Generalized K-Means Clustering

For people who are unfamiliar, k-means is a partitioning algorithm that aims to group observations into a specific number (k) of clusters in such a way that each observation ends up in the cluster with the “nearest” mean. So say you want 5 groups, it will make five groups so that every observation is in the group where it’s nearest to the mean.

And so that raises the question of what “nearest” means, and here this allows you to replace Euclidian distance with things like Kullback-Leibler divergence (that’s the KL below) which make more sense than Euclidian distance if you’re trying to measure how close two probability distributions are to each other.

Can folks comment on what applications they use k-means for? It was a basic technique I learned in school, but honestly I am not really familiar with a single use case that is very clearly motivated besides "pretty pictures".

So I do a bit of work in geospatial analysis, and hotspots are better represented by DBSCAN (do not need to assign every point a cluster). I just do not even use clustering very often in gig (supervised ML and anomaly detection are much more prevalent in the rest of my work).

# HackerNews Announcement

## Title

Generalized K-Means Clustering for Apache Spark with Bregman Divergences

## Body (3,982 characters)

I've built a production-ready K-Means library for Apache Spark that supports multiple distance functions beyond Euclidean.

*Why use this instead of Spark MLlib?*

MLlib's KMeans is hard-coded to Euclidean distance, which is mathematically wrong for many data types:

- *Probability distributions* (topic models, histograms): KL divergence is the natural metric. Euclidean treats [0.5, 0.3, 0.2] and [0.49, 0.31, 0.2] as similar even though they represent different distributions. - *Audio/spectral data*: Itakura-Saito respects multiplicative power spectra. Euclidean incorrectly treats -20dB and -10dB as closer than -10dB and 0dB. - *Count data* (traffic, sales): Generalized-I divergence for Poisson-distributed data. - *Outlier robustness*: L1/Manhattan gives median-based clustering vs mean-based (L2).

Using the wrong divergence yields mathematically valid but semantically meaningless clusters.

*Available divergences:* KL, Itakura-Saito, L1/Manhattan, Generalized-I, Logistic Loss, Squared Euclidean

*What's included:* - 6 algorithms: GeneralizedKMeans, BisectingKMeans, XMeans (auto k), SoftKMeans (fuzzy), StreamingKMeans, KMedoids - Drop-in MLlib replacement (same DataFrame API) - 740 tests, deterministic behavior, cross-version persistence (Spark 3.4↔3.5, Scala 2.12↔2.13) - Automatic optimization (broadcast vs crossJoin based on k×dim to avoid OOM) - Python and Scala APIs

*Example:*

```scala // Clustering topic distributions from LDA val topics: DataFrame = // probability vectors

// WRONG: MLlib with Euclidean new org.apache.spark.ml.clustering.KMeans() .setK(10).fit(topics)

// CORRECT: KL divergence for probabilities new GeneralizedKMeans() .setK(10) .setDivergence("kl") .fit(topics)

// For standard data, drop-in replacement: new GeneralizedKMeans() .setDivergence("squaredEuclidean") .fit(numericData) ```

*Quick comparison:*

| Use Case | MLlib | This Library | |----------|-------|--------------| | General numeric | L2 | L2 (compatible) | | Probability distributions | Wrong | KL divergence | | Outlier-robust | | L1 or KMedoids | | Auto k selection | | XMeans (BIC/AIC) | | Fuzzy clustering | | SoftKMeans |

*Performance:* ~870 pts/sec (SE), ~3,400 pts/sec (KL) on modest hardware. Scales to billions of points with automatic strategy selection.

*Production-ready:* - Cross-version model persistence - Scalability guardrails (chunked assignment) - Determinism tests (same seed → identical results) - Performance regression detection - Executable documentation

GitHub: https://github.com/derrickburns/generalized-kmeans-clusterin...

This started as an experiment to understand Bregman divergences. Surprisingly, KL divergence is often faster than Euclidean for probability data. Open to feedback!