Publication

What is Better: GMM of Two Gaussians or Two Clusters With One Gaussian?

2002
Reports

Abstract

In this report, we provide a theoretical discussion on temporal data cluster analysis: does the data come from one source or two sources; is it better to cluster the data into two clusters or leave it as one cluster. Here we analyse only the simplest case: when the data comes from two symmetric Gaussian probability-density-functions (pdfs), i.e., with same variance and same absolute value of the mean, with the same prior probability per Gaussian. The data consists of segments with an a-priori known segment length. It will be shown that if the data belongs to two different Gaussian models, the likelihood of two clusters is always higher or equal than the one of a GMM with two Gaussians for any mean, variance, and segment length. If the data belongs to the GMM, the likelihood of two clusters might be either higher or less than the GMM one.

Official source

https://infoscience.epfl.ch/entities/publication/8b8a3203-51a9-4ba0-8bd1-4b29ef64273d

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2002
Reports

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/8b8a3203-51a9-4ba0-8bd1-4b29ef64273d

About this result

Related concepts (32)

Prior probability

A prior probability distribution of an uncertain quantity, often simply called the prior, is its assumed probability distribution before some evidence is taken into account. For example, the prior could be the probability distribution representing the relative proportions of voters who will vote for a particular politician in a future election. The unknown quantity may be a parameter of the model or a latent variable rather than an observable variable.

Gaussian function

In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form and with parametric extension for arbitrary real constants a, b and non-zero c. It is named after the mathematician Carl Friedrich Gauss. The graph of a Gaussian is a characteristic symmetric "bell curve" shape. The parameter a is the height of the curve's peak, b is the position of the center of the peak, and c (the standard deviation, sometimes called the Gaussian RMS width) controls the width of the "bell".

Gaussian process

In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution, i.e. every finite linear combination of them is normally distributed. The distribution of a Gaussian process is the joint distribution of all those (infinitely many) random variables, and as such, it is a distribution over functions with a continuous domain, e.g.

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