This paper presents two algorithms for generating artificial mixtures of univariate normal densities with controlled component overlap. Such mixtures are used basically as test benchmarks for the evaluation of clustering algorithms. Although the algorithms are different, they are based on the same definition. Both algorithms use formal methods to ensure the generation of “non totally overlapped...

In recent years, there has been a growing interest in learning tractable graphical models in which exact inference is efficient. Two main approaches are to restrict the inference complexity directly, as done by low-treewidth graphical models and arithmetic circuits (ACs), or introduce latent variables, as done by mixtures of trees, latent tree models, and sum-product networks (SPNs). In this pa...

Carreira-Perpinan and Williams (2003) conjectured that a homoscedastic Gaussian mixture of M components in d 1 dimensions has at most M modes. Prof. J. J. Duistermaat (personal communication, 2003) provided the counterexample of a 3–component mixture in d = 2 where the Gaussians are located at the vertices of an equilateral triangle; for a certain range of variances modes are present near to th...

This paper addresses the problem of resource allocation in local linear models for non-linear principal component analysis (PCA). In the local PCA model, the data space is partitioned into regions and PCA is performed in each region. Our primary result is that the advantage of these models over conventional PCA has been signiicantly underestimated in previous work. We apply local PCA models to ...

This work investigates a combined stochastic and deterministic optimization approach for multivariate mixture density estimation. Mixture probability density models are selected and optimized by combining the optimization characteristics of a multiagent stochastic optimization algorithm based on evolutionary programming and the expectation-maximization algorithm. Unlike the traditional finite m...

1 Variational Dirichlet Process mixtures Assume two infinite sets φ = {φ1, φ2, . . .} and v = {v1, v2, . . . , } of component parameter vectors and beta distributed random variables. Each φk is independently drawn from the prior pφ(φk|λ) with hyperparameter λ and each vk is independently drawn from B(vk|1, α) with hyperparameter α. Given these sets a Dirichlet Process (DP) mixture model is writ...

Abstract. The inferential problem of associating data to mixture components is difficult when components are nearby or overlapping. We introduce a new split-merge Markov chain Monte Carlo technique that efficiently classifies observations by splitting and merging mixture components of a nonconjugate Dirichlet process mixture model. Our method, which is a Metropolis-Hastings procedure with split...

By generating a composition gradient on a highly uniform SERS substrate and applying independent component analysis, we demonstrate that one can extract the intrinsic SERS spectrum of individual components from SERS spectra obtained from a two-component mixture.