Signal Threshold Selection¶
All options which use SVD (Singular Value Decomposition) for solving matrices offer this option for graphically selecting the number of eigenmodes that are to be included in the signal space. The retained eigenmodes should represent the signal or principal components since these are used for the procedure's solution. The discarded eigenmodes should represent the noise since this information is zeroed and does not factor into the solution. This signal-noise separation is intrinsic to SVD procedures.
Singular Value Plot¶
When a sufficient matrix order exists to effect this signal-noise separation, and provided signal strengths and properties are such that eigendecomposition can isolate signal components, the singular value plot will reveal a threshold that reveals a clear demarcation between signal and noise. The singular values usually require a log scale in order to perceive this transition.
Thresholding¶
To select the optimum signal space, simply left click the mouse on the last singular value that represents signal. This eigenmode and all prior ones will be processed while all subsequent singular values will be zeroed. The only harm in fitting very high orders with SVD is the increased processing time. In general, you will need to strike a balance between SVD processing time and model order. With SVD, you must choose a high enough model order to threshold the signal and noise effectively.
Model Order Considerations¶
If you can tolerate the processing time and have sufficient free memory available, a very high order can be safely used. The higher the order, the more complete the signal-noise thresholding can be. The AR Modeling and Prediction procedure offers SVD normal equations algorithms which are appreciably faster with large data sets than processing the full data matrix.
Noise Types¶
White (Gaussian distributed) noise is most easily thresholded using SVD. Red noise, which decreases in power as frequency increases, is not as readily partitioned using the SVD. Also, bear in mind that all eigendecomposition procedures partition based upon signal strength. When noise is present at levels that start to approach that of the signal, the characteristic transition may be impossible to achieve. Fitting the highest order for a given algorithm is one way to confirm whether or not this signal-noise transition can be achieved.
Lack of Visual Threshold¶
When this transition cannot be achieved, you can use the Eigendecomposition Filtering option to isolate components by selecting pairs of nearly equal magnitude singular values. It may also be possible to determine from reconstructing select eigenmodes where noise finally overwhelms signal elements.
List¶
The List Data option lists a table of the singular values. The listing uses the TableCurve 2D text viewer facility.
Copy¶
The Copy Data to Clipboard option copies the singular values to the clipboard. Formats include full precision binary (for spreadsheets such as Excel) and ASCII (for pasting into text editors).
Save¶
The Save Data to Disk option writes the singular values to a supported file format. These formats include ASCII, Excel 97/2000, Excel 95, Lotus WK3, Lotus WK1, SPSS, or Systat.