Disjoint Manifold Modeling With Grouped Generative Sub-Models
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Solution Overview
Problem
Existing computer modeling systems fail to effectively model data as disjoint manifolds, leading to inaccurate representation and classification due to the assumption of a single continuous manifold, which overlooks the intrinsic dimensionality and complexity of different data groups.
Innovation Solution
The system models data as a union of manifolds by grouping training data into separate sub-models, each with estimated intrinsic dimensionality, and adjusts weights based on complexity to improve generative and classification tasks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If data is modeled as a single continuous manifold, then the model structure is simple and unified, but the accuracy of representing disjoint data regions deteriorates
Solution Approach 1:
The patent divides the data modeling task into multiple separate manifolds, each representing a distinct data region or cluster. Instead of forcing all data into a single continuous manifold, the system identifies and models disjoint regions independently, allowing each manifold to accurately capture the local structure of its corresponding data region while maintaining overall model accuracy.
2Ease of manufacture
If a single generative model is used for the entire data set, then the model is easier to train and manage, but the ability to capture distinct manifold structures of different data groups deteriorates
Solution Approach 1:
The patent implements a segmented generative modeling approach where the data set is divided into multiple groups, each with its own generative model. This allows each sub-model to specialize in capturing the specific manifold structure of its assigned data group, improving overall reliability while maintaining manageable model complexity through modular architecture.
Solution Approach 2:
Each generative sub-model is trained to capture the local characteristics and manifold structure of its specific data group rather than attempting to model global patterns. This local specialization enables more accurate representation of distinct data regions while allowing the overall system to handle diverse data types effectively.
3Ease of operation
If all classes are treated with equal weighting in classification, then the training process is simpler, but the performance on high-complexity classes deteriorates
Solution Approach 1:
The patent applies differential weighting to different classes based on their intrinsic dimensionality and complexity. High-complexity classes with higher intrinsic dimensionality receive increased weighting in the loss function, ensuring they receive sufficient attention during training. This localized adjustment to training dynamics improves classification accuracy for difficult classes without significantly complicating the overall training process.
Data Source
AI summary
A computer model is trained to account for data samples in a high-dimensional space as lying on different manifolds, rather than a single manifold to represent the data set, accounting for the data set as a whole as a union of manifolds. Different data samples that may be expected to belong to the same underlying manifold are determined by grouping the data. For generative models, a generative model may be trained that includes a sub-model for each group trained on that group's data samples, such that each sub-model can account for the manifold of that group. The overall generative model includes information describing the frequency to sample from each sub-model to correctly represent the data set as a whole in sampling. Multi-class classification models may also use the grouping to improve classification accuracy by weighing group data samples according to the estimated latent dimensionality of the group.