Documentation

Choose a method, select one or several signals in the Selection of Data pane using the mouse and keys. Then click the Selected button. You can select another group of signals using the same method. Press the Denoise button to denoise the selected signal(s).

You can also use manual threshold tuning. Click the Enable Manual Thresholding Tuning button.

The horizontal lines in the wavelet coefficient axes (cd1, ..., cd4) can be dragged using the mouse. This may be done individually, by group or all together depending on the values in the Select Signal and Selected Level fields in the Manual Threshold Tuning pane.

In the Wavelet 1-D Multisignal Analysis Compression tool, you can use two methods for threshold tuning: the By level thresholding method which is used in the Wavelet 1-D Multisignal Analysis Denoising tool, and the Global thresholding method.

You can drag the vertical lines in the Energy and Nb. Zeros Performances axes using the mouse. This can be done individually or all together depending on the values of Select Signal in the Manual Threshold Tuning pane.

The threshold value, L2 performance, and number of zeros performance are updated in the corresponding edit buttons in the Manual Threshold Tuning pane.

You can display various statistical parameters related to the signals and their components. From the Wavelet 1-D Multisignal Analysis tool, click the Statistics button. Then select the signal 1 in the Selection of Data Sets pane.

Select the signals 1, 2, 3, 7, 9 and 11 in the Selection of Data pane, and display the corresponding boxplots and correlation plots.

To display statistics on many wavelet components, in the Selection Data Sets pane, in the left column, select Orig.Signals, APP 1, DET 1, Denoised and Residuals signals. Then choose Separate Mode, and click the Asc. button in the Sort pane. The selected data are sorted in ascending order with respect to Idx Sig parameter. In the Selection of Data pane, select data related to signal 1.

Click the Clustering button located in the Command Frame, which is in the lower right of the Wavelet 1-D Multisignal Analysis window to open the Clustering tool.

You can cluster various type of signals and wavelet components: original, denoised or compressed, residuals, and approximations or details (reconstructed or coefficients). Similarly, there are several methods for constructing partitions of data.

Use the default parameters (Original and Signal in Data to Cluster, and in Ascending Hierarchical, euclidean, ward, and 6 in Clustering) and click the Compute Clusters button.

A full dendrogram and a restricted dendrogram display in the Selection by Dendrogram pane. For each signal, the cluster number displays in the Selection of Data pane.

Select one cluster, several clusters, or a part of a cluster.

Click the xticklabel 3 at the bottom of the restricted dendrogram. The links of the third cluster blink in the full dendrogram and the 24 signals of this class display in the Visualization of Selected Data pane. You can see their numbers in the Selection of Data pane.

Clicking the line in the restricted or in the full dendrogram lets you select one cluster, several linked clusters, or a part of a cluster. For a more accurate selection, use the Dilate X and the Translate X sliders under the full dendrogram. You can also use the Yscale button located above the full dendrogram. The corresponding signals display in the Visualization of Selected Data pane and in the list of the Selection of Data pane.

You can use the horizontal line in the full dendrogram to change the number of clusters. Use the left mouse button to drag the line up or down.

Use the Show Clusters button to examine the clusters of the current partition. You can display the mean (or the median) of each cluster, the global standard deviation and the pointwise standard deviation distance around the mean (or the median). Each plot title contains: the number of signals in the cluster (Nb) and percent of total, the global standard deviation (D) of the cluster, and two indices of quality, Q1 and Q2.

The Q1 and Q2 indices can be interpreted as measures of how well a cluster is concentrated in multidimensional space. The values min and max are the minimum and maximum values, respectively, of the absolute values of the signal samples in the cluster. If the global standard deviation D is small, then Q1 is close to 1 and Q2 is close to 0. In this case, the cluster is considered well-concentrated. If D is large, then Q1 is small and Q2 is large. In this case, the cluster is considered more disperse. For example, in Cluster 3 the minimum and maximum values of the absolute values of the signal samples are 5 and 220, respectively. Then Q1 = 1 − 37.208/220 = 0.831 and Q2 = 37.208/(220-5) = 0.173.

Click the Store Current Partition button below the Clustering pane to store the current partition for further comparisons. A default name is suggested. Note that the 1-D Wavelet Multisignal Analysis tool stores the partitions and they are not saved on the disk.

Build and store several partitions (for example, partitions with signals, denoised signals approximations at level 1, 2 and 3, and denoised signals). Then, click the Open Partition Manager button below the Store Current Partition button. The Partitions Management pane appears. The names of all stored partitions are listed.

Now, you can show, clear, or save the partitions (individually, selected ones, or all together).

To display partitions, select the Ori Signals and the Den Signals partitions, and click the Selected button next to the Show Partitions label.

The clusters are almost the same, but it is difficult to see this on the Selected Partitions axis, due to the scaling difference. Press the Apply button to renumber the clusters (starting from the selected partition as basic numbering) to compare the two partitions.

Only three signals are not classified in the same cluster for the two considered partitions.

Select the partitions you want to save and click the Save Partitions button below the Store Current Partition button in the Partitions Management pane.

Partitions are saved as an array of integers, where each column corresponds to one partition and contains the indices of clusters. When you choose the Full Partitions option, an array object (wpartobj) is saved.

To load or clear stored partitions use File > Partitions in the Wavelet 1-D Multisignal Analysis tool. (File > Partitions is also available in the Wavelet 1-D Multisignal Analysis Clustering tool and you can also save the current partition.)

To clear one or more stored partitions, select File > Partitions > Clear Partition.

Select File > Partitions > Load Partition to load one or several partitions from the disk. The loaded partitions are stored in Wavelet 1-D Multisignal Analysis tool with any previously stored partitions. A partition can also be a manually created column vector.

In each subcomponent of the Wavelet 1-D Multisignal Analysis tool (main, statistics, denoising, compression, clustering), you can import a stored partition from the list in the Selection of Data pane. Click the Import Part button at the bottom of the Selection of Data pane, the Partition Set Manager window appears. Select one partition and click the Import button.

For this example, go back to the main window, import the Ori Signals partition and sort the signals in descending order with respect to A4 energy percentage.

You can compare partitions with the Partition tool. To display the Partition tool, click the More on Partitions button at the bottom of the Partitions Management pane. By default, when the Partition tool opens, the currently selected partition, in this case Ori Signals, is compared with itself. In the lower left plot, an integer N at (i,j) means there is a group of N signals in the i^th cluster of P1 and the j^th cluster of P2. Since the Partition tool is comparing a partition with itself, all the numbers are plotted on the main diagonal.

Statistics measuring the similarity of the partitions P1 and P2 are displayed in the panels on the right. The Partitions Pairs Links panel counts pairs of signals. Two signals x and y are considered a pair if they are in the same cluster. For any two signals x and y, there are four possibilities.

The Partitions Pairs Links shows the percentages of each of the four possibilities. In this example, since there are 192 signals, there are total of 192*191/2 = 18336 possible pairs. Slightly more than 19% of the linked pairs are considered true positives, and approximately 80% are true negatives. Since the partition is being compared with itself, no pair is considered a false positive or false negative.

You can also measure how similar two partitions are by assigning a distance (or index) between them [1]. The distance is based on the number of true and false positives and negatives. Distance can be defined in different ways. Let R be the number of true positives, S be the number of true negatives, U be the number of false positives, and V be the number of false negatives. The Partitions Similarity Indices panel shows the distance between the P1 and P2 partitions using different definitions of distance:

Select the Den Signals in Sel P2 in the upper-right corner of the window. Then, in the lower left axis, click the yellow text containing the value 2 (the coordinates of the corresponding point are (4,5)). The corresponding signals are displayed together with all related information.

Open the Wavelet 1-D Multisignal Analysis main tool and load the example analysis by selecting File > Example > Ex 21: Thinker (rows).

Save the data from this analysis, using the menu option File > Save Decompositions.

A dialog box appears that lets you specify a folder and filename for storing the decomposition data. For this example, use the name decORI.mat.

Type the name decORI.

After saving the decomposition data to the file decORI.mat, load the variables into your workspace:

load decORI 
whos

dec
dec =
         dirDec: 'r'
          level: 4
          wname: 'db2'
     dwtFilters: [1x1 struct]
        dwtEXTM: 'sym'
       dwtShift: 0
       dataSize: [192 96]
             ca: [192x8 double]
             cd: {1x4 cell}

The field ca of the structure dec gives the coefficients of approximation at level 4, the field cd is a cell array which contains the coefficients of details.

size(dec.cd{1})
ans = 
   192    49 
size(dec.cd{2})
ans = 
   192    26 
size(dec.cd{3})
ans = 
   192    14 
size(dec.cd{4})
ans = 
   192     8

You can change the coefficients using the chgwdeccfs function.

Open the Wavelet 1-D Multisignal Analysis main tool and load the example analysis using File > Example > Ex 21: Thinker (rows).

Click the Clustering button. The Wavelet 1-D Multisignal Analysis Clustering window appears.

Click the Compute Clusters button, and then save the current partition using menu option File > Partitions > Save Current Partition. A dialog box appears that lets you specify the type of data to save.

Click the Save Curr. button.

Another dialog box appears that lets you specify a folder and filename for storing the partition data. Type the name curPART.

After saving the partition data to the file curPART.mat, load the variables into your workspace:

load curPART
whos

You can modify the array tab_IdxCLU in the workspace, and save the partition data in a file. For example to create two new partitions with four and two clusters, type the following lines:

tab_IdxCLU(:,2) = rem((1:192)',4) + 1; 
tab_IdxCLU(:,3) = double((1:192)'>96) + 1; 
save newpart tab_IdxCLU

Now you can use three partitions for the example Ex 21: Thinker (rows). Then, you can load the partitions stored in the file newPART.mat in the Wavelet 1-D Multisignal Analysis main tool and clustering tool.