Manifold Learning Graph Wavelet Clustering
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing clustering methods and manifold learning techniques struggle with complex data sets that have nonlinear separation boundaries and high noise levels, leading to less effective clustering results and limited interpretability of feature dimensions.
Innovation Solution
The proposed software technology for manifold learning involves constructing a graph structure from data points, generating a multi-scale representation of the feature space, regularizing this representation, and using it to identify clusters. This approach enhances data representation and interpretability by maintaining correspondence between original feature dimensions and the new representation space.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If existing clustering methods (K-means, hierarchical, AP, mean shift, GMM) are used, then clustering is fast and effective on data with well-separated clusters, but clustering results deteriorate when complex patterns exist (nonlinear separation boundaries, high noise)
Solution Approach 1:
The patent segments the feature space into multiple scales using spectral graph wavelets, allowing different regions of the data to be analyzed at appropriate resolution levels. This multi-scale segmentation enables the system to capture both local cluster structures and global data patterns, improving accuracy on complex datasets while maintaining computational efficiency through hierarchical processing.
Solution Approach 2:
The patent transforms the clustering problem from the original feature space into a multi-scale spectral domain using graph wavelet transforms. By operating in this transformed dimensional space, the system can handle nonlinear separation boundaries and high-dimensional data more effectively, then map results back to the original space for interpretation.
2Device complexity
If nonlinear dimensionality reduction (manifold learning) is used as pre-processing, then dimensionality reduction and visualization are improved, but interpretability of original feature dimensions is lost
Solution Approach 1:
The patent changes the parameter representation from raw feature values to spectral graph wavelet coefficients that encode both the transformed space structure and the original feature space relationships. These coefficients serve as a bridge between the reduced-dimensional manifold representation and the interpretable original features, allowing the system to gain dimensionality reduction benefits while preserving feature interpretability through the spectral domain mapping.
3Reliability
If existing manifold learning techniques (UMAP) are used, then clustering results are improved in some scenarios, but performance deteriorates on complex data with high noise and interpretability remains limited
Solution Approach 1:
The patent introduces spectral graph wavelets as an intermediary transformation that connects the original feature space with the manifold learning process. These wavelets serve as a mediating representation that captures complex patterns and noise robustly while maintaining a structured relationship to original features, enabling both improved clustering accuracy on noisy complex data and preserved feature interpretability through the spectral domain bridge.
Data Source
AI summary
A computing platform may be configured to: (i) based on a set of data points defining a feature space, construct a graph structure associated with the set of data points; (ii) generate a multi-scale representation that represents the feature space, wherein each feature of a plurality of features from the feature space is represented in a respective plurality of scales with respect to the graph structure; (iii) regularize the multi-scale representation; (iv) based on the regularized multi-scale representation, identify a plurality of clusters associated with the set of data points; and (v) transmit, to a client station, data regarding the plurality of clusters and thereby cause an indication of the plurality of clusters to be presented at a user interface of the client station.