Gaussian Mixture Model Parameter Computation via EM Algorithm and Data Reduction
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Solution Overview
Problem
Existing methods for computing parameters of Gaussian Mixture Models (GMMs) in big data processing are inefficient, especially when dealing with large volumes of complex data, as they struggle with analytical computations and are affected by outliers.
Innovation Solution
The method involves iteratively deriving parameters of constituent Gaussian distributions using an Expectation-Maximization (EM) algorithm, modifying the data set by replacing values close to the distribution center with a mean value, and reducing the data footprint through continued iterative derivation of parameters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If analytical methods are used to compute parameters of Gaussian distributions, then computation accuracy may be maintained, but computation becomes difficult or impossible for large data sets
Solution Approach 1:
The patent replaces traditional analytical computation methods with an iterative Expectation-Maximization (EM) algorithm. This substitution transforms the intractable analytical problem into a series of simpler iterative steps that can be efficiently computed using standard numerical linear algebra operations, making parameter computation feasible for large data sets while maintaining accuracy.
Solution Approach 2:
The patent employs a dynamic iterative approach where the EM algorithm repeatedly updates parameter estimates until convergence. This dynamic process allows the computation to adapt to the data characteristics and converge to accurate solutions, overcoming the static limitations of direct analytical methods for large-scale problems.
2Measurement precision
If all data points are retained in the data set, then model approximation accuracy is improved, but data footprint and computational complexity increase
Solution Approach 1:
The patent extracts and removes redundant information from the data set by identifying and eliminating data points that do not contribute meaningfully to the GMM approximation. This extraction process reduces data footprint while preserving the essential characteristics needed for accurate model approximation.
Solution Approach 2:
The patent transforms the original data into a reduced representation by computing sufficient statistics (means, covariances, and mixture weights) that capture the essential distributional properties. This parameter transformation compresses the data while maintaining the information necessary for accurate GMM approximation.
Data Source
AI summary
Disclosed are a method and devices of an efficient Gaussian Mixture Model (GMM) distribution based approximation of a data set in a computing environment. In accordance therewith, parameters of constituent Gaussian distributions of the GMM distribution are iteratively derived based on execution of an Expectation-Maximization (EM) algorithm incorporating the data set as an input thereto. The data set is modified by replacing, for each constituent Gaussian distribution of the GMM distribution, numeric values and/or vectors of the numeric values of the data set that differ in magnitude from a center of the each constituent Gaussian distribution by less than a threshold with a mean value of the data set, with a weight of the mean value being indicative of a cardinality thereof within the modified data set. Subsequently, the iterative derivation of the parameters of the constituent Gaussian distributions of the GMM distribution is continued.