Loess Curve in Machine Learning

A loess curve is an important exploratory graphic aid that adds a smooth curve to a scatter plot in order to provide a better perception of the pattern of dependence. The word loess os short for ' local regression'. Fig shows a loess curve for the set of data in a table

A loess curve

Two parameters are needed to fit a loess curve. (alpha), a smoothing parameter, and (Gama), the degree of the polynomials. While alpha can be any positive number, Gama can be 1 or 2. The goal of choosing alpha is to produce a fit that is as smooth as possible without unduly distorting the underlying pattern in the data. The curve becomes smoother as alpha increases. There may be some lack of fit, however, indicating possible "missing" data patterns. If alpha is very small, the underlying pattern is tracked, yet overfitting of data may occur where local "wiggles" in the curve may not be supported by the data. If the underlying pattern of the data has a 'gentle' curvature with no local maxima and minima, then the local linear fitting is usually sufficient (Gama =1). However, if there are local maxima or minima, then local quadratic fitting (gama=2) typically does a better job of following the pattern of the data and maintaining local smoothness.