k-Plane Clustering

By Paul S. Bradley, Olvi L. Mangasarian. Journal of Global Optimization, 2000

434 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7400912ca8c9ffbe2b9435ea9e4d97776b002228

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Citations in the corpus

Testing the Manifold Hypothesis (2013, background): “A natural generalization of k-means was proposed in [6] wherein one fits k ddimensional planes to data in a manner that minimizes the average squared distance of a data point to the nearest d dimensional plane.”
Spectral Curvature Clustering (SCC) (2009, methodology): “There are also algorithms that iterate between the two components of data clustering and subspace modeling (see e.g., Mixtures of PPCA (MoPPCA) (Tipping and Bishop 1999), K-Subspaces (Ho et al. 2003)/kPlanes (Bradley and Mangasarian 2000; Tseng 1999)).”
Regularized Principal Manifolds (1999, background): “Bradley & Mangasarian 8] show that this can improve results on certain datasets.”
Subspace Clustering by Block Diagonal Representation (2018, methodology): “Representative methods are K-plane [3] and Q-flat [36].”
Robust and Efficient Subspace Segmentation via Least Squares Regression (2012, background): “According to their mechanisms of representing the subspaces, existing works can be roughly divided into four categories: algebraic methods [5] [6], iterative methods [7] [8], statistical methods [9] [10] and spectral clustering-based methods [11] [12] [13] [14].”
Multisurface proximal support vector machine classification via generalized eigenvalues (2006, background): “Related work is the k-plane clustering of [3], where clusters are determined by proximity to various nonparallel planes based on the smallest eigenvector of a matrix generated by given data points.”
Robust recovery of multiple subspaces by geometric l_p minimization (2011, methodology): “3, 26]). HLM is the simplest nonlinear data modeling and ﬁts within the broader frameworks of modeling data by mixture of manifolds [3] and by Whitney’s stratiﬁed space [4]. The K-subspaces algorithm [5, 10, 22] is the most basic heuristic for HLM, and it suggests an iterative procedure attempting t”
Generalized Latent Multi-View Subspace Clustering (2020, background): “Existing subspace clustering approaches can be categorized into iterative methods [3], [4], algebraic approaches [5], [6], statistical methods and spectral clustering-based methods [7], [8].”
Nearest q-Flat to m Points (2000, background): “Notice that, without loss of generality, we can assume that the columns of W in ( 1 ) form an orthonormal set, i.e.,”
Low rank subspace clustering (LRSC) (2014, methodology): “…(Boult and Brown, 1991; Costeira and Kanade, 1998; Gear, 1998; Vidal et al., 2003a; Vidal et al., 2004; Vidal et al., 2005), iterative methods (Bradley and Mangasarian, 2000; Tseng, 2000; Agarwal and Mustafa, 2004; Lu and Vidal, 2006; Zhang et al., 2009), statistical methods (Tipping and…”
A Divisive Information-Theoretic Feature Clustering Algorithm for Text Classification (2003, background): “The result follows since the algorithm monotonically decreases the objective function value, and since the number of distinct clusterings is finite (see Bradley and Mangasarian, 2000, for a similar argument).”
Robust Subspace Clustering (2013, methodology): “Other examples of iterative methods may be found in [1,10,25,48].”
Identification of Hybrid Systems: A Tutorial (2007, background): “An alternative to the formulation (13) is the clustering algorithm proposed in [12], which groups the given data points intos clusters by generating s planes that represent a local solution to the non-convex problem of minimizing the sum of squares of the 2-norm distances between each point and a ne”