A local search approximation algorithm for k-means clustering

Kanungo, Tapas; Mount, David M.; Netanyahu, Nathan S.; Piatko, Christine D.; Silverman, Ruth; Wu, Angela Y.

doi:10.1145/513400.513402

Cited by 211 publications

(87 citation statements)

References 21 publications

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“…where μ= 10 5 , λ= 0.20max(| a |, | b |), L min = 0.15 max( L ) and L max = 0.95 max( L ). For this initial segmentation, we use the k‐means implementation from Kanungo et al [KMN*04]. Gehler and colleagues [GRK*11] also used k‐means for their global sparse reflectance prior, which along with their shading prior and their gradient consistency term, fit into their global optimization system.…”

Section: Algorithmmentioning

confidence: 99%

Intrinsic Images by Clustering

Garcés

Muñoz

López‐Moreno

et al. 2012

Computer Graphics Forum

123

101

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Decomposing an input image into its intrinsic shading and reflectance components is a long-standing ill-posed problem. We present a novel algorithm that requires no user strokes and works on a single image. Based on simple assumptions about its reflectance and luminance, we first find clusters of similar reflectance in the image, and build a linear system describing the connections and relations between them. Our assumptions are less restrictive than widely-adopted Retinex-based approaches, and can be further relaxed in conflicting situations. The resulting system is robust even in the presence of areas where our assumptions do not hold. We show a wide variety of results, including natural images, objects from the MIT dataset and texture images, along with several applications, proving the versatility of our method.

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Section: Algorithmmentioning

confidence: 99%

Intrinsic Images by Clustering

Garcés

Muñoz

López‐Moreno

et al. 2012

Computer Graphics Forum

123

101

View full text Add to dashboard Cite

show abstract

“…Ideally, if the clustering algorithm converges to a local minimum closer to the global minimum, then each cluster is relatively denser and we may reduce the number of distance calculations in the searching stage. Some k -means clustering algorithms [2] [15] have shown to be able to produce better results than Lloyd’s algorithm, but for this paper, we already achieve excellent performance by using the naive Lloyd’s algorithm. It will be interesting to see how performance can be further improved by integrating these algorithms.…”

Section: Methodsmentioning

confidence: 83%

Fast exact k nearest neighbors search using an orthogonal search tree

Wang

2010

Pattern Recognition

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The k-nearest neighbors (k-NN) algorithm is a widely used machine learning method that finds nearest neighbors of a test object in a feature space. We present a new exact k-NN algorithm called kMkNN (k-Means for k-Nearest Neighbors) that uses the k-means clustering and the triangle inequality to accelerate the searching for nearest neighbors in a high dimensional space. The kMkNN algorithm has two stages. In the buildup stage, instead of using complex tree structures such as metric trees, kd-trees, or ball-tree, kMkNN uses a simple k-means clustering method to preprocess the training dataset. In the searching stage, given a query object, kMkNN finds nearest training objects starting from the nearest cluster to the query object and uses the triangle inequality to reduce the distance calculations. Experiments show that the performance of kMkNN is surprisingly good compared to the traditional k-NN algorithm and tree-based k-NN algorithms such as kd-trees and ball-trees. On a collection of 20 datasets with up to 106 records and 104 dimensions, kMkNN shows a 2-to 80-fold reduction of distance calculations and a 2- to 60-fold speedup over the traditional k-NN algorithm for 16 datasets. Furthermore, kMkNN performs significant better than a kd-tree based k-NN algorithm for all datasets and performs better than a ball-tree based k-NN algorithm for most datasets. The results show that kMkNN is effective for searching nearest neighbors in high dimensional spaces.

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“…To prove the correctness of our new and novel k-means algorithm, we will need the following definitions from Kumar et al [23] and Kanungo et al [24].…”

Section: Methodsmentioning

confidence: 99%

Reducing the Time Requirement of k-Means Algorithm

et al. 2012

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Traditional k-means and most k-means variants are still computationally expensive for large datasets, such as microarray data, which have large datasets with large dimension size d. In k-means clustering, we are given a set of n data points in d-dimensional space Rd and an integer k. The problem is to determine a set of k points in Rd, called centers, so as to minimize the mean squared distance from each data point to its nearest center. In this work, we develop a novel k-means algorithm, which is simple but more efficient than the traditional k-means and the recent enhanced k-means. Our new algorithm is based on the recently established relationship between principal component analysis and the k-means clustering. We provided the correctness proof for this algorithm. Results obtained from testing the algorithm on three biological data and six non-biological data (three of these data are real, while the other three are simulated) also indicate that our algorithm is empirically faster than other known k-means algorithms. We assessed the quality of our algorithm clusters against the clusters of a known structure using the Hubert-Arabie Adjusted Rand index (ARIHA). We found that when k is close to d, the quality is good (ARIHA>0.8) and when k is not close to d, the quality of our new k-means algorithm is excellent (ARIHA>0.9). In this paper, emphases are on the reduction of the time requirement of the k-means algorithm and its application to microarray data due to the desire to create a tool for clustering and malaria research. However, the new clustering algorithm can be used for other clustering needs as long as an appropriate measure of distance between the centroids and the members is used. This has been demonstrated in this work on six non-biological data.

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A local search approximation algorithm for k-means clustering

Cited by 211 publications

References 21 publications

Intrinsic Images by Clustering

Intrinsic Images by Clustering

Fast exact k nearest neighbors search using an orthogonal search tree

Reducing the Time Requirement of k-Means Algorithm

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