相关论文: MCbiF: Measuring Topological Autocorrelation in Mu…

This work introduces a number of algebraic topology approaches, such as multicomponent persistent homology, multi-level persistent homology and electrostatic persistence for the representation, characterization, and description of small…

Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…

We use methods from computational algebraic topology to study functional brain networks, in which nodes represent brain regions and weighted edges encode the similarity of fMRI time series from each region. With these tools, which allow one…

Bipartite graph embedding (BGE) maps nodes to compressed embedding vectors that can reflect the hidden topological features of the network, and learning high-quality BGE is crucial for facilitating downstream applications such as…

With the increasing prevalence of graph-structured data, multi-view graph clustering has been widely used in various downstream applications. Existing approaches primarily rely on a unified message passing mechanism, which significantly…

Technological advances facilitate the ability to acquire multimodal data, posing a challenge for recognition systems while also providing an opportunity to use the heterogeneous nature of the information to increase the generalization…

Topology and machine learning are two actively researched topics not only in condensed matter physics, but also in data science. Here, we propose the use of topological data analysis in unsupervised learning of the topological phase…

In the era of big data, data mining has become indispensable for uncovering hidden patterns and insights from vast and complex datasets. The integration of multimodal data sources further enhances its potential. Multimodal Federated…

We discuss topological aspects of cluster analysis and show that inferring the topological structure of a dataset before clustering it can considerably enhance cluster detection: theoretical arguments and empirical evidence show that…

We propose a topological learning algorithm for the estimation of the conditional dependency structure of large sets of random variables from sparse and noisy data. The algorithm, named Maximally Filtered Clique Forest (MFCF), produces a…

It is important to identify the discriminative features for high dimensional clustering. However, due to the lack of cluster labels, the regularization methods developed for supervised feature selection can not be directly applied. To learn…

Proteins are the most important biomolecules for living organisms. The understanding of protein structure, function, dynamics and transport is one of most challenging tasks in biological science. In the present work, persistent homology is,…

The clustering of unlabeled raw images is a daunting task, which has recently been approached with some success by deep learning methods. Here we propose an unsupervised clustering framework, which learns a deep neural network in an…

Co-clustering targets on grouping the samples (e.g., documents, users) and the features (e.g., words, ratings) simultaneously. It employs the dual relation and the bilateral information between the samples and features. In many realworld…

Hierarchical classification is significant for complex tasks by providing multi-granular predictions and encouraging better mistakes. As the label structure decides its performance, many existing approaches attempt to construct an excellent…

Subsequence clustering of multivariate time series is a useful tool for discovering repeated patterns in temporal data. Once these patterns have been discovered, seemingly complicated datasets can be interpreted as a temporal sequence of…

We investigate the adaptation and performance of modularity-based algorithms, designed in the scope of complex networks, to analyze the mesoscopic structure of correlation matrices. Using a multi-resolution analysis we are able to describe…

Many keypoint detection and description methods have been proposed for image matching or registration. While these methods demonstrate promising performance for single-modality image matching, they often struggle with multimodal data…

Matrix factorization (MF) is a simple collaborative filtering technique that achieves superior recommendation accuracy by decomposing the user-item interaction matrix into user and item latent matrices. Because the model typically learns…

In this paper, we introduce multiscale persistent functions for biomolecular structure characterization. The essential idea is to combine our multiscale rigidity functions with persistent homology analysis, so as to construct a series of…