Klustermodeller

Klustermodeller, or cluster models, are techniques in statistics and data science used to identify groups of similar observations within data without using predefined labels. The aim is to partition data so that points within the same cluster are more alike according to a chosen similarity measure than to points in other clusters.

Two broad approaches dominate clustering: distance-based methods that optimize an objective function to assign samples to a fixed number of clusters, and model-based methods that assume the data are generated by a mixture of probability distributions. Distance-based methods include K-means and K-medoids for partitioning data, and hierarchical clustering which builds a tree of clusters. Model-based clustering uses probabilistic models such as Gaussian mixture models and estimates parameters via the Expectation-Maximization algorithm.

Common algorithms include K-means, K-medoids, hierarchical clustering, Gaussian mixture models, DBSCAN, and spectral clustering. The choice depends on data type, cluster shape, and scaling considerations. For mixed or categorical data, distance measures like Gower distance or specialized methods are used.

A central challenge is selecting the number of clusters, with methods such as the elbow method, silhouette score, gap statistic, and cross-validation variants guiding the choice. Other issues include sensitivity to initialization (notably in K-means), handling high dimensionality, outliers, and computational scalability.

Klustermodeller are applied in market research, image and text clustering, bioinformatics, document organization, and anomaly detection. The field has roots in mid-20th century methods such as K-means, with probabilistic clustering gaining prominence through Gaussian mixtures and the EM algorithm.