How do Gaussian mixture models differ from K-means clustering?

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AcadiFi · Accepted Answer

Gaussian mixture models (GMM) assume the data are generated from a weighted sum of K multivariate Gaussian distributions, each with its own mean, covariance, and mixing weight. Unlike K-means, which produces hard cluster assignments, GMM produces soft probabilities that a point belongs to each component. It is fitted using the Expectation-Maximization (EM) algorithm.

EM alternates two steps. The E-step computes the posterior probability that each point belongs to each Gaussian given current parameters. The M-step updates means, covariances, and weights to maximize the expected log-likelihood. Iterate until convergence.

For market regime detection at a firm like Kilvane Macro, an analyst might fit a 3-component GMM to weekly returns of equities, bonds, and commodities. The three components might map to a risk-on regime (high equity mean, low bond variance), a risk-off regime (negative equity, flight-to-quality bond gains), and a stagflation regime (mixed). Soft assignments reveal transition periods where probabilities are split 0.45/0.45/0.10.

GMM is preferred over K-means when clusters have different shapes and variances (ellipsoidal rather than spherical), when soft probabilities are useful (for risk-weighted portfolio tilts), or when the data-generating process is plausibly Gaussian mixtures. The trade-off is more parameters to estimate and potential convergence to local optima; run EM from multiple random starts. For CFA candidates, GMM is the probabilistic cousin of K-means and bridges into hidden Markov models when time structure matters.

How do Gaussian mixture models differ from K-means clustering?

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