# Beyond Labels: Advancing Cluster Analysis with the Entropy of Distance Distribution (EDD)

arXiv: https://arxiv.org/abs/2311.16621 · HTML: https://mlsanity.com/paper/2311.16621/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 15 references that are in the map.
- First posted on arXiv 28 Nov 2023.

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Cognitive computational neuroscience](https://mlsanity.com/paper/1807.11819/) (2018)
- [How deep is deep enough? -- Quantifying class separability in the hidden layers of deep neural networks](https://mlsanity.com/paper/1811.01753/) (2018)
- [A Novel Intrinsic Measure of Data Separability](https://mlsanity.com/paper/2109.05180/) (2021)
- [Neural Network based Successor Representations of Space and Language](https://mlsanity.com/paper/2202.11190/) (2022)
- [Word class representations spontaneously emerge in a deep neural network trained on next word prediction](https://mlsanity.com/paper/2302.07588/) (2023)
- [Neural Network based Formation of Cognitive Maps of Semantic Spaces and the Emergence of Abstract Concepts](https://mlsanity.com/paper/2210.16062/) (2022)
- [DCSI -- An improved measure of cluster separability based on separation and connectedness](https://mlsanity.com/paper/2310.12806/) (2023)
- [Conceptual Cognitive Maps Formation with Neural Successor Networks and Word Embeddings](https://mlsanity.com/paper/2307.01577/) (2023)

## Built on by (most cited first, 1 of 1)

- [Analyzing Narrative Processing in Large Language Models (LLMs): Using GPT4 to test BERT](https://mlsanity.com/paper/2405.02024/) (2024)

## Abstract (arXiv)

In the evolving landscape of data science, the accurate quantification of clustering in high-dimensional data sets remains a significant challenge, especially in the absence of predefined labels. This paper introduces a novel approach, the Entropy of Distance Distribution (EDD), which represents a paradigm shift in label-free clustering analysis. Traditional methods, reliant on discrete labels, often struggle to discern intricate cluster patterns in unlabeled data. EDD, however, leverages the characteristic differences in pairwise point-to-point distances to discern clustering tendencies, independent of data labeling. Our method employs the Shannon information entropy to quantify the 'peakedness' or 'flatness' of distance distributions in a data set. This entropy measure, normalized against its maximum value, effectively distinguishes between strongly clustered data (indicated by pronounced peaks in distance distribution) and more homogeneous, non-clustered data sets. This label-free quantification is resilient against global translations and permutations of data points, and with an additional dimension-wise z-scoring, it becomes invariant to data set scaling. We demonstrate the efficacy of EDD through a series of experiments involving two-dimensional data spaces with Gaussian cluster centers. Our findings reveal a monotonic increase in the EDD value with the widening of cluster widths, moving from well-separated to overlapping clusters. This behavior underscores the method's sensitivity and accuracy in detecting varying degrees of clustering. EDD's potential extends beyond conventional clustering analysis, offering a robust, scalable tool for unraveling complex data structures without reliance on pre-assigned labels.