# Fast Spectral Clustering Using Autoencoders and Landmarks

## TL;DR

This paper presents a fast spectral clustering algorithm that leverages autoencoders and landmarks to reduce computational complexity, enabling efficient clustering of large datasets.

## Contribution

The authors introduce a novel spectral clustering method that uses landmarks and autoencoders to significantly improve efficiency over traditional approaches.

## Key findings

- Achieves eigen decomposition complexity of O(np)
- Performs well on large datasets in experiments
- Reduces computational time compared to classical spectral clustering

## Abstract

In this paper, we introduce an algorithm for performing spectral clustering efficiently. Spectral clustering is a powerful clustering algorithm that suffers from high computational complexity, due to eigen decomposition. In this work, we first build the adjacency matrix of the corresponding graph of the dataset. To build this matrix, we only consider a limited number of points, called landmarks, and compute the similarity of all data points with the landmarks. Then, we present a definition of the Laplacian matrix of the graph that enable us to perform eigen decomposition efficiently, using a deep autoencoder. The overall complexity of the algorithm for eigen decomposition is $O(np)$, where $n$ is the number of data points and $p$ is the number of landmarks. At last, we evaluate the performance of the algorithm in different experiments.