GMM Approximation of Multi-Dimensional Numeric Arrays
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Solution Overview
Problem
Processing large datasets of multi-dimensional numeric arrays in a computing environment is complex and computationally difficult, especially when applying probabilistic models like Gaussian Mixture Models (GMMs).
Innovation Solution
The method involves distributing the data set across a multi-dimensional grid with integer coordinates and assigning a hypercube to each constituent Gaussian distribution of the GMM distribution as a subspace of the grid, thereby reducing the data footprint.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a Gaussian Mixture Model (GMM) is applied to represent multi-dimensional numeric arrays, then the data can be modeled probabilistically, but the computational complexity and difficulty increase extremely
Solution Approach 1:
The patent segments the multi-dimensional data space into discrete grid cells with integer coordinates. Each grid cell serves as an independent unit for storing GMM parameters, dividing the complex continuous probabilistic modeling problem into manageable discrete segments. This segmentation reduces computational complexity by avoiding continuous space operations while maintaining probabilistic modeling capability.
Solution Approach 2:
The patent uses a simplified discrete grid representation that copies the essential structure of the continuous multi-dimensional space. Instead of working with continuous coordinates, the system creates a discrete copy of the data space where each cell represents a region, enabling efficient GMM parameter storage and retrieval without the full computational burden of continuous space operations.
2Loss of information
If GMM distribution is used to approximate multi-dimensional numeric arrays, then data representation is achieved, but data footprint and storage requirements increase
Solution Approach 1:
The patent applies local quality by assigning GMM parameters specifically to discrete grid cells where they are needed, rather than uniformly across the entire data space. Each grid cell contains GMM parameters only for the regional data distribution it represents, reducing overall storage requirements while maintaining accurate local data representation where it matters most.
Solution Approach 2:
The patent transforms the continuous multi-dimensional data space into a discrete grid structure with integer coordinates, adding a discretization dimension. This dimensional transformation allows GMM parameters to be stored at discrete locations rather than continuously, significantly reducing the data footprint while preserving the essential probabilistic structure of the original multi-dimensional arrays.
Data Source
AI summary
Disclosed are a method and devices of an efficient Gaussian Mixture Model (GMM) distribution based approximation of a data set including a collection of multi-dimensional numeric arrays in a computing environment. In accordance therewith, the data set is distributed across a multi-dimensional grid having integer coordinates associated therewith, and a hypercube is assigned to each constituent Gaussian distribution of constituent Gaussian distributions of the GMM distribution as a subspace of the multi-dimensional grid to form a number of hypercubes. A data footprint of the data set is reduced through the GMM distribution based on assigning the hypercube to the each constituent Gaussian distribution of the constituent Gaussian distributions of the GMM distribution.