# Some methods for classification and analysis of multivariate observations

@inproceedings{MacQueen1967SomeMF, title={Some methods for classification and analysis of multivariate observations}, author={J. MacQueen}, year={1967} }

The main purpose of this paper is to describe a process for partitioning an N-dimensional population into k sets on the basis of a sample. The process, which is called 'k-means,' appears to give partitions which are reasonably efficient in the sense of within-class variance. That is, if p is the probability mass function for the population, S = {S1, S2, * *, Sk} is a partition of EN, and ui, i = 1, 2, * , k, is the conditional mean of p over the set Si, then W2(S) = ff=ISi f z u42 dp(z) tends…

## 25,715 Citations

### Supervised Nested Algorithm for Classification Based on K-Means

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This paper presents an extension of the k-means algorithm based on the idea of recursive partitioning that can be used as a classification algorithm in the case of supervised classification and carries the integration of parametric model into trees one step further.

### Implementation of the k-means Method for Single and Multi - Dimensions

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The k-means method uses the Euclidean distance measure, which appears to work well with compact clusters, and is scalable and efficient, and guaranteed to find a local minimum, and has ample interesting applications.

### Method of Classification through Normal Distribution Approximation Using Estimating the Adjacent and Multidimensional Scaling

- Computer Science2016 5th IIAI International Congress on Advanced Applied Informatics (IIAI-AAI)
- 2016

This study proposes machine learning algorithms that approximates the density of the influence of the training data using a density function of normal distribution and proposes improved method that relocates theTraining data from the distance between the trainingData by multidimensional scaling as preprocessing.

### Variable Selection in K-Means Clustering via Regularization

- Computer Science
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A new method of K-means clustering is proposed to detect irrelevant variables to the cluster structure and achieves the purpose of calculating variable weights using an entropy regularization method.

### Improved Clustering with Augmented k-means

- Computer Science
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Augmented k-means frequently outperforms k-Means by more accurately classifying observations into known clusters and / or converging in fewer iterations, which can be valuable when the data exhibit many characteristics of real datasets such as heterogeneity, non-sphericity, substantial overlap, and high scatter.

### A Comparison of K-Means and Mean Shift Algorithms

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This paper is intended to compare and study two different clustering algorithms, k-mean and mean shift, and determines and presents the intrinsic grouping of objects present in the data, based on their attributes, in a batch of unlabeled raw data.

### Model Based Penalized Clustering for Multivariate Data

- Computer Science
- 2007

This paper has developed a decision theoretic framework by which traditional K-means can be given a probabilistic footstep, which will not only enable us to do a soft clustering, rather the whole optimization problem could be recasted into Bayesian modeling framework, in which the knowledge of cluster number could be treated as an unknown parameter of interest, thus removing a severe constrain of K- means algorithm.

### Asymptotics for The k-means

- Computer ScienceArXiv
- 2022

A new concept called clustering consistency is proposed, which is more appropriate than the previous criterion consistency for the clustering methods and has lower clustering error rates and is more robust to small clusters and outliers than existing k -means methods.

### A Comparison of Latent Class, K-Means, and K-Median Methods for Clustering Dichotomous Data

- PsychologyPsychological methods
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Simulation-based comparisons of the latent class, K-means, and K-median approaches for partitioning dichotomous data found that the 3 approaches can exhibit profound differences when applied to real data.

### Automation of Data Clusters based on Layered HMM

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A novel method is proposed based on Layered Hidden Markov Model (LHMM) to identify a suitable number of clusters in a given unlabeled dataset without using prior knowledge about the number of clustering, and the experimental results indicate the efficacy of this method.

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