Logdecay: Difference between revisions
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===Purpose=== | ===Purpose=== | ||
Scales a matrix using the inverse log decay of the variable axis. | |||
===Synopsis=== | ===Synopsis=== | ||
| Line 12: | Line 11: | ||
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 | 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 which is applied to the last column of x (the last variable): | ||
{| class="wikitable" | |||
! tau !! scaling | |||
|- | |||
| 1 || 2.7183 | |||
|- | |||
| 1/2 || 7.3891 | |||
|- | |||
| 1/3 || 20.0855 | |||
|- | |||
| 1/4 || 54.5982 | |||
|- | |||
| 1/5 || 148.4132 | |||
|} | |||
===See Also=== | ===See Also=== | ||
[[ | [[auto]], [[scale]] | ||
Latest revision as of 10:50, 7 June 2016
Purpose
Scales a matrix using the inverse 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 which is applied to the last column of x (the last variable):
| tau | scaling |
|---|---|
| 1 | 2.7183 |
| 1/2 | 7.3891 |
| 1/3 | 20.0855 |
| 1/4 | 54.5982 |
| 1/5 | 148.4132 |