L1metriek

L1metriek is a term used to describe a specific type of metric or distance calculation in mathematics and computer science, particularly in fields like signal processing and machine learning. The "L1" refers to the L1 norm, which is a way of measuring the "size" or "magnitude" of a vector. Unlike the more common L2 norm (Euclidean distance), the L1 norm sums the absolute values of the vector's components.

In practical terms, when L1metriek is applied, it means that the distance between two points is calculated by adding up the absolute differences of their corresponding coordinates. For example, if you have two points in a 2D space, A = (x1, y1) and B = (x2, y2), the L1 distance between them would be |x1 - x2| + |y1 - y2|. This is often referred to as the Manhattan distance or taxicab distance because it represents the distance a taxi would travel on a grid of city blocks.

The L1 norm is known for its sparsity-inducing properties. This means that when used in optimization problems, it tends to favor solutions where many of the vector components are zero. This characteristic makes L1metriek useful in applications where feature selection or identifying important components is crucial, such as in compressed sensing or in regularizing models to prevent overfitting. Its computational simplicity and distinct geometric interpretation also contribute to its utility in various analytical contexts.