Related papers: Analysing Multiscale Clusterings with Persistent H…

Persistent homology is a method for computing the topological features present in a given data. Recently, there has been much interest in the integration of persistent homology as a computational step in neural networks or deep learning. In…

Persistent homology is a powerful mathematical tool that summarizes useful information about the shape of data allowing one to detect persistent topological features while one adjusts the resolution. However, the computation of such…

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…

Spectral clustering has gained importance in recent years due to its ability to cluster complex data as it requires only pairwise similarity among data points with its ease of implementation. The central point in spectral clustering is the…

Convection is a well-studied topic in fluid dynamics, yet it is less understood in the context of networks flows. Here, we incorporate techniques from topological data analysis (namely, persistent homology) to automate the detection and…

The increasing nature of World Wide Web has imposed great challenges for researchers in improving the search efficiency over the internet. Now days web document clustering has become an important research topic to provide most relevant…

Typically clustering algorithms provide clustering solutions with prespecified number of clusters. The lack of a priori knowledge on the true number of underlying clusters in the dataset makes it important to have a metric to compare the…

We analyze the structure and connectivity of the distinct morphologies that define the Cosmic Web. With the help of our Multiscale Morphology Filter (MMF), we dissect the matter distribution of a cosmological $\Lambda$CDM N-body computer…

We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…

A wide range of Bayesian models have been proposed for data that is divided hierarchically into groups. These models aim to cluster the data at different levels of grouping, by assigning a mixture component to each datapoint, and a mixture…

The persistence barcode is a topological descriptor of data that plays a fundamental role in topological data analysis. Given a filtration of data, the persistence barcode tracks the evolution of its homology groups. In this paper, we…

Multi-view clustering has attracted growing attention owing to its capabilities of aggregating information from various sources and its promising horizons in public affairs. Up till now, many advanced approaches have been proposed in recent…

Bilateral filtering (BF) is one of the most classical denoising filters, however, the manually initialized filtering kernel hampers its adaptivity across images with various characteristics. To deal with image variation (i.e.,…

We introduce a novel set of observables associated to the rapidly developing field of persistent homology for the quantitative characterization of nuclear collisions and their evolution. Persistent homology allows for the identification of…

Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such…

We present an approach to model-based hierarchical clustering by formulating an objective function based on a Bayesian analysis. This model organizes the data into a cluster hierarchy while specifying a complex feature-set partitioning that…

Persistent homology has recently emerged as a powerful technique in topological data analysis for analyzing the emergence and disappearance of topological features throughout a filtered space, shown via persistence diagrams. Additionally,…

Persistent homology is a popular computational tool for analyzing the topology of point clouds, such as the presence of loops or voids. However, many real-world datasets with low intrinsic dimensionality reside in an ambient space of much…

The goal of fair clustering is to find clusters such that the proportion of sensitive attributes (e.g., gender, race, etc.) in each cluster is similar to that of the entire dataset. Various fair clustering algorithms have been proposed that…

In online clustering problems, there is often a large amount of uncertainty over possible cluster assignments that cannot be resolved until more data are observed. This difficulty is compounded when clusters follow complex distributions, as…