Klustertyper

Klustertyper, in the context of cluster analysis, refers to the characteristic shapes and structures that clustering results may exhibit in a dataset. The concept helps describe what a given clustering solution represents and informs the choice of methods and distance measures.

Common klustertyper include:

- Globular or spherical clusters: roughly round and equally dense in all directions, often well captured by methods like k-means.

- Elongated or elliptical clusters: stretched shapes that follow a covariance structure, better modeled by algorithms such as Gaussian mixture models.

- Anisotropic clusters: directionally biased shapes that vary in density along different axes, challenging for simple distance-based methods.

- Density-based clusters: clusters formed by high-density regions with arbitrary shapes, including irregular contours; DBSCAN and OPTICS are typical examples and are robust to noise.

- Nested or hierarchical clusters: clusters within clusters, which can be revealed by hierarchical or dendrogram-based approaches.

- Overlapping clusters: regions where points may reasonably belong to more than one cluster, often addressed by fuzzy clustering or probabilistic models.

- Noise and outliers: points that do not fit any cluster well, which some algorithms can designate as noise.

Identifying klustertyper involves visual inspection when possible, examination of shape and covariance hints in lower dimensions, and the use of validity indices and diagnostic plots. Statistical properties such as covariance matrices, density estimates, and silhouette scores can aid in characterizing cluster shapes.

Algorithm choices reflect klustertyper expectations: k-means favors globular clusters and can struggle with irregular shapes; Gaussian mixture models handle elliptical clusters with differing covariances; DBSCAN and OPTICS excel with density-based, arbitrary shapes and noise; hierarchical methods reveal nested structures; spectral clustering can capture complex, non-convex shapes. Practical analysis often combines methods and domain knowledge to interpret the detected klustertyper.