Improved k-means
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This presentation summarizes a research paper that proposes improvements to the K-means clustering algorithm. It describes K-means clustering and its goal of assigning data points to clusters based on centroid distances. However, K-means is prone to getting stuck in local optima based on the initial random centroid selection. The paper suggests an algorithm to select initial centroids that aims to improve accuracy and efficiency by choosing centroids farther apart from each other and from existing clusters.
![Algorithm selection of initial centroids
1. Set m = 1;
2. Compute the distance between each data point and all
other data points in the set;
3. Find the closest pair of data points from the set X and
form a data point set A[m] (1 <= m <= K) which
contains these two data points. Delete these two data
points from the set;
4. Find the data point in X that is closest to the data
points set. Add it to A[m] and delete it from X;
5. Repeat step 4 until the number of data points in A[m]
reaches 0.75*(n/k);](https://image.slidesharecdn.com/improved-k-means-130411004948-phpapp02/85/Improved-k-means-7-320.jpg)
![Algorithm selection of initial centroids
continued…
6. If m < k then m = m + 1, find another pair of data
points from X between which the distance is the
shortest, form another data point set A[m] and delete
them from X. Go to step 4;
7. For each data point set A[m] (1 <= m <= K) find the
arithmetic mean of the vectors of data points in A[m].
These means will be the initial centroids.](https://image.slidesharecdn.com/improved-k-means-130411004948-phpapp02/85/Improved-k-means-8-320.jpg)
Improved k-means
- 1. Improving the accuracy of K-means clustering algorithm Kasun Ranga Wijeweera (krw19870829@gmail.com)
- 2. This presentation is based on the following research paper K. A. Abdul Nazeer, M. P. Sebastian, Improving the Accuracy and Efficiency of the k-means Clustering Algorithm, Proceedings of the World Congress on Engineering 2009 Vol I, WCE 2009, July 1 – 3, 2009, London, U. K.
- 3. Consider a Set of Data Points, And a Set of Clusters,
- 4. The Goal,
- 5. Algorithm k-means 1.Randomly choose K data items from X as initial centroids. 2.Repeat Assign each data point to the cluster which has the closest centroid. Calculate new cluster centroids. Until the convergence criteria is met.
- 6. K-means gets stuck in a local optima
- 7. Algorithm selection of initial centroids 1. Set m = 1; 2. Compute the distance between each data point and all other data points in the set; 3. Find the closest pair of data points from the set X and form a data point set A[m] (1 <= m <= K) which contains these two data points. Delete these two data points from the set; 4. Find the data point in X that is closest to the data points set. Add it to A[m] and delete it from X; 5. Repeat step 4 until the number of data points in A[m] reaches 0.75*(n/k);
- 8. Algorithm selection of initial centroids continued… 6. If m < k then m = m + 1, find another pair of data points from X between which the distance is the shortest, form another data point set A[m] and delete them from X. Go to step 4; 7. For each data point set A[m] (1 <= m <= K) find the arithmetic mean of the vectors of data points in A[m]. These means will be the initial centroids.
- 10. Thanks for your attention !