Afstandsmetrieken

Afstandsmetrieken, or distance metrics, are fundamental concepts in mathematics and computer science used to quantify the separation between two points in a given space. These metrics provide a consistent way to measure "how far apart" things are, which is crucial for various applications such as clustering, classification, and search algorithms. A distance metric, often denoted by d(x, y), must satisfy specific properties: non-negativity (the distance is always zero or positive), identity of indiscernibles (the distance is zero if and only if the points are identical), symmetry (the distance from x to y is the same as from y to x), and the triangle inequality (the distance between two points is less than or equal to the sum of the distances from each point to a third point).

There are numerous types of distance metrics, each suited for different data types and problem domains. The Euclidean distance, perhaps the most common, calculates the straight-line distance between two points in Euclidean space. For binary data, the Hamming distance counts the number of positions at which the corresponding symbols are different. The Manhattan distance (or L1 norm) measures the distance by summing the absolute differences of their Cartesian coordinates, akin to navigating a city grid. Other metrics include Chebyshev distance, Minkowski distance, and cosine similarity, which is often used for text analysis. The choice of an appropriate distance metric significantly impacts the performance and outcome of algorithms that rely on measuring similarity or dissimilarity between data points.