Logdecay: Difference between revisions
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imported>Jeremy (Importing text file) |
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===Purpose=== | ===Purpose=== | ||
Variance scales a matrix using the log decay of the variable axis. | Variance scales a matrix using the log decay of the variable axis. | ||
===Synopsis=== | ===Synopsis=== | ||
:[sx,logscl] = logdecay(x,tau) | :[sx,logscl] = logdecay(x,tau) | ||
===Description=== | ===Description=== | ||
Inputs are data to be scaled (x), and the decay rate (tau). Outputs are the variance scaled matrix (sx) and the log decay based variance scaling parameters (logscl). | Inputs are data to be scaled (x), and the decay rate (tau). Outputs are the variance scaled matrix (sx) and the log decay based variance scaling parameters (logscl). | ||
For an m x n matrix 'x' the variance scaling used for variable 'i' is exp(-(i-1)/((n-1)\*tau)). This gives a scaling of 1 on the first variable (i.e. no scaling), and a scaling of 1/exp(-1/tau) on the last variable. The following table gives example values of tau and the scaling on the last variable: | For an m x n matrix 'x' the variance scaling used for variable 'i' is exp(-(i-1)/((n-1)\*tau)). This gives a scaling of 1 on the first variable (i.e. no scaling), and a scaling of 1/exp(-1/tau) on the last variable. The following table gives example values of tau and the scaling on the last variable: | ||
: tau scaling | : tau scaling | ||
: 1 2.7183 | : 1 2.7183 | ||
: 1/2 7.3891 | : 1/2 7.3891 | ||
: 1/3 20.0855 | : 1/3 20.0855 | ||
: 1/4 54.5982 | : 1/4 54.5982 | ||
: 1/5 148.4132 | : 1/5 148.4132 | ||
===See Also=== | ===See Also=== | ||
[[autoscale]], [[scale]] | [[autoscale]], [[scale]] | ||
Revision as of 15:25, 3 September 2008
Purpose
Variance scales a matrix using the log decay of the variable axis.
Synopsis
- [sx,logscl] = logdecay(x,tau)
Description
Inputs are data to be scaled (x), and the decay rate (tau). Outputs are the variance scaled matrix (sx) and the log decay based variance scaling parameters (logscl).
For an m x n matrix 'x' the variance scaling used for variable 'i' is exp(-(i-1)/((n-1)\*tau)). This gives a scaling of 1 on the first variable (i.e. no scaling), and a scaling of 1/exp(-1/tau) on the last variable. The following table gives example values of tau and the scaling on the last variable:
- tau scaling
- 1 2.7183
- 1/2 7.3891
- 1/3 20.0855
- 1/4 54.5982
- 1/5 148.4132