metriky

Metriky (singular metrika) is a term used in mathematics and related disciplines to describe a function that assigns a nonnegative real number to a pair of elements from a set, measuring distance or dissimilarity. In mathematics a metric d on a set X satisfies nonnegativity, identity of indiscernibles (d(x,y) = 0 iff x = y), symmetry (d(x,y) = d(y,x)), and the triangle inequality (d(x,z) ≤ d(x,y) + d(y,z)). A set equipped with a metric is called a metric space.

Examples of metry include the Euclidean metric on R^n, defined by d(x,y) = sqrt(sum_i (x_i - y_i)^2). More generally, Lp metrics take the form d_p(x,y) = (sum_i |x_i - y_i|^p)^{1/p} for p ≥ 1, with p = 1 giving the Manhattan distance, p = 2 the Euclidean distance, and p = ∞ the Chebyshev distance. The discrete metric d(x,y) = 0 if x = y and 1 otherwise is another common example. Metrics can also be defined from norms by d(x,y) = ||x - y||.

Applications of metry extend beyond pure math. They quantify similarity or difference between objects, guide clustering and nearest-neighbor methods, and underpin evaluation measures in various fields. In data analysis and machine learning, distance metrics influence algorithms and results in tasks such as classification, clustering, and dimensionality reduction. In statistics and information retrieval, dissimilarity measures contribute to model assessment, ranking, and decision-making.

In Czech usage, metrika can also refer to broader measurement systems or performance indicators, such as business metrics or key performance indicators, reflecting its role in assessment and comparison across contexts.