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101,305
Clustering with Bregman Divergences
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2005
"... A wide variety of distortion functions are used for clustering, e.g., squared Euclidean distance, Mahalanobis distance and relative entropy. In this paper, we propose and analyze parametric hard and soft clustering algorithms based on a large class of distortion functions known as Bregman divergence ..."
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Cited by 434 (58 self)
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divergences. The proposed algorithms unify centroidbased parametric clustering approaches, such as classical kmeans and informationtheoretic clustering, which arise by special choices of the Bregman divergence. The algorithms maintain the simplicity and scalability of the classical kmeans algorithm, while
Discriminant Adaptive Nearest Neighbor Classification
, 1994
"... Nearest neighbor classification expects the class conditional probabilities to be locally constant, and suffers from bias in high dimensions. We propose a locally adaptive form of nearest neighbor classification to try to ameliorate this curse of dimensionality. We use a local linear discriminant an ..."
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Cited by 317 (1 self)
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analysis to estimate an effective metric for computing neighborhoods. We determine the local decision boundaries from centroid information, and then shrink neighborhoods in directions orthogonal to these local decision boundaries, and elongate them parallel to the boundaries. Thereafter, any neighborhood
Scripts Centroid
"... Circle through 3 pts Altitude feet Buried treasure solution Day 3 assignment Scrambled proofs in envelopes Flowchart proof templates TEAXTEAM Geometry Institute 2.2THE BURIED TREASURE Among his greatgrandfather’s papers, José found a parchment describing the location of a hidden treasure. The treas ..."
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Circle through 3 pts Altitude feet Buried treasure solution Day 3 assignment Scrambled proofs in envelopes Flowchart proof templates TEAXTEAM Geometry Institute 2.2THE BURIED TREASURE Among his greatgrandfather’s papers, José found a parchment describing the location of a hidden treasure. The treasure was buried by a band of pirates on a deserted island which contained an oak tree, a pine tree, and a gallows where the pirates hanged traitors. The map looked like the accompanying figure and gave the following directions. “Count the steps from the gallows to the oak tree. At the oak, turn 90 ° to the right. Take the same number of steps and then put a spike in the ground. Next, return to the gallows and walk to the pine tree, counting the number of steps. At the pine tree, turn 90° to the left, take the same number of steps, and then put another spike in the ground. The treasure is buried halfway between the spikes.” José found the island and the trees but could not find the gallows or the spikes, which had long since rotted. José dug all over the island, but because the island was large, he gave up. Devise a plan to help José find the treasure.
Discovering Word Senses from Text
 In Proceedings of ACM SIGKDD Conference on Knowledge Discovery and Data Mining
, 2002
"... Inventories of manually compiled dictionaries usually serve as a source for word senses. However, they often include many rare senses while missing corpus/domainspecific senses. We present a clustering algorithm called CBC (Clustering By Committee) that automatically discovers word senses from text ..."
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Cited by 292 (18 self)
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text. It initially discovers a set of tight clusters called committees that are well scattered in the similarity space. The centroid of the members of a committee is used as the feature vector of the cluster. We proceed by assigning words to their most similar clusters. After assigning an element to a
Sided and symmetrized Bregman centroids
 IEEE Transactions on Information Theory
, 2009
"... Abstract—We generalize the notions of centroids (and barycenters) to the broad class of informationtheoretic distortion measures called Bregman divergences. Bregman divergences form a rich and versatile family of distances that unifies quadratic Euclidean distances with various wellknown statistic ..."
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Cited by 37 (13 self)
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Abstract—We generalize the notions of centroids (and barycenters) to the broad class of informationtheoretic distortion measures called Bregman divergences. Bregman divergences form a rich and versatile family of distances that unifies quadratic Euclidean distances with various well
The BurbeaRao and Bhattacharyya centroids
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2011
"... We study the centroid with respect to the class of informationtheoretic BurbeaRao divergences that generalize the celebrated JensenShannon divergence by measuring the nonnegative Jensen difference induced by a strictly convex and differentiable function. Although those BurbeaRao divergences are ..."
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Cited by 26 (14 self)
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We study the centroid with respect to the class of informationtheoretic BurbeaRao divergences that generalize the celebrated JensenShannon divergence by measuring the nonnegative Jensen difference induced by a strictly convex and differentiable function. Although those BurbeaRao divergences
Bregman sided and symmetrized centroids
 in ICPR. 2008, IEEE CS
"... We generalize the notions of centroids and barycenters to the broad class of informationtheoretic distortion measures called Bregman divergences. Because Bregman divergences are typically asymmetric, we consider both the leftsided and rightsided centroids and the symmetrized centroids, and prove ..."
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Cited by 3 (3 self)
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We generalize the notions of centroids and barycenters to the broad class of informationtheoretic distortion measures called Bregman divergences. Because Bregman divergences are typically asymmetric, we consider both the leftsided and rightsided centroids and the symmetrized centroids, and prove
The Centroid Decomposition: Relationships Between
 SIAM J. Matrix Anal. Appl
, 2002
"... The centroid decomposition, an approximation for the singular value decomposition, had a long history among the statistics/psychometrics community for factor analysis research. We revisit the centroid method first in its original context of factor analysis and then adapt it to other than a covarianc ..."
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covariance matrix. The centroid method can be cast as an ascent method on a hypercube. It is shown empirically that the centroid decomposition provides a measurement of second order statistical information of the original data in the direction of the corresponding left centroid vectors. A major purpose
Results 1  10
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101,305