ML//unsupervised learning

Unsupervised learning is the branch of machine learning whose methods find structure in data without labels: directions of variation, groups, rarities and low-dimensional representations. PCA keeps the directions of largest variance, clustering groups similar samples (K-means around centroids, spectral clustering through the connectivity between them), and anomaly detection learns what normal looks like and flags what departs from it.

Unsupervised learning is the branch of machine learning whose methods find structure in data without labels: directions of variation, groups, rarities and low-dimensional representations. PCA keeps the directions of largest variance, clustering groups similar samples (K-means around centroids, spectral clustering through the connectivity between them), and anomaly detection learns what normal looks like and flags what departs from it.

It is where most industrial projects actually land. Labels for failures are scarce (three bearing failures in five years, written down at the repair date), while healthy operation fills the historian for free, so the question changes from what does a failure look like? to what does normal look like? The most profitable uses in a plant are finding the operating regimes (start-up, partial load, full load, cleaning) and watching a process for departures from its normal correlations (multivariate statistical process control).

What it finds is a property of the data and of the choices made, never a fact about the machine. A clustering always returns as many groups as it was asked for, and PCA always returns orthogonal directions; whether those groups are real modes or those directions mean anything is checked against the physics or an expert, not against the algorithm's own score.

Scaling decides what counts. Every one of these methods measures distance or variance, so a variable in pascals beside one in degrees dominates by units alone unless the data are standardized.

Without labels there is no test score in the usual sense. Detectors are evaluated with injected faults, past incidents and the judgement of maintenance staff on the top alarms of each week.

Their mathematical foundations live under Math: the covariance matrix, projection and spectral coordinates. With labels the problem is supervised learning.