There are many tools that can be used to summarize similarity measurements, but some of the most common include:
Hierarchical clustering is a method of clustering that starts by treating each data point as its own cluster. Then, it repeatedly merges the two most similar clusters until there is only one cluster left. This method can be used to summarize similarity measurements by plotting the dendrogram, which is a tree-like diagram that shows how the clusters are merged together.
K-means clustering is another popular method of clustering that divides the data into k clusters of equal size. The algorithm starts by randomly assigning each data point to a cluster. Then, it repeatedly updates the cluster centroids (the average of all the data points in each cluster) and reassigns each data point to the cluster with the closest centroid. This method can be used to summarize similarity measurements by plotting the cluster centroids and the data points.
Principal component analysis (PCA) is a dimensionality reduction technique that can be used to summarize similarity measurements by finding the directions in which the data points vary the most. The PCA scores for each data point can then be used to measure the similarity between the data points.
The distance between an object and a cluster can be measured in a number of ways, but some of the most common methods include:
Euclidean distance is the most common way to measure the distance between two points in Euclidean space. It is calculated by taking the square root of the sum of the squared differences between the two points.
Manhattan distance is another common way to measure the distance between two points in Euclidean space. It is calculated by taking the sum of the absolute differences between the two points.
Minkowski distance is a generalization of Euclidean and Manhattan distance that can be used to measure the distance between points in any metric space. It is calculated by taking the pth root of the sum of the pth powers of the differences between the two points.
Cosine similarity is a measure of similarity between two vectors that takes into account the direction as well as the magnitude of the vectors. It is calculated by taking the dot product of the two vectors and dividing it by the product of their norms.