超级平滑
supsmu: Smoothing of scatterplots using Friedman's supersmoother algorithm.Syntax:
Y_SMOOTH = supsmu(X,Y,'PropertyName',PropertyValue,...)
Inputs:
X, Y are same-length vectors.
Output
Y_SMOOTH is a smoothed version of Y.
Example,
x = linspace(0,1,201);
y = sin(2.5*x) + 0.05*randn(1,201);
smo = supsmu(x,y);
plot(x,y,'o',x,smo)
The supersmoother algorithm computes three separate smooth curves from
the input data with symmetric spans of 0.05*n, 0.2*n and 0.5*n, where n
is the number of data points.The best of the three smooth curves is
chosen for each predicted point using leave-one-out cross validation. The
best spans are then smoothed by a fixed-span smoother (span = 0.2*n) and
the prediction is computed by linearly interpolating between the three
smooth curves.This final smooth curve is then smmothed again with a
fixed-span smoother (span = 0.05*n).
According to comments by Friedman, "For small samples (n < 40) or if
there are substantial serial correlations between observations close in
x-value, then a prespecified fixed span smoother (span > 0) should be
used.Reasonable span values are 0.2 to 0.4."
The following optional property/value pairs can be specified as arguments
to control the indicated behavior:
Property Value
--------------------------------------------------------------------
Weights Vector of relative weights of each data point.Default is
for all points to be weighted equally.
Span Sets the width of a fixed-width smoothing operation
relative to the number of data points, 0 < SPAN < 1.
Setting this to be non-zero disables the supersmoother
algorithm.Default is 0 (use supersmoother).
Period Sets the period of periodic data.Default is Inf
(infinity) which implies that the data is not periodic.
Can also be set to zero for the same effect.
Alpha Sets a small-span penalty to produce a greater smoothing
effect.0 < Alpha < 10, where 0 does nothing and 10
produces the maximum effect.Default = 0.
Unsorted If the data points are not already sorted in order of the X
values then setting this to true will sort them for you.
Default = false.
All properties names are case-insensitive and need only be unambiguous.
For example,
Y_SMOOTH = supsmu(X,Y,'weights',ones(n,1),'per',2*pi)
is valid usage.
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