Fast Large-Scale Spectral Clustering via Explicit Feature Mapping.

Area of Science:

• Machine Learning
• Data Science
• Computer Vision

Background:

• Spectral clustering is a powerful technique for data analysis.
• Existing methods like Nyström approximations struggle with large-scale datasets due to high computational complexity.
• Efficiently handling high-dimensional and large datasets is crucial for modern machine learning applications.

Purpose of the Study:

• To develop an efficient spectral clustering method for large-scale data.
• To reduce the computational complexity of spectral clustering compared to existing methods.
• To improve the speed and scalability of spectral clustering without sacrificing accuracy.

Main Methods:

• Employs random Fourier features for explicit data representation in kernel space.
• Reduces computational complexity from O(nmd+m^3+nm^2) for Nyström to O(nDd+D^3+n'D^2) for the proposed method.
• Demonstrates effectiveness on large datasets like MNIST, achieving similar accuracy to Nyström methods but with twice the speed.

Main Results:

• The proposed method offers a lower computational complexity for large-scale spectral clustering.
• Random Fourier features enable efficient eigenvector approximation and faster prediction.
• Achieved a twofold speed increase over Nyström methods on the MNIST dataset with comparable clustering accuracy.

Conclusions:

• The proposed spectral clustering method is efficient and scalable for large datasets.
• Explicitly mapping data using random Fourier features is a viable strategy for improving spectral clustering performance.
• This approach offers significant advantages for applications requiring fast and accurate clustering of massive data.