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Many application areas collect unstructured trajectory data. In subtrajectory clustering, one is interested to find patterns in this data using a hybrid combination of segmentation and clustering. We analyze two variants of this problem…

Computational Geometry · Computer Science 2025-04-25 Jacobus Conradi , Anne Driemel

Spectral clustering is one of the most popular clustering algorithms that has stood the test of time. It is simple to describe, can be implemented using standard linear algebra, and often finds better clusters than traditional clustering…

Machine Learning · Computer Science 2023-05-12 Timothy Chu , Gary Miller , Noel Walkington

Spectral clustering (SC) and graph-based semi-supervised learning (SSL) algorithms are sensitive to how graphs are constructed from data. In particular if the data has proximal and unbalanced clusters these algorithms can lead to poor…

Machine Learning · Statistics 2013-02-22 Jing Qian , Venkatesh Saligrama

Clustering is one of the most crucial problems in unsupervised learning, and the well-known $k$-means clustering algorithm has been shown to be implementable on a quantum computer with a significant speedup. However, many clustering…

Quantum Physics · Physics 2023-01-03 Qingyu Li , Yuhan Huang , Shan Jin , Xiaokai Hou , Xiaoting Wang

The neural ordinary differential equation (neural ODE) model has attracted increasing attention in time series analysis for its capability to process irregular time steps, i.e., data are not observed over equally-spaced time intervals. In…

Machine Learning · Computer Science 2021-07-23 Mingyuan Bai , S. T. Boris Choy , Junping Zhang , Junbin Gao

Clustering, as an unsupervised technique, plays a pivotal role in various data analysis applications. Among clustering algorithms, Spectral Clustering on Euclidean Spaces has been extensively studied. However, with the rapid evolution of…

Machine Learning · Computer Science 2024-12-09 Sagar Ghosh , Swagatam Das

We consider the problem of approximate $K$-means clustering with outliers and side information provided by same-cluster queries and possibly noisy answers. Our solution shows that, under some mild assumptions on the smallest cluster size,…

Machine Learning · Statistics 2018-11-13 I Chien , Chao Pan , Olgica Milenkovic

We present a structural clustering algorithm for large-scale datasets of small labeled graphs, utilizing a frequent subgraph sampling strategy. A set of representatives provides an intuitive description of each cluster, supports the…

Databases · Computer Science 2016-10-03 Till Schäfer , Petra Mutzel

Clustering is an important technique for identifying structural information in large-scale data analysis, where the underlying dataset may be too large to store. In many applications, recent data can provide more accurate information and…

Data Structures and Algorithms · Computer Science 2023-11-02 David P. Woodruff , Peilin Zhong , Samson Zhou

Spectral clustering is one of the most popular clustering methods. However, how to balance the efficiency and effectiveness of the large-scale spectral clustering with limited computing resources has not been properly solved for a long…

Machine Learning · Computer Science 2022-07-12 Hongmin Li , Xiucai Ye , Akira Imakura , Tetsuya Sakurai

Graph-Laplacians and their spectral embeddings play an important role in multiple areas of machine learning. This paper is focused on graph-Laplacian dimension reduction for the spectral clustering of data as a primary application. Spectral…

Machine Learning · Computer Science 2021-09-08 Vladimir Druskin , Alexander V. Mamonov , Mikhail Zaslavsky

Motivated by many applications, we study clustering with a faulty oracle. In this problem, there are $n$ items belonging to $k$ unknown clusters, and the algorithm is allowed to ask the oracle whether two items belong to the same cluster or…

Machine Learning · Computer Science 2022-07-13 Jinghui Xia , Zengfeng Huang

Spectral clustering is a popular method for community detection in network graphs: starting from a matrix representation of the graph, the nodes are clustered on a low dimensional projection obtained from a truncated spectral decomposition…

Machine Learning · Statistics 2022-08-10 Francesco Sanna Passino , Nicholas A. Heard , Patrick Rubin-Delanchy

Ashtiani et al. (NIPS 2016) introduced a semi-supervised framework for clustering (SSAC) where a learner is allowed to make same-cluster queries. More specifically, in their model, there is a query oracle that answers queries of the form…

Data Structures and Algorithms · Computer Science 2017-12-20 Nir Ailon , Anup Bhattacharya , Ragesh Jaiswal

Spectral clustering is sensitive to how graphs are constructed from data particularly when proximal and imbalanced clusters are present. We show that Ratio-Cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced data…

Machine Learning · Statistics 2013-09-11 Jing Qian , Venkatesh Saligrama

We present an algorithm that takes as input an $n$-vertex planar graph $G$ and a $k$-vertex pattern graph $P$, and computes the number of (induced) copies of $P$ in $G$ in $2^{O(k/\log k)}n^{O(1)}$ time. If $P$ is a matching, independent…

Data Structures and Algorithms · Computer Science 2019-04-26 Jesper Nederlof

Patchwork learning arises as a new and challenging data collection paradigm where both samples and features are observed in fragmented subsets. Due to technological limits, measurement expense, or multimodal data integration, such patchwork…

Methodology · Statistics 2024-06-21 Lili Zheng , Andersen Chang , Genevera I. Allen

Spectral clustering is one of the most widely used techniques for extracting the underlying global structure of a data set. Compressed sensing and matrix completion have emerged as prevailing methods for efficiently recovering sparse and…

Numerical Analysis · Mathematics 2010-11-05 Blake Hunter , Thomas Strohmer

We build upon recent advances in graph signal processing to propose a faster spectral clustering algorithm. Indeed, classical spectral clustering is based on the computation of the first k eigenvectors of the similarity matrix' Laplacian,…

Social and Information Networks · Computer Science 2015-09-30 Nicolas Tremblay , Gilles Puy , Pierre Borgnat , Remi Gribonval , Pierre Vandergheynst

Spectral clustering is a well-known technique which identifies $k$ clusters in an undirected graph with weight matrix $W\in\mathbb{R}^{n\times n}$ by exploiting its graph Laplacian $L(W)$, whose eigenvalues $0=\lambda_1\leq \lambda_2 \leq…

Numerical Analysis · Mathematics 2023-06-08 Nicola Guglielmi , Stefano Sicilia