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

Chandrani Kumari, Rahul Siddharthan

TL;DR

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 is demonstrated.

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.

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

TL;DR

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 is demonstrated.

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.
Paper Structure (32 sections, 31 equations, 5 figures)

This paper contains 32 sections, 31 equations, 5 figures.

Table of Contents

  1. Abstract
  2. Introduction
  3. Materials and methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. Funding
  8. Author contributions
  9. Code availability
  10. Declaration of interests

Figures (5)

  • Figure 1: For a dataset of 20 rows, the marginal likelihood can be calculated exactly (solid line); this is compared with TI and with HM$\beta$ at various $\beta$. $\beta=0.5$ gives results close to the exact value.
  • Figure 2: Clustering of four kinds of synthetic datasets: (A) purely numeric (normally distributed, differing means and variances), (B) purely numeric (normally distributed, same mean but differing variances), (C) purely categorical, and (D) mixed.
  • Figure 3: Optimal number of clusters obtained by TI, HM$\beta$ and Bayesian Information Criterion (BIC), on mixed categorical+numeric data with true cluster number ranging from 2 to 10. TI and HM$\beta$ show comparably good results while, in our data, BIC is mostly unable to predict the true number of clusters.
  • Figure 4: Performance of MMM, using the TI criterion, and "MMM, true Nclust" where it is told the true number of clusters versus other programs, on eight datasets from ClustBench (A) and six datasets from UCI (B). Performance is reported using Adjusted Rand Index.
  • Figure 5: Logistic regression (A) and random forest (B) models were trained on the real data and on synthetic data generated using MMMSynth, TVAE, GC, CGAN and CTGAN and their predictive performance evaluated on the real datasets. The AUC (area under ROC curve, averaged over 20 runs) is shown for each method and each dataset, and errorbars are shown too.