Additive and multiplicative mixed normal distributions and finding cluster centers

作者：Lipovetsky Stan^*

来源：International Journal of Machine Learning and Cybernetics, 2013, 4(1): 1-11.

DOI：10.1007/s13042-012-0070-3

• Mixed-normal distribution
• Additive and multiplicative aggregations
• Cluster analysis
• Nonlinear modeling

Mixed normal distributions are considered in additive and multiplicative forms. While the weighted arithmetic mean of the probability density functions typically demonstrates several peaks corresponding to the parent sub-distributions, their weighted geometric mean is always expressed in one unimodal multivariate normal distribution. Estimation of the cluster center parameters from such a synthesized distribution is considered. The problem is solved by a non-linear least squares optimization yielding the cluster centers and sizes. The relationship to factor analysis by unweighted least squares and generalized least squares is noted, and numerical results are discussed. The described approach uses only the sample variance-covariance matrix and not the observations, so it can be applied for difficult clustering tasks on huge data sets from data bases and for data mining problems such as finding the approximation for the cluster centers and sizes. The suggested techniques can enrich both theoretical consideration and practical applications for clustering problems.

• 出版日期2013-2