Self-Tuning Spectral Clustering

By Lihi Zelnik-Manor, Pietro Perona. 2004

2,442 citations recorded by the source corpus.

Subfields: Representation & Self-Supervised Learning

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Citations in the corpus

Deep Convolutional Networks on Graph-Structured Data (2015, methodology): “This distance is then used to build a Gaussian diffusion Kernel [1] In our experiments, we also consider the variant of self-tuning diffusion kernel [21] ω ( i, j ) = exp , where σ i is computed as the distance d ( i, i k ) corresponding to the k -th nearest neighbor i k of feature i .”
Invariant Information Clustering for Unsupervised Image Classification and Segmentation (2018, background): “gmentation, as well as two semi-supervised settings. Ex1The core differentiable operator in spatial transformer networks [32]. STL10 CIFAR10 CFR100-20 MNIST Random network 13.5 13.1 5.93 26.1 K-means [53]y 19.2 22.9 13.0 57.2 Spectral clustering [49] 15.9 24.7 13.6 69.6 Triplets [46]z 24.4 20.5 9.94”
Word Translation Without Parallel Data (2017, neutral): “Various solutions have been proposed to mitigate this issue, some being reminiscent of pre-processing already existing in spectral clustering algorithms (Zelnik-manor & Perona, 2005).”
TriMap: Large-scale Dimensionality Reduction Using Triplets (2019, methodology): “We also apply the scaling introduced in (Zelnik-Manor & Perona, 2005), where σ ij = σ i σ j and σ i is set to the average Euclidean distance between x i and the set of nearest-neighbors of x i from 4 -th to 6 -th neighbors.”
Nonparametric Divergence Estimation with Applications to Machine Learning on Distributions (2011, methodology): “To cluster these images, we feed the divergences to the spectral clustering algorithm by Zelnik-Manor and Perona (2004). To evaluate the clustering results, we first form a confusion matrix from the category labels and the cluster labels, then permute the columns to maximize the trace of this matrix”
Joint Unsupervised Learning of Deep Representations and Image Clusters (2016, methodology): “We compare our approach with 12 clustering algorithms, including K-means [36], NJW spectral clustering (SCNJW) [40], self-tuning spectral clustering (SC-ST)[61], large-scale spectral clustering (SC-LS) [3], agglomerative clustering with average linkage (AC-Link)[24], Zeta function based agglomerativ”
Learning Discrete Representations via Information Maximizing Self-Augmented Training (2017, methodology): “Inspired by the automatic kernel width selection in spectral clustering (Zelnik-Manor & Perona, 2004), the perturbation range, , in VAT for data point x was set as (x) = α · σt(x), (16) where α is a scalar and σt(x) is the Euclidian distance to the t-th neighbor of x.”
OpenMix: Reviving Known Knowledge for Discovering Novel Visual Categories in an Open World (2020, methodology): “Many classic methods [15, 30] and deep learning methods [5, 27, 28] have been proposed.”
LanczosNet: Multi-Scale Deep Graph Convolutional Networks (2019, background): “This class of anisotropic kernels is very expressive and includes self-tuning kernel [15] and the Gaussian kernel with Mahalanobis distances [16].”
Large-Scale Multi-View Spectral Clustering via Bipartite Graph (2015, background): “Recently, spectral clustering (SC) is drawing more and more attention because of its effectiveness (Shi and Malik 2000; Von Luxburg 2007; Ng et al. 2002; Zelnik-Manor and Perona 2004; Nie, Wang, and Huang 2014; Chang et al. 2015).”
Visual Motif Discovery via First-Person Vision (2016, background): “Some studies on spectral clustering proposed to observe eigenvalues to determine the number of clusters [32, 39].”
Scalable Person Re-identification on Supervised Smoothed Manifold (2017, methodology): “The affinity graph is constructed by applying self-tuning [56] Gaussian kernel to pairwise distances following [31].”
Handbook of Cluster Analysis (2015, methodology): “A simple and widely used way to “tune” the similarity function to the local density [49] is to set Sij = exp ( −||xi − xj || 2 σiσj )”
Foreground Focus: Unsupervised Learning from Partially Matching Images (2009, methodology): “The number of clusters can be automatically determined by the self-tuning spectral clustering method (Zelnik-Manor and Perona 2004), which was demonstrated in Lee and Grauman (2008b) to find different aspects/views of tourist attractions.”
Learning to Propagate Labels: Transductive Propagation Network for Few-Shot Learning (2018, methodology): “In addition, we observe that there is no principled way to tune the scale parameter in meta-learning framework, though there exist some heuristics for dimensionalty reduction methods (Zelnik-Manor and Perona, 2004; Sugiyama, 2007).”
The Constrained Laplacian Rank Algorithm for Graph-Based Clustering (2016, methodology): “For RCut and NCut methods, we utilized the widely used self-tune Gaussian method (Zelnik-Manor and Perona 2004) to construct the afﬁnity matrix (the value of σ is self-tuned).”
Ieee Transactions on Knowledge and Data Engineering Context-aware Hypergraph Construction for Robust Spectral Clustering (neutral): “In the literature, Zelnik-Manor and Perona [11] attempt to address issues i) and ii) by designing a local scaling mechanism, which adaptively calculates the affinity matrix and explores the intrinsic structural information on the energy eigenvalue spectrum of the normalized graph Laplacian to…”
Modelling Crowd Scenes for Event Detection (2006, methodology): “The similarity matrix is subject to spectral clustering using the algorithm described [13] to automatically find the number of groups in the video data.”
Non-linear independent component analysis with diffusion maps (2008, methodology): “For one-dimensional manifolds (i.e., curves) the Jacobian is merely a scalar and the anisotropic diffusion kernel is identical to the self-tuning spectral clustering algorithm [14].”