k-means

I wonder if Triangle inequality is necessary for the distance measure used in kmeans. k-means is designed for Euclidean distance, which happens to satisfy triangle inequality. Using other distance functions is risky, as it may stop converging . The reason however is not the triangle inequality, but the mean might not minimize the distance function . (The arithmetic mean minimizes the sum-of-squares, not arbitrary distances!) There are faster methods for k-means that exploit the triangle inequality to avoid recomputations. But if you stick to classic MacQueen or Lloyd k-means, then you do not

The k-means++ algorithm helps in two following points of the original k-means algorithm: The original k-means algorithm has the worst case running time of super-polynomial in input size, while k-means++ has claimed to be O(log k). The approximation found can yield a not so satisfactory result with respect to objective function compared to the optimal clustering. But are there any drawbacks of k-means++? Should we always used it instead of k-means from now on? Nobody claims k -means++ runs in O(lg k ) time; it's solution quality is O(lg k )-competitive with the optimal solution. Both k -means++

聚类算法 简介 聚类就是对大量 未知标注的数据集 ，按照数据 内部存在的数据特征 将数据集划分为多个不同的类别，使类别内的数据比较相似，类别之间的数据相似度比较小； 属于无监督学习 。 聚类算法的重点是计算样本项之间的 相似度 ，有时候也称为样本间的 距离 相似度/距离 闵可夫斯基距离 \[ dist(X,Y)=\quad\sqrt[p]{\sum_{i=1}^{n}{|x_i-y_i|^p}} \] \[ 其中X=(x_1,x_2,...,x_n),Y=(y_1,y_2,...,y_n) \] 当p是1的时候为哈曼顿距离(Manhattan)/城市距离： \[ dist(X,Y)=\sum_{i=1}^{n}{|x_i-y_i|} \] 当p为2的时候为欧式距离(Euclidean)： \[ E\_dist(X,Y)=\sqrt{\sum_{i=1}^{n}{|x_i-y_i|^2}} \] 当p为无穷大的时候是切比雪夫距离(Chebyshew)： \[ C\_dist(X,Y)=max(|x_i-y_i|) \] 有数学性质可得，当p为无穷大时，有如下： \[ dist(X,Y)=\quad\sqrt[p]{\sum_{i=1}^{n}{|x_i-y_i|^p}} \] \[ \leq\quad\sqrt[p]{n\times max(|x_i-y_i|^p)}=max(|x

I'm using this script to cluster a set of 3D points using the kmeans matlab function but I always get this error "Empty cluster created at iteration 1". The script I'm using: [G,C] = kmeans(XX, K, 'distance','sqEuclidean', 'start','sample'); XX can be found in this link XX value and the K is set to 3 So if anyone could please advise me why this is happening. Amro It is simply telling you that during the assign-recompute iterations, a cluster became empty (lost all assigned points). This is usually caused by an inadequate cluster initialization, or that the data has less inherent clusters than

I've been looking around scipy and sklearn for clustering algorithms for a particular problem I have. I need some way of characterizing a population of N particles into k groups, where k is not necessarily know, and in addition to this, no a priori linking lengths are known (similar to this question ). I've tried kmeans, which works well if you know how many clusters you want. I've tried dbscan, which does poorly unless you tell it a characteristic length scale on which to stop looking (or start looking) for clusters. The problem is, I have potentially thousands of these clusters of particles,