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

Cloud detection is an important preprocessing step for the precise application of optical satellite imagery. In this paper, we propose a deep learning based cloud detection method named multi-scale convolutional feature fusion (MSCFF) for…

We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…

Spectral clustering is a celebrated algorithm that partitions objects based on pairwise similarity information. While this approach has been successfully applied to a variety of domains, it comes with limitations. The reason is that there…

Summarizing topological information from datasets and maps defined on them is a central theme in topological data analysis. \textsf{Mapper}, a tool for such summarization, takes as input both a possibly high dimensional dataset and a map…

We study the convergence properties of the Gibbs Sampler in the context of posterior distributions arising from Bayesian analysis of conditionally Gaussian hierarchical models. We develop a multigrid approach to derive analytic expressions…

We study the persistent homology of both functional data on compact topological spaces and structural data presented as compact metric measure spaces. One of our goals is to define persistent homology so as to capture primarily properties…

3-D shape is important to chemistry, but how important? Machine learning works best when the inputs are simple and match the problem well. Chemistry datasets tend to be very small compared to those generally used in machine learning so we…

Persistent homology is a widely used tool in Topological Data Analysis that encodes multiscale topological information as a multi-set of points in the plane called a persistence diagram. It is difficult to apply statistical theory directly…

We present here a new method, MMF, for automatically segmenting cosmic structure into its basic components: clusters, filaments, and walls. Importantly, the segmentation is scale independent, so all structures are identified without…

As multipath components (MPCs) are experimentally observed to appear in clusters, cluster-based channel models have been focused in the wireless channel study. However, most of the MPC clustering algorithms for MIMO channels with delay and…

Given an unknown $\mathbb{R}^n$-valued function $f$ on a metric space $X$, can we approximate the persistent homology of $f$ from a finite sampling of $X$ with known pairwise distances and function values? This question has been answered in…

Many learning tasks represent responses as multivariate probability measures, requiring repeated computation of weighted barycenters in Wasserstein space. In multivariate settings, transport barycenters are often computationally demanding…

Compactly expressing large-scale datasets through Multivariate Functional Approximations (MFA) can be critically important for analysis and visualization to drive scientific discovery. Tackling such problems requires scalable data…

In this paper, we consider topological featurizations of data defined over simplicial complexes, like images and labeled graphs, obtained by convolving this data with various filters before computing persistence. Viewing a convolution…

Medical image analysis models can exhibit performance disparities across patient subgroups, threatening clinical safety and fairness. Existing methods typically address this issue by optimizing accuracy and fairness metrics for visible…

Discriminative Correlation Filters based tracking algorithms exploiting conventional handcrafted features have achieved impressive results both in terms of accuracy and robustness. Template handcrafted features have shown excellent…

Unsupervised learning has gained prominence in the big data era, offering a means to extract valuable insights from unlabeled datasets. Deep clustering has emerged as an important unsupervised category, aiming to exploit the non-linear…

Topological clustering, and its main algorithm ToMATo, is a clustering method from Topological Data Analysis (TDA) which has been applied successfully in several applications during the last few years. This is due to its high versatility,…

When approaching a clustering problem, choosing the right clustering algorithm and parameters is essential, as each clustering algorithm is proficient at finding clusters of a particular nature. Due to the unsupervised nature of clustering…

Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample---not necessarily a uniform one---of some high-dimensional…