# Notion - (Best approximation|Closest|Closeness)

This notion of “best approximates” comes up again and again:

• in least-squares, a fundamental data analysis technique,
• image compression,
• in principal component analysis, another data analysis technique, and
• in latent semantic analysis, an information retrieval technique.

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Data Mining - Multi-class (classification|problem)

Multiclass classification is used to predict: one of three or more possible outcomes and the likelihood of each one. Generally, there is no notion of closeness because the target class is nominal....
File - File System (filesystem)

A file system (often also written as filesystem) is an application that stores and organizes files and their data (content). Essentially, it organizes these files for storage, organization, manipulation,...
Linear Algebra - Closest Point on a Line

How to find the closest point on a line from a point ? How to find the vector on the line that best approximates the given vector b (the closest point on the line) Letb be a vector Leta be a...
Linear Algebra - Closest point in a plane

Given a point b and a plane, find the point in the plane closest to b. By , we can assume the plane includes the origin. The plane is a vector space V. Let {v1, v2} be a basis for V. Goal: Given...
Linear Algebra - Closest point in higher dimension than a plane

Solving closest point in the span of many vectors Goal: An algorithm that, given a vector b and vectors v1, . . . , vn, finds the vector in Span {v1, . . . , vn} that is closest to b. Special case:...
Statistics - Regression

Regression is a statistical analysis used: to predict scores on an numeric outcome variable, based on scores of: one predictor variable: simple regression or multiple predictor variables: multiple...