One of the most common clustering algorithms is K-means clustering. It partitions the data into K distinct clusters by assigning each object to the nearest cluster centroid. Another important algorithm is DBSCAN (Density-Based Spatial Clustering of Applications with Noise), which is particularly useful for identifying clusters of varying shapes and sizes and is robust to outliers.

Euclidean distance is a widely used metric for measuring the similarity between objects. It calculates the straight-line distance between two points in a multidimensional space. Hierarchical clustering uses this metric to build a dendrogram, a tree-like diagram that represents the nested grouping of objects and helps in visualizing the arrangement of clusters based on their similarity.

To evaluate the quality and validity of the clusters formed, various validation techniques are employed. The Silhouette Score measures how similar an object is to its own cluster compared to other clusters. The Elbow Method is another technique used to determine the optimal number of clusters by plotting the variance explained as a function of the number of clusters and identifying the point where the rate of variance reduction decreases sharply.

Geodemographic segmentation is an application of cluster analysis in marketing, where consumers are grouped based on their geographic and demographic characteristics. This helps in targeting specific market segments more effectively. Outlier detection is another application where cluster analysis is used to identify data points that do not fit into any cluster and may indicate anomalies or errors in the data.

Hierarchical clustering can be divided into agglomerative and divisive methods. Agglomerative clustering starts with each object as a separate cluster and merges them based on their similarity, while divisive clustering starts with all objects in a single cluster and splits them recursively. Both methods produce a dendrogram to represent the nested grouping of objects, aiding in the interpretation of the hierarchical structure of the data.