Klaszterelemzési

Klaszterelemzési, often translated as cluster analysis, is a statistical method used to group a set of objects in such a way that objects in the same group (called a cluster) are more similar to each other than to those in other groups. It is an unsupervised learning technique, meaning it does not require pre-labeled data. The primary goal is to discover inherent structures and relationships within the data.

The process begins with a dataset containing observations, each described by a set of variables or features. The similarity or dissimilarity between objects is typically measured using a distance metric, such as Euclidean distance or Manhattan distance. Different algorithms exist for performing cluster analysis, each with its own approach to defining clusters and their relationships. Common methods include k-means, hierarchical clustering, and DBSCAN.

K-means is an iterative algorithm that partitions the data into a pre-defined number of clusters, 'k'. It assigns each data point to the cluster whose mean (centroid) is nearest. Hierarchical clustering, on the other hand, builds a hierarchy of clusters, either by successively merging smaller clusters (agglomerative) or by splitting larger ones (divisive). DBSCAN (Density-Based Spatial Clustering of Applications with Noise) groups together points that are closely packed together, marking as outliers points that lie alone in low-density regions.

The results of cluster analysis can be visualized through dendrograms (for hierarchical clustering) or scatter plots. Applications of cluster analysis are widespread, spanning fields such as marketing for customer segmentation, biology for gene expression analysis, image processing for object recognition, and social sciences for identifying social groups. The effectiveness of cluster analysis depends heavily on the chosen algorithm, the distance metric, and the interpretation of the resulting clusters.