# Random projection tree similarity metric for SpectralNet

## TL;DR

This paper introduces a new similarity metric for SpectralNet based on random projection trees, improving clustering accuracy and computational efficiency over traditional k-NN graphs.

## Contribution

The paper proposes a novel rpTree-based similarity metric for SpectralNet, demonstrating enhanced clustering performance and robustness to parameter choices.

## Key findings

- rpTree similarity improves clustering accuracy over k-NN graphs
- Clustering performance is robust to rpTree parameter variations
- Using random directions is computationally efficient

## Abstract

SpectralNet is a graph clustering method that uses neural network to find an embedding that separates the data. So far it was only used with $k$-nn graphs, which are usually constructed using a distance metric (e.g., Euclidean distance). $k$-nn graphs restrict the points to have a fixed number of neighbors regardless of the local statistics around them. We proposed a new SpectralNet similarity metric based on random projection trees (rpTrees). Our experiments revealed that SpectralNet produces better clustering accuracy using rpTree similarity metric compared to $k$-nn graph with a distance metric. Also, we found out that rpTree parameters do not affect the clustering accuracy. These parameters include the leaf size and the selection of projection direction. It is computationally efficient to keep the leaf size in order of $\log(n)$, and project the points onto a random direction instead of trying to find the direction with the maximum dispersion.