Etäisyysmatriisi

An etäisyysmatriisi, or distance matrix in English, is a table that shows the distance between each pair of elements in a set. In the context of graph theory, it represents the shortest path distance between all pairs of vertices in a graph. The matrix is typically square, with the number of rows and columns equal to the number of vertices. The value at the intersection of row i and column j represents the shortest distance from vertex i to vertex j. If there is no path between two vertices, the corresponding entry in the matrix might be represented by infinity or a very large number.

Distance matrices are fundamental in various fields, including computer science, operations research, and bioinformatics. They are used to solve problems such as the traveling salesman problem, where the goal is to find the shortest possible route that visits each city exactly once and returns to the origin city. The construction of a distance matrix can be achieved using algorithms like the Floyd-Warshall algorithm or by running a shortest path algorithm like Dijkstra's from each vertex.

In data analysis, a distance matrix quantifies the dissimilarity between observations. For example, in clustering algorithms, a distance matrix helps determine which data points are closest to each other, facilitating the formation of clusters. The nature of the distance metric used (e.g., Euclidean distance, Manhattan distance) significantly influences the resulting matrix and subsequent analyses.