Application Center - Maplesoft

App Preview:

The Curse of Dimensionality

You can switch back to the summary page by clicking here.

Learn about Maple
Download Application




````

NULL

NULL

NULL

``

``

 

``

The Curse of Dimensionality

````

``

````

The following was implemented in Maple by Marcus Davidsson (2013)

 davidsson_marcus@hotmail.com

``

``

``

NULL

 

 

 

 

From Wikipidia

"The curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces (often with hundreds or thousands of dimensions) that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience. The common theme of these problems is that when the dimensionality increases, the volume of the space increases so fast that the available data becomes sparse. This sparsity is problematic for any method that requires statistical significance. In order to obtain a statistically sound and reliable result, the amount of data needed to support the result often grows exponentially with the dimensionality."

NULL

NULL

NULL

# of Rows in (#, 4) Return Matrix =       

 

 

 

                 Covariance Matrix                                   Standard Error (SE) Covariance Matrix

 

NULL      

NULL

``

NULL

NULL

restart; randomize(); with(Statistics); with(LinearAlgebra); nrows := 25; R := RandomMatrix(nrows, 4, generator = -15 .. 15, outputoptions = [datatype = float[8]]); CovarianceMatrix(R); StandardError(Variance, R); X := proc (nrows) local R; R := RandomMatrix(nrows, 1, generator = -15 .. 15, outputoptions = [datatype = float[8]]); StandardError(Variance, R)[] end proc; LineChart(Vector([seq(X(i), i = 3 .. 50)]), title = "SE Covariance Matrix for # of Rows", titlefont = [TIMES, ROMAN, 16])

restart; randomize(); with(Statistics); with(LinearAlgebra); with(plots); X := proc (nrows) local R; R := RandomMatrix(nrows, 2, generator = -15 .. 15, outputoptions = [datatype = float[8]]); StandardError(Variance, R) end proc; data := [seq(X(i), i = 3 .. 50)]; kk := Transpose(Matrix([[seq(data[i][1], i = 1 .. 48)], [seq(data[i][2], i = 1 .. 48)], [seq(i, i = 3 .. 50)]])); surfdata(kk, axes = boxed, labels = ["Variable 1 SE CovMatrix", "Variable 2 SE CovMatrix", "Number of Rows"], labeldirections = [horizontal, horizontal, vertical], labelfont = [Times, Roman, 14])

 

NULL

 

 

NULL

``

NULL