Years and Authors of Summarized Original Work
2001; Arya, Garg, Khandekar, Meyerson, Munagala, Pandit
Problem Definition
Clustering is a form of unsupervised learning, where the goal is to “learn” useful patterns in a data set \( { \mathcal{D} } \) of size n. It can also be thought of as a data compression scheme where a large data set is represented using a smaller collection of “representatives”. Such a scheme is characterized by specifying the following:
- 1.
A distance metric \( { \mathbf{d} } \) between items in the data set. This metric should satisfy the triangle inequality: \( { \mathbf{d}(i,j) \le \mathbf{d}(j,k) + \mathbf{d}(k,i) }\) for any three items \( { i,j,k \in \mathcal{D} }\). In addition, \( { \mathbf{d}(i,j) = \mathbf{d}(j,i) }\) for all \( { i,j \in \mathcal{S} }\) and \( { \mathbf{d}(i,i) = 0 }\).Intuitively,if the distance between two items is smaller, they are more similar. The items are usually points in some high dimensional Euclidean space \( { \mathcal{R}^d }\)...
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Recommended Reading
Arya V, Garg N, Khandekar R, Meyerson A, Munagala K, Pandit V (2004) Local search heuristics for k-median and facility location problems. SIAM J Comput 33(3):544–562
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Munagala, K. (2016). Local Search for K-medians and Facility Location. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_212
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