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

Persistent homology has emerged as a popular technique for the topological simplification of big data, including biomolecular data. Multidimensional persistence bears considerable promise to bridge the gap between geometry and topology.…

Semi-supervised clustering is the task of clustering data points into clusters where only a fraction of the points are labelled. The true number of clusters in the data is often unknown and most models require this parameter as an input.…

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…

Clustering multivariate binary data is of interest in many scientific fields, including ecology, biomedicine, and social policy. Beyond heuristic clustering algorithms, such data can be modelled using multivariate Bernoulli mixture models.…

This article introduces an algorithm to compute the persistent homology of a filtered complex with various coefficient fields in a single matrix reduction. The algorithm is output-sensitive in the total number of distinct persistent…

Multi-parameter persistent homology naturally arises in applications of persistent topology to data that come with extra information depending on additional parameters, like for example time series data. We introduce the concept of a…

One of the main challenges in data mining is choosing the optimal number of clusters without prior information. Notably, existing methods are usually in the philosophy of cluster validation and hence have underlying assumptions on data…

Minkowski functionals and Shapefinders shed light on the connectedness of large-scale structure by determining its topology and morphology. We use a sophisticated code, SURFGEN2, to measure the Minkowski functionals and Shapefinders of…

In this paper, we propose a novel semi-supervised feature selection framework by mining correlations among multiple tasks and apply it to different multimedia applications. Instead of independently computing the importance of features for…

Convolutional neural networks can be trained to perform histology slide classification using weak annotations with multiple instance learning (MIL). However, given the paucity of labeled histology data, direct application of MIL can easily…

We present a novel hybrid algorithm for Bayesian network structure learning, called H2PC. It first reconstructs the skeleton of a Bayesian network and then performs a Bayesian-scoring greedy hill-climbing search to orient the edges. The…

The following article is an application of commutative algebra to the study of multiparameter persistent homology in topological data analysis. In particular, the theory of finite free resolutions of modules over polynomial rings is applied…

Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically -- as long as the algorithm does not…

Multiple clustering aims at exploring alternative clusterings to organize the data into meaningful groups from different perspectives. Existing multiple clustering algorithms are designed for single-view data. We assume that the…

Community detection algorithms have been widely used to study the organization of complex systems like the brain. A principal appeal of these techniques is their ability to identify a partition of brain regions (or nodes) into communities,…

White matter fiber clustering (WMFC) enables parcellation of white matter tractography for applications such as disease classification and anatomical tract segmentation. However, the lack of ground truth and the ambiguity of fiber data (the…

Clustering can be used to extract insights from data or to verify some of the assumptions held by the domain experts, namely data segmentation. In the literature, few methods can be applied in clustering qualitative values using the context…

Persistence diagrams are important descriptors in Topological Data Analysis. Due to the nonlinearity of the space of persistence diagrams equipped with their {\em diagram distances}, most of the recent attempts at using persistence diagrams…

Multifractal analysis (MFA) provides a framework for the global characterization of image textures by describing the spatial fluctuations of their local regularity based on the multifractal spectrum. Several works have shown the interest of…

The integration of Unmanned Aerial Vehicles(UAVs) into Intelligent Transportation Systems (ITS) offers synoptic visibility for traffic monitoring, yet scalable deployment is hindered by trajectory fragmentation, where vehicle identity…