Related papers: Robust Multi-Manifold Clustering via Simplex Paths
In this paper, we propose a method to cluster multiple intersected manifolds. The algorithm chooses several landmark nodes randomly and then checks whether there is an angle constrained path between each landmark node and every other node…
In this work we study statistical properties of graph-based algorithms for multi-manifold clustering (MMC). In MMC the goal is to retrieve the multi-manifold structure underlying a given Euclidean data set when this one is assumed to be…
We present massively parallel (MPC) algorithms and hardness of approximation results for computing Single-Linkage Clustering of $n$ input $d$-dimensional vectors under Hamming, $\ell_1, \ell_2$ and $\ell_\infty$ distances. All our…
The Massive Parallel Computation (MPC) model is a theoretical framework for popular parallel and distributed platforms such as MapReduce, Hadoop, or Spark. We consider the task of computing a large matching or small vertex cover in this…
A novel multi-resolution cluster detection (MCD) method is proposed to identify irregularly shaped clusters in space. Multi-scale test statistic on a single cell is derived based on likelihood ratio statistic for Bernoulli sequence, Poisson…
We present a robust multiple manifolds structure learning (RMMSL) scheme to robustly estimate data structures under the multiple low intrinsic dimensional manifolds assumption. In the local learning stage, RMMSL efficiently estimates local…
We propose a graph-based clustering method based on Cluster Catch Digraphs (CCDs) that extends their applicability to moderate-dimensional data settings. Existing CCD variants, such as RK-CCDs, rely on spatial randomness tests based on…
The problem of multiple surface clustering is a challenging task, particularly when the surfaces intersect. Available methods such as Isomap fail to capture the true shape of the surface nearby the intersection and result in incorrect…
Matching datasets of multiple modalities has become an important task in data analysis. Existing methods often rely on the embedding and transformation of each single modality without utilizing any correspondence information, which often…
Data structures that allow efficient distance estimation (distance oracles, distance sketches, etc.) have been extensively studied, and are particularly well studied in centralized models and classical distributed models such as CONGEST. We…
In this paper, we propose a new method called Clustering Topological PRM (CTopPRM) for finding multiple homotopically distinct paths in 3D cluttered environments. Finding such distinct paths, e.g., going around an obstacle from a different…
Correlation clustering is a central topic in unsupervised learning, with many applications in ML and data mining. In correlation clustering, one receives as input a signed graph and the goal is to partition it to minimize the number of…
This paper focuses on the Matrix Factorization based Clustering (MFC) method which is one of the few closed form algorithms for the subspace clustering problem. Despite being simple, closed-form, and computation-efficient, MFC can…
We consider the problem of clustering with the longest-leg path distance (LLPD) metric, which is informative for elongated and irregularly shaped clusters. We prove finite-sample guarantees on the performance of clustering with respect to…
In this paper, we introduce a novel algorithm for segmentation of imperfect boundary probability maps (BPM) in connectomics. Our algorithm can be a considered as an extension of spectral clustering. Instead of clustering the diffusion maps…
Cross-manifold clustering is a hard topic and many traditional clustering methods fail because of the cross-manifold structures. In this paper, we propose a Multiple Flat Projections Clustering (MFPC) to deal with cross-manifold clustering…
Spectral clustering requires the time-consuming decomposition of the Laplacian matrix of the similarity graph, thus limiting its applicability to large datasets. To improve the efficiency of spectral clustering, a top-down approach was…
We propose a novel probabilistic approach to multilevel clustering problems based on composite transportation distance, which is a variant of transportation distance where the underlying metric is Kullback-Leibler divergence. Our method…
Identifying the connected components of a graph, apart from being a fundamental problem with countless applications, is a key primitive for many other algorithms. In this paper, we consider this problem in parallel settings. Particularly,…
We propose a new clustering technique that can be regarded as a numerical method to compute the proximity gestalt. The method analyzes edge length statistics in the MST of the dataset and provides an a contrario cluster detection criterion.…