# MMM and MMMSynth: Clustering of heterogeneous tabular data, and synthetic data generation

## TL;DR

This paper introduces new methods for clustering and generating synthetic data from heterogeneous tabular datasets, improving performance over existing techniques.

## Contribution

The paper introduces MMM and MMMSynth, novel algorithms for clustering and synthetic data generation in heterogeneous tabular data.

## Key findings

- MMM outperforms standard algorithms in clustering synthetic and real heterogeneous data.
- MMMSynth generates high-quality synthetic data that approaches the performance of real data in ML tasks.
- The synthetic data generation method outperforms existing literature approaches.

## Abstract

We provide new algorithms for two tasks relating to heterogeneous tabular datasets: clustering, and synthetic data generation. Tabular datasets typically consist of heterogeneous data types (numerical, ordinal, categorical) in columns, but may also have hidden cluster structure in their rows: for example, they may be drawn from heterogeneous (geographical, socioeconomic, methodological) sources, such that the outcome variable they describe (such as the presence of a disease) may depend not only on the other variables but on the cluster context. Moreover, sharing of biomedical data is often hindered by patient confidentiality laws, and there is current interest in algorithms to generate synthetic tabular data from real data, for example via deep learning. We demonstrate a novel EM-based clustering algorithm, MMM (“Madras Mixture Model”), that outperforms standard algorithms in determining clusters in synthetic heterogeneous data, and recovers structure in real data. Based on this, we demonstrate a synthetic tabular data generation algorithm, MMMsynth, that pre-clusters the input data, and generates cluster-wise synthetic data assuming cluster-specific data distributions for the input columns. We benchmark this algorithm by testing the performance of standard ML algorithms when they are trained on synthetic data and tested on real published datasets. Our synthetic data generation algorithm outperforms other literature tabular-data generators, and approaches the performance of training purely with real data.