sequence can be challenging. To address this, modern deep learning methods for time series analysis combine a shared (global) model with local layers,…
Recently, methods have been developed to accurately predict the testing performance of a Deep Neural Network (DNN) on a particular task, given statistics of its underlying topological structure. However, further leveraging this newly found…