Estimating Gaussian Mixture Densities via an implemetation of the Expectaation Maximization Algorithm
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The document discusses the implementation of the expectation maximization (EM) algorithm for estimating Gaussian mixture densities, focusing on its application in cluster analysis and sentiment analysis. It outlines the process of modeling data distributions as sums of Gaussian densities while providing a probabilistic description of data points. The results emphasize the algorithm's capacity to effectively estimate parameters and characterize data in both one-dimensional and multi-dimensional contexts.
Estimating Gaussian Mixture Densities via an implemetation of the Expectaation Maximization Algorithm
- 1. ESTIMATING GAUSSIAN MIXTURE DENSITIES VIA A MATLAB IMPLEMETATION OF THE EXPECTATION MAXIMIZATION ALGORITHM DR. ASOKA KORALE, C.ENG. MIET & MIESL
- 2. APPLICATIONS FOR GAUSSIAN MIXTURE DECOMPOSITION MODELING ANALYSIS Slide | 2 Cluster Analysis – Data mapped to a set of Normal Densities – with specified degree of membership – a model based clustering Customer Profiling – Characterizing the Distributions encountered – Age, ARPU, Net Stay… leading to a probabilistic description / modeling of the dataSentiment Analysis via Independent Term Matching where each word is drawn from a specified Normal Distribution – combined by their sum to determine overall sentiment score A model based approach to data analysis Goal: model arbitrary distributions as sums of Gaussian densities (with parameters estimated via expectation maximization algorithm) – so that each data point is characterized with respect to a distribution from which it is expected to have originated
- 3. PARAMETER ESTIMATION VIA EXPECTATION MAXIMIZATION ALGORITHM Slide | 3 Ref: Estimating Gaussian Mixture Densities with EM, Carlo Tomasi, Duke University
- 4. PARAMETER ESTIMATION VIA EXPECTATION MAXIMIZATION ALGORITHM Slide | 4 Ref: Estimating Gaussian Mixture Densities with EM, Carlo Tomasi, Duke University
- 5. RESULTS – ESTIMATING THE COMPONENT GAUSSIAN DENSITIES Slide | 5 II. Standardize the Data and estimate empirical Probability Density Function I. Histogram of original Data – (which composite densities to be estimated) III. Estimate Gaussian Component Densities (fx1/2/3) via EM Algorithm and their scaled Sum (fx) IV. fx: Sum of the individual component densities scaled by their mixing probabilities (for comparison with II the empirical PDF of Data)
- 6. CONVERGENCE OF THE EM ALGORITHM FOR THE PARAMETERS Slide | 6
- 7. RESULTS – INTERPRETATION OF CLUSTER MEMBERSHIP Slide | 7 Test with one dimensional data, through EM algorithm can estimate parameters for sums of “D” dimensional data *Applicable for multi dimensional data and need to explore correlated random variables