Related papers: Interpretable Classification of Time Series Using …
We introduce Explicit Neural Surfaces (ENS), an efficient smooth surface representation that directly encodes topology with a deformation field from a known base domain. We apply this representation to reconstruct explicit surfaces from…
Ensemble smoother (ES) has been widely used in various research fields to reduce the uncertainty of the system-of-interest. However, the commonly-adopted ES method that employs the Kalman formula, that is, ES$_\text{(K)}$, does not perform…
Univariate time series (UTS), where each timestamp records a single variable, serve as crucial indicators in web systems and cloud servers. Anomaly detection in UTS plays an essential role in both data mining and system reliability…
Persistent Homology (PH) is a fundamental tool in computational topology, designed to uncover the intrinsic geometric and topological features of data across multiple scales. Originating within the broader framework of Topological Data…
Persistent homology (PH) is one of the most popular methods in Topological Data Analysis. Even though PH has been used in many different types of applications, the reasons behind its success remain elusive; in particular, it is not known…
Persistent homology is a popular method for computing topological features of (metric) data. Standard approaches based on the \v{C}ech or Rips filtration are stable under small perturbations of the data, but highly sensitive to outliers.…
We propose a novel method for topological analysis of unweighted graphs which is based on \textit{persistent homology}. The proposed method maps the input graph to a complete weighted graph where the weighting function maps each edge to a…
A time-delay embedding (TDE), grounded in the framework of Takens's Theorem, provides a mechanism to represent and analyze the inherent dynamics of time-series data. Recently, topological data analysis (TDA) methods have been applied to…
We develop in this paper a theoretical framework for the topological study of time series data. Broadly speaking, we describe geometrical and topological properties of sliding window (or time-delay) embeddings, as seen through the lens of…
This paper presents a novel fusion of low-level approaches for dimensionality reduction into an effective approach for high-level objects in neuromorphic camera data called Inceptive Event Time-Surfaces (IETS). IETSs overcome several…
We revisit Allendoerfer-Weil's formula for the Euler characteristic of embedded hypersurfaces in constant sectional curvature manifolds, first taking some time to re-prove it while demonstrating techniques of [2] and then applying it to…
Early time series classification (eTSC) is the problem of classifying a time series after as few measurements as possible with the highest possible accuracy. The most critical issue of any eTSC method is to decide when enough data of a time…
Topological descriptors, such as the Euler characteristic function and the persistence diagram, have grown increasingly popular for representing complex data. Recent work showed that a carefully chosen set of these descriptors encodes all…
While generative models have shown promise in pediatric sleep analysis, the latent structure of their multimodal embeddings remains poorly understood. This work investigates session-wide diagnostic information contained in the sequences of…
Early and optimal identification of cardiac anomalies, especially Myocardial infarction (MCI) can aid the individual in obtaining prompt medical attention to mitigate the severity. Electrocardiogram (ECG) is a simple non-invasive…
Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a…
In recent years, the preliminary diagnosis of ADHD using EEG has attracted the attention from researchers. EEG, known for its expediency and efficiency, plays a pivotal role in the diagnosis and treatment of ADHD. However, the…
Information networks are becoming increasingly popular to capture complex relationships across various disciplines, such as social networks, citation networks, and biological networks. The primary challenge in this domain is measuring…
Time series shapelets are discriminative subsequences that have been recently found effective for time series clustering (TSC). The shapelets are convenient for interpreting the clusters. Thus, the main challenge for TSC is to discover…
Euler's elastica constitute an appealing variational image inpainting model. It minimises an energy that involves the total variation as well as the level line curvature. These components are transparent and make it attractive for shape…