Related papers: Clustering with UMAP: Why and How Connectivity Mat…

Reduced k-means clustering is a method for clustering objects in a low-dimensional subspace. The advantage of this method is that both clustering of objects and low-dimensional subspace reflecting the cluster structure are simultaneously…

This thesis consists of two topics related to computational geometry and one topic related to topological data analysis (TDA), which combines fields of computational geometry and algebraic topology for analyzing data. The first part studies…

Magnitude pruning is one of the mainstream methods in lightweight architecture design whose goal is to extract subnetworks with the largest weight connections. This method is known to be successful, but under very high pruning regimes, it…

The K-means one-step dimensionality reduction clustering method has made some progress in addressing the curse of dimensionality in clustering tasks. However, it combines the K-means clustering and dimensionality reduction processes for…

In this work, we revisit fast dimension reduction approaches, as with random projections and random sampling. Our goal is to summarize the data to decrease computational costs and memory footprint of subsequent analysis. Such dimension…

Graph clustering plays a pivotal role in unsupervised learning methods like spectral clustering, yet traditional methods for graph clustering often perpetuate bias through unfair graph constructions that may underrepresent some groups. The…

k nearest neighbor join (kNN join), designed to find k nearest neighbors from a dataset S for every object in another dataset R, is a primitive operation widely adopted by many data mining applications. As a combination of the k nearest…

In many networks such as transportation or communication networks, distance is certainly a relevant parameter. In addition, real-world examples suggest that when long-range links are existing, they usually connect to hubs-the well connected…

Recent work has established clear links between the generalization performance of trained neural networks and the geometry of their loss landscape near the local minima to which they converge. This suggests that qualitative and quantitative…

Dimensionality reduction methods, also known as projections, are frequently used for exploring multidimensional data in machine learning, data science, and information visualization. Among these, t-SNE and its variants have become very…

Subspace clustering methods face inherent scalability limits due to the $O(n^3)$ cost (with $n$ denoting the number of data samples) of constructing full $n\times n$ affinities and performing spectral decomposition. While deep…

Particle Swarm Optimization is a global optimizer in the sense that it has the ability to escape poor local optima. However, if the spread of information within the population is not adequately performed, premature convergence may occur.…

This paper, based on $k$-NN graph, presents symmetric $(k,j)$-NN graph $(1 \leq j < k)$, a brand new topology which could be adopted by a series of network-based structures. We show that the $k$ nearest neighbors of a node exert disparate…

This paper shows that dimensionality reduction methods such as UMAP and t-SNE, can be approximately recast as MAP inference methods corresponding to a model introduced in Ravuri et al. (2023), that describes the graph Laplacian (an estimate…

Recently, graph based nearest neighbor search gets more and more popular on large-scale retrieval tasks. The attractiveness of this type of approaches lies in its superior performance over most of the known nearest neighbor search…

The Renormalization Group is crucial for understanding systems across scales, including complex networks. Renormalizing networks via network geometry, a framework in which their topology is based on the location of nodes in a hidden metric…

This paper deals with the use of self-organizing protocols to improve the reliability of dynamic Peer-to-Peer (P2P) overlay networks. We present two approaches, that employ local knowledge of the 2nd neighborhood of nodes. The first scheme…

Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which…

Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…

Spatial clustering is a crucial field, finding universal use across criminology, pathology, and urban planning. However, most spatial clustering algorithms cannot pull information from nearby nodes and suffer performance drops when dealing…