Virtual SOM Using Parametric Functions for High-Dimensional Data
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Solution Overview
Problem
Traditional Self-Organizing Maps (SOMs) require excessive memory and time for training due to large weight vectors, especially when handling high-dimensional data, leading to inefficient storage and processing of information.
Innovation Solution
The method employs a virtual SOM (VSOM) that uses M functions to represent information items, eliminating the need for weight vectors and allowing for reduced storage capacity and faster training by calculating virtual map units, which are monotonically decreasing functions associated with feature points, enabling efficient mapping of information items into an N-dimensional space.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional SOM with weight vectors is used to represent high-dimensional data, then the topological properties and pattern recognition capability are maintained, but the memory consumption becomes excessively high
Solution Approach 1:
The patent extracts only the essential information from weight vectors by identifying feature points and representing the weight space through a reduced set of control points and basis functions. This extraction approach maintains the topological properties needed for pattern recognition while eliminating redundant data storage requirements.
Solution Approach 2:
The patent transforms the representation from fixed weight vectors to a parametric model using control points and basis functions. By changing the parameters from dense weight matrices to sparse control point coordinates, the memory consumption is dramatically reduced while preserving the functional capabilities of the SOM.
2Measurement precision
If large SOMs are used to represent huge sets of input data, then the data representation quality is improved, but the memory space requirement increases significantly
Solution Approach 1:
The patent changes the parameter representation from fixed-dimensional weight vectors to adaptive parametric functions. This allows the system to maintain high representation quality for large datasets without proportionally increasing memory usage, as the parametric model size remains relatively constant regardless of the number of map units.
Solution Approach 2:
Instead of storing complete weight vectors for each map unit, the patent creates a parametric copy that can generate weight vectors on-demand. This virtualization approach allows large SOMs to be represented with minimal memory while maintaining full functionality.
3Quantity of substance
If the dimension of input space is reduced to decrease memory needs, then the memory consumption is reduced, but necessary information is lost
Solution Approach 1:
The patent introduces a functional dimension by representing weight vectors through parametric functions rather than fixed arrays. This dimensional transformation allows the system to compress high-dimensional data without losing information, as the parametric representation preserves the continuous relationships in the data space.
4Ease of manufacture
If traditional SOM training algorithm is used, then the simplicity of the algorithm is maintained, but the training time becomes very long for large number of map units
Solution Approach 1:
The patent extracts the essential training dynamics by working directly with control points and basis functions rather than updating all weight vectors. This extraction of key elements maintains algorithmic simplicity while dramatically reducing the computational burden of training large SOMs.
Solution Approach 2:
Instead of updating all weight vectors during training, the patent performs partial updates on control points that represent the essential structure. This partial action approach maintains the core learning dynamics while reducing training time for large networks.
Data Source
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AI summary
A new and improved approach to processing digital information is proposed which allows to map information items into an N-dimensional map such that similar information items are mapped to similar positions within the map, wherein in particular less storage capacity is needed than in solutions known in the prior art. For this purpose the invention proposes a method with the steps of providing at least one information item and mapping said information item into an N-dimensional map by determining a matching position within the map for the information item, wherein each information item is represented by a multi-dimensional vector with M components, the N-dimensional map is represented by a set of M functions of the map position, and each of said M functions is associated with a respective one of the M vector components of the information item. The invention further proposes a process control system, an information retrieval system and a digital storage medium.