相关论文: ToMAToMP: Robust and Multi-Parameter Topological C…

Graph-based clustering methods have demonstrated the effectiveness in various applications. Generally, existing graph-based clustering methods first construct a graph to represent the input data and then partition it to generate the…

Topological Data Analysis (TDA) offers a suite of computational tools that provide quantified shape features in high dimensional data that can be used by modern statistical and predictive machine learning (ML) models. In particular,…

We present Agglomerative Token Clustering (ATC), a novel token merging method that consistently outperforms previous token merging and pruning methods across image classification, image synthesis, and object detection & segmentation tasks.…

The problem of multimodal clustering arises whenever the data are gathered with several physically different sensors. Observations from different modalities are not necessarily aligned in the sense there there is no obvious way to associate…

In this paper, we propose a unified framework for sampling, clustering and embedding data points in semi-metric spaces. For a set of data points $\Omega=\{x_1, x_2, \ldots, x_n\}$ in a semi-metric space, we consider a complete graph with…

The topological patterns exhibited by many real-world networks motivate the development of topology-based methods for assessing the similarity of networks. However, extracting topological structure is difficult, especially for large and…

With rapidly increasing data, clustering algorithms are important tools for data analytics in modern research. They have been successfully applied to a wide range of domains; for instance, bioinformatics, speech recognition, and financial…

Motivated by applications in social and biological network analysis, we introduce a new form of agnostic clustering termed~\emph{motif correlation clustering}, which aims to minimize the cost of clustering errors associated with both edges…

Many complex systems in the real world can be characterized by attributed networks. To mine the potential information in these networks, deep embedded clustering, which obtains node representations and clusters simultaneously, has been paid…

Visual robot navigation within large-scale, semi-structured environments deals with various challenges such as computation intensive path planning algorithms or insufficient knowledge about traversable spaces. Moreover, many…

In this work, to facilitate the real-time processing of multi-scan registration error minimization on factor graphs, we devise a point cloud downsampling algorithm based on coreset extraction. This algorithm extracts a subset of the…

The Mapper algorithm, a technique within topological data analysis (TDA), constructs a simplified graphical representation of high-dimensional data to uncover its underlying shape and structural patterns. The algorithm has attracted…

Large language models (LLMs) have proven to be very capable, but access to frontier models currently relies on inference providers. This introduces trust challenges: how can we be sure that the provider is using the model configuration they…

Matrix valued data has become increasingly prevalent in many applications. Most of the existing clustering methods for this type of data are tailored to the mean model and do not account for the dependence structure of the features, which…

Density-based mode-seeking methods generate a \emph{density-ascending dependency} from low-density points towards higher-density neighbors. Current mode-seeking methods identify modes by breaking some dependency connections, but relying…

Topological Data Analysis (TDA) can broadly be described as a collection of data analysis methods that find structure in data. This includes: clustering, manifold estimation, nonlinear dimension reduction, mode estimation, ridge estimation…

Data stream clustering is a critical operation in various real-world applications, ranging from the Internet of Things (IoT) to social media and financial systems. Existing data stream clustering algorithms, while effective to varying…

Persistent (co)homology is a central construction in topological data analysis, where it is used to quantify prominence of features in data to produce stable descriptors suitable for downstream analysis. Persistence is challenging to…

Topological Data Analysis (TDA) has been applied with success to solve problems across many scientific disciplines. However, in the setting of a point cloud $X$ sampled from a shape $\mathcal{S}$ of low intrinsic dimension embedded within…

Clustering algorithms are pivotal in data analysis, enabling the organization of data into meaningful groups. However, individual clustering methods often exhibit inherent limitations and biases, preventing the development of a universal…