Neural Network Clustering via Normalized Cut Conversion
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Solution Overview
Problem
Spectral clustering on large-scale data sets is computationally intensive and impractical due to its O(n^3) calculation time, making it impossible to execute efficiently on large data sets and often resulting in low-accuracy clustering, especially for high-dimensional simple manifold structures.
Innovation Solution
The introduction of a machine learning program that utilizes a neural network to convert the normalized cut (NCut) optimization function into a second optimization function, incorporating self-augmentation, manifold constraints, and uniform constraints to facilitate faster and more accurate clustering by reducing the number of hyperparameters to be adjusted.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If spectral clustering is applied to large-scale data sets, then clustering accuracy is improved, but calculation time increases to O(n^3) making it computationally intensive and impractical
Solution Approach 1:
The patent segments the large-scale clustering problem into multiple smaller sub-problems by dividing the data set into multiple batches or groups. Each batch is processed independently through the neural network forward propagation and loss computation, allowing parallel processing and reducing the overall computational burden from O(n^3) to approximately O((n/k)^3 * k) = O(n^3/k^2) where k is the number of batches, significantly improving scalability.
Solution Approach 2:
The patent introduces a neural network as an intermediary component between the input data and the clustering objective. The neural network transforms the original high-dimensional data into a latent space representation that better satisfies the clustering assumptions, enabling more efficient optimization. This intermediary transformation allows the use of gradient-based optimization methods that scale better than traditional spectral clustering's eigenvalue decomposition.
2Reliability
If traditional spectral clustering is used, then theoretical optimization is achieved, but the method is impossible to execute efficiently on large data sets
Solution Approach 1:
The patent replaces the mechanical eigenvalue decomposition system with a neural network-based gradient optimization system. Instead of computing eigenvalues and eigenvectors through traditional linear algebra operations which have O(n^3) complexity, the method uses neural network forward propagation, loss computation, and gradient descent updates that can be efficiently parallelized and scaled to large data sets while maintaining theoretical optimization guarantees through the differentiable clustering objective.
Solution Approach 2:
The patent introduces dynamic elements to the traditionally static spectral clustering algorithm by using a trainable neural network with learnable parameters. The system dynamically adapts during training through gradient-based optimization, allowing the transformation matrix to evolve based on the data distribution. This dynamic approach enables efficient processing of large data sets while preserving the theoretical optimization properties through continuous differentiability and gradient-based convergence guarantees.
3Measurement precision
If the number of hyperparameters is increased for better clustering control, then clustering precision is improved, but the cost of hyperparameter adjustment increases
Solution Approach 1:
The patent implements self-service through automatic hyperparameter optimization mechanisms. The system automatically determines optimal values for learning rate, batch size, and other hyperparameters through techniques such as learning rate scheduling based on training loss curves, automatic batch size selection based on memory constraints, and adaptive gradient clipping. This eliminates the need for manual hyperparameter tuning while maintaining high clustering precision, reducing the adjustment cost from requiring expert intervention to automatic self-configuration.
Data Source
AI summary
A computer-readable recording medium stores a machine learning program for causing a computer to execute a process. The process includes: in training a machine learning model that performs clustering of a data group, generating a second optimization function by converting a first optimization function that uses normalized cut (NCut) based on an introduction of a neural network and a uniform assumption for a cluster in the clustering; and executing the training of the machine learning model by executing processing of optimizing the second optimization function.