Multidimensional Tensor Clustering for Efficient Data Analysis
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Solution Overview
Problem
Existing clustering techniques are inefficient and require significant computational resources, often losing information about interconnections between data types and providing limited insight into complex data relationships, especially when dealing with massive datasets in multiple dimensions.
Innovation Solution
The method involves convolving a first tensor representing interconnections across three or more dimensions with a second tensor, performing singular value decomposition on the convolution result, and using Fourier transforms to enhance data processing and clustering, allowing for more efficient and accurate identification of clusters and relationships in multidimensional data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing clustering techniques such as k-means are used to process massive amounts of data, then clustering can be performed, but computational resources (processor cycles and memory) are excessively consumed
Solution Approach 1:
The patent transforms the clustering problem from traditional 2D space into N-dimensional tensor space, where data points are represented as tensors with multiple dimensions corresponding to different features and relationships. This dimensional transformation enables the use of tensor decomposition techniques that exploit the multi-linear structure of the data, achieving better clustering accuracy with reduced computational complexity compared to conventional methods that process data in flat 2D matrices.
2Reliability
If existing clustering techniques are used, then data can be grouped, but information about interconnections between different types of data is lost
Solution Approach 1:
The patent constructs a composite tensor structure that integrates multiple types of data and their interconnections into a unified N-dimensional framework. Different dimensions of the tensor represent different data types, features, and relationship types, allowing the model to preserve and simultaneously analyze multiple sources of information including interconnections between different data types, rather than processing them separately as in traditional clustering methods.
3Reliability
If ad hoc iterative approaches are used for clustering, then clustering can be achieved, but processing speed is slow and requires multiple iterations
Solution Approach 1:
The patent replaces the mechanical iterative search-and-eliminate process with an analytical solution based on tensor decomposition. Instead of repeatedly iterating through data points to find clusters, the method uses mathematical decomposition of the N-dimensional tensor into lower-rank components, which directly reveals the cluster structure in a single computational pass or with minimal iterations, dramatically improving processing speed while maintaining clustering effectiveness.
4Reliability
If data sets are treated independently in processing, then individual clustering can be performed, but insights into complex relationships among data points are limited
Solution Approach 1:
The patent merges multiple independent data sets and their relationships into a single N-dimensional tensor structure, where different dimensions represent different data types, features, and relationship types. This unified representation allows simultaneous analysis of all data and their interconnections, revealing complex relationships that would be invisible when analyzing data sets independently, while the tensor decomposition methodology provides an efficient framework for handling the complexity.
Data Source
AI summary
A tensor processing technique includes: accessing a first tensor representing interconnections of a plurality of nodes, the first tensor being a tensor of three or more dimensions; accessing a second tensor; convolving the first tensor with the second tensor to generate a convolution result tensor; and outputting at least a portion of the convolution result tensor.