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

This paper studies the homotopy-type of bi-filtrations of compact manifolds induced as the pre-image of filtrations of the plane for generic smooth functions f : M --> R^2. The primary goal of the paper is to allow for a simple description…

Understanding the response of an output variable to multi-dimensional inputs lies at the heart of many data exploration endeavours. Topology-based methods, in particular Morse theory and persistent homology, provide a useful framework for…

We present a scalable Bayesian framework for the analysis of confocal fluorescence spectroscopy data, addressing key limitations in traditional fluorescence correlation spectroscopy methods. Our framework captures molecular motion,…

Persistent homology is a common technique in topological data analysis providing geometrical and topological information about the sample space. All this information, known as topological features, is summarized in persistence diagrams, and…

Interacting, self-propelled particles such as epithelial cells can dynamically self-organize into complex multicellular patterns, which are challenging to classify without a priori information. Classically, different phases and phase…

Different cell types aggregate and sort into hierarchical architectures during the formation of animal tissues. The resulting spatial organization depends (in part) on the strength of adhesion of one cell type to itself relative to other…

The machinery of topological data analysis becomes increasingly popular in a broad range of machine learning tasks, ranging from anomaly detection and manifold learning to graph classification. Persistent homology is one of the key…

Multi-view subspace clustering aims to discover the inherent structure of data by fusing multiple views of complementary information. Most existing methods first extract multiple types of handcrafted features and then learn a joint affinity…

Models of High-level Computation (MHCs) provide effective means to describe complex real-world computing systems because they offer formal foundations for the specification of interacting computing devices, as opposed to describing…

Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one-parameter persistent homology have been established to…

Motivated by applications in community detection and dense subgraph discovery, we consider new clustering objectives in hypergraphs and bipartite graphs. These objectives are parameterized by one or more resolution parameters in order to…

The text clustering technique is an unsupervised text mining method which are used to partition a huge amount of text documents into groups. It has been reported that text clustering algorithms are hard to achieve better performance than…

Understanding structure-property relationships in complex materials requires integrating complementary measurements across multiple length scales. Here we propose an interpretable "multimodal" machine learning framework that unifies…

The learning and aggregation of multi-scale features are essential in empowering neural networks to capture the fine-grained geometric details in the point cloud upsampling task. Most existing approaches extract multi-scale features from a…

Let a cluster (network) of sensors be connected by the communication links, each link having a capacity upper bound. Each sensor observes a discrete random variable in private and one sensor serves as a cluster header or sink. Here, we…

In the theory of persistent homology, a well known duality relates the barcodes of the absolute homology and relative cohomology of a one-parameter simplicial filtration. Motivated by the problem of computing free presentations of the…

In topological data analysis, persistent homology is used to study the "shape of data". Persistent homology computations are completely characterized by a set of intervals called a bar code. It is often said that the long intervals…

Subspace clustering has become widely adopted for the unsupervised analysis of hyperspectral images (HSIs). Recent model-aware deep subspace clustering methods often use a two-stage framework, involving the calculation of a…

Correlation clustering is a central topic in unsupervised learning, with many applications in ML and data mining. In correlation clustering, one receives as input a signed graph and the goal is to partition it to minimize the number of…

Hyper-Connections (HC) generalizes residual connections by introducing dynamic residual matrices that mix information across multiple residual streams, accelerating convergence in deep neural networks. However, unconstrained residual…