Gscale: Difference between revisions
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===Purpose=== | ===Purpose=== | ||
Group/block scaling for a single or multiple blocks. | Group/block scaling for a single or multiple blocks. | ||
===Synopsis=== | ===Synopsis=== | ||
:[gxs,mxs,stdxs] = gscale(xin,numblocks) | :[gxs,mxs,stdxs] = gscale(xin,numblocks) | ||
===Description=== | ===Description=== | ||
GSCALE scales an input matrix xin such that the columns have mean zero, and variance in each block/sub-matrix relative to the total variance in xin equal to one. The purpose is to provide equal sum-of-squares weighting to each block in xin. | GSCALE scales an input matrix xin such that the columns have mean zero, and variance in each block/sub-matrix relative to the total variance in xin equal to one. The purpose is to provide equal sum-of-squares weighting to each block in xin. | ||
Inputs are a matrix xin (class "double") and the number of sub-matrices or blocks numblocks. Note that size(xin,2)/numblocks must be an integer. If numblocks is not included, it is assumed to 1 i.e. the matrix xin is treated as a single block. | Inputs are a matrix xin (class "double") and the number of sub-matrices or blocks numblocks. Note that size(xin,2)/numblocks must be an integer. If numblocks is not included, it is assumed to 1 i.e. the matrix xin is treated as a single block. | ||
If (numblocks) is 0 (zero) then automatic mode is used based on the dimensions of the (xin) matrix: | If (numblocks) is 0 (zero) then automatic mode is used based on the dimensions of the (xin) matrix: | ||
If (xin) is a three-way array, it is unfolded (combining the first two modes as variables) and the size of the original second mode (size(xin,2)) is used as (numblocks). The output is re-folded back into the original three-way array. | If (xin) is a three-way array, it is unfolded (combining the first two modes as variables) and the size of the original second mode (size(xin,2)) is used as (numblocks). The output is re-folded back into the original three-way array. | ||
Note that the unfold operation is: xin = unfoldmw(xin,3); | Note that the unfold operation is: xin = unfoldmw(xin,3); | ||
If (xin) is a two-way array, each variable is treated on its own and GSCALE is equivalent to autoscale (see the AUTO function). | If (xin) is a two-way array, each variable is treated on its own and GSCALE is equivalent to autoscale (see the AUTO function). | ||
Outputs are the scaled matrix (gxs), a rowvector of means (mxs), and a row vector of "block standard deviations" stdxs. | Outputs are the scaled matrix (gxs), a rowvector of means (mxs), and a row vector of "block standard deviations" stdxs. | ||
===Examples=== | ===Examples=== | ||
Scale a matrix a that has two blocks augmented together: | Scale a matrix a that has two blocks augmented together: | ||
>> a = [[1 2 3; 4 5 6; 7 8 9] [11 12 13; 14 15 16; 17 18 19]] | >> a = [[1 2 3; 4 5 6; 7 8 9] [11 12 13; 14 15 16; 17 18 19]] | ||
a = | a = | ||
1 2 3 11 12 13 | 1 2 3 11 12 13 | ||
4 5 6 14 15 16 | 4 5 6 14 15 16 | ||
7 8 9 17 18 19 | 7 8 9 17 18 19 | ||
>> [gxs,mxs,stdxs] = gscale(a,2); | >> [gxs,mxs,stdxs] = gscale(a,2); | ||
>> gxs | >> gxs | ||
gxs = | gxs = | ||
-0.5774 -0.5774 -0.5774 -0.5774 -0.5774 -0.5774 | -0.5774 -0.5774 -0.5774 -0.5774 -0.5774 -0.5774 | ||
0 0 0 0 0 0 | 0 0 0 0 0 0 | ||
0.5774 0.5774 0.5774 0.5774 0.5774 0.5774 | 0.5774 0.5774 0.5774 0.5774 0.5774 0.5774 | ||
>> mxs | >> mxs | ||
mxs = | mxs = | ||
4 5 6 14 15 16 | 4 5 6 14 15 16 | ||
>> stdxs | >> stdxs | ||
stdxs = | stdxs = | ||
3 3 3 3 3 3 | 3 3 3 3 3 3 | ||
===See Also=== | ===See Also=== | ||
[[auto]], [[gscaler]], [[mncn]], [[mpca]], [[scale]], [[unfoldm]] | [[auto]], [[gscaler]], [[mncn]], [[mpca]], [[scale]], [[unfoldm]] | ||
Revision as of 14:25, 3 September 2008
Purpose
Group/block scaling for a single or multiple blocks.
Synopsis
- [gxs,mxs,stdxs] = gscale(xin,numblocks)
Description
GSCALE scales an input matrix xin such that the columns have mean zero, and variance in each block/sub-matrix relative to the total variance in xin equal to one. The purpose is to provide equal sum-of-squares weighting to each block in xin.
Inputs are a matrix xin (class "double") and the number of sub-matrices or blocks numblocks. Note that size(xin,2)/numblocks must be an integer. If numblocks is not included, it is assumed to 1 i.e. the matrix xin is treated as a single block.
If (numblocks) is 0 (zero) then automatic mode is used based on the dimensions of the (xin) matrix:
If (xin) is a three-way array, it is unfolded (combining the first two modes as variables) and the size of the original second mode (size(xin,2)) is used as (numblocks). The output is re-folded back into the original three-way array.
Note that the unfold operation is: xin = unfoldmw(xin,3);
If (xin) is a two-way array, each variable is treated on its own and GSCALE is equivalent to autoscale (see the AUTO function).
Outputs are the scaled matrix (gxs), a rowvector of means (mxs), and a row vector of "block standard deviations" stdxs.
Examples
Scale a matrix a that has two blocks augmented together:
>> a = [[1 2 3; 4 5 6; 7 8 9] [11 12 13; 14 15 16; 17 18 19]]
a =
1 2 3 11 12 13
4 5 6 14 15 16
7 8 9 17 18 19
>> [gxs,mxs,stdxs] = gscale(a,2);
>> gxs
gxs =
-0.5774 -0.5774 -0.5774 -0.5774 -0.5774 -0.5774
0 0 0 0 0 0
0.5774 0.5774 0.5774 0.5774 0.5774 0.5774
>> mxs
mxs =
4 5 6 14 15 16
>> stdxs
stdxs =
3 3 3 3 3 3