相关论文: Persistent Patterns in Eye Movements: A Topologica…

Topological data analysis (TDA) studies the shape patterns of data. Persistent homology is a widely used method in TDA that summarizes homological features of data at multiple scales and stores them in persistence diagrams (PDs). In this…

Persistent homology is a tool from Topological Data Analysis (TDA) used to summarize the topology underlying data. It can be conveniently represented through persistence diagrams. Observing a noisy signal, common strategies to infer its…

We propose a graph-based mechanism to extract rich-emotion bearing patterns, which fosters a deeper analysis of online emotional expressions, from a corpus. The patterns are then enriched with word embeddings and evaluated through several…

Emotion recognition is essential for applications in affective computing and behavioral prediction, but conventional systems relying on single-modality data often fail to capture the complexity of affective states. To address this…

We use topological data analysis to study neural population activity in the Sensorium 2023 dataset, which records responses from thousands of mouse visual cortex neurons to diverse video stimuli. For each video, we build frame-by-frame…

Machine learning has emerged as a powerful approach in materials discovery. Its major challenge is selecting features that create interpretable representations of materials, useful across multiple prediction tasks. We introduce an…

In this article, we introduce a Topological Data Analysis (TDA) pipeline for neural spike train data. Understanding how the brain transforms sensory information into perception and behavior requires analyzing coordinated neural population…

Persistent homology is a topological data analysis tool that has been widely generalized, extending its scope beyond the field of topology. Among its extensions, steady and ranging persistence were developed to study a wide variety of graph…

The existence of characteristic structure, or shape, in complex data sets has been recognized as increasingly important for mathematical data analysis. This realization has motivated the development of new tools such as persistent homology…

In this work, we develop a pipeline that associates Persistence Diagrams to digital data via the most appropriate filtration for the type of data considered. Using a grid search approach, this pipeline determines optimal representation…

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…

We propose a method, based on persistent homology, to uncover topological properties of a priori unknown covariates of neuron activity. Our input data consist of spike train measurements of a set of neurons of interest, a candidate list of…

This paper presents the first approach to visualize the importance of topological features that define classes of data. Topological features, with their ability to abstract the fundamental structure of complex data, are an integral…

Topological methods can provide a way of proposing new metrics and methods of scrutinising data, that otherwise may be overlooked. In this work, a method of quantifying the shape of data, via a topic called topological data analysis will be…

Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features (2000) as one varies a tuning parameter. Features with short…

High-quality training data is the foundation of machine learning and artificial intelligence, shaping how models learn and perform. Although much is known about what types of data are effective for training, the impact of the data's…

Data analysis that uses the output of topological data analysis as input for machine learning algorithms has been the subject of extensive research. This approach offers a means of capturing the global structure of data. Persistent homology…

We start with a simple introduction to topological data analysis where the most popular tool is called a persistent diagram. Briefly, a persistent diagram is a multiset of points in the plane describing the persistence of topological…

Topological statistics, in the form of persistence diagrams, are a class of shape descriptors that capture global structural information in data. The mapping from data structures to persistence diagrams is almost everywhere differentiable,…

In this paper, we exploit minimal sensing information gathered from biologically inspired sensor networks to perform exploration and mapping in an unknown environment. A probabilistic motion model of mobile sensing nodes, inspired by motion…