from a vector space X over the field of real or complex numbers into the real numbers that abides by the principle of superposition. Norms are often a measure of an object size and hence they are distance functions (from the origin) e.g. metrics. There exist a myriad of norms with Lebesgue’s Lp norms being perhaps the most familiar.The specific case of the L1 norm is a popular choice as a penalty term in regularization techniques to encourage sparse solutions. In fNIRS analysis, the L1 norm has found many uses; for instance in image reconstruction. It has also been used in sparsity regularization, where the goal is to identify the regions of the brain that are most active during a task. Sparsity regularization involves adding a penalty term to the objective function that is minimized when estimating the changes in hemoglobin concentration. The penalty term encourages the solution to have many zero or near-zero coefficients, which indicates that only a few regions of the brain are active during the task.
Category: Math
Related terms:
Abbreviation or symbol: L1 Norm (or ![\[||v||_1\]](https://openfnirs.org/wp-content/ql-cache/quicklatex.com-1ad4e0711ec1d8de8e945d3c2b5bfb4b_l3.png "Rendered by QuickLaTeX.com")
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