Rotating 3-Dimensional Scatter Plot Enhances Visualization

Scatter plots are often used to present information about a data set, presenting each sample on a 2-dimensional graphic with one variable on the x-axis and another on the y-axis. When a data set has more than 2 variables, the information from the 3rd variable is not visible in a 2-dimensional plot. A 3-dimensional scatter plot can offer more information in a single view and is the default plot format for most of Pirouette’s data viewing. But, a static 3-dimensional view is only part of the picture. Free rotation of the 3-D view will reveal relationships among samples or variables not visible in a static 2-D plot. And, if there are more than 3 variables, Pirouette® makes it easy to swap which variables get plotted.

Dynamic Linking Highlights Samples Across Views

Visualization is a key component in multivariate analysis, and Pirouette makes this easy. In particular, with large data sets, it is critical to know how samples appear in relation to others. A simple way to do this is by “highlighting” a sample to make it stand out (also applicable to groups of samples). In Pirouette, we have taken this to the next step that those in dynamic graphics call linking. A highlighted sample will appear highlighted in all sample-oriented views, whether presented as a table or a graphic. Combined with Cloaking, this is a powerful tool for investigating relationships in your data.

Cloaking Allows Focus on Selected Samples/Variables

As powerful as dynamic linking is, there are times when there is so much data, that it is hard to see where highlighted samples appear in a sea of samples. Cloaking comes to the rescue. The cloaking button is a 3-way toggle: hit it once to temporarily hide all highlighted samples; hit it a second time to show only the highlighted samples; and, a third time to once again show all samples, highlighted or not. Cloaking can be used on scatter plots or line plots, on plots that are sample-oriented or those that are variable-oriented. Combined with dynamic linking, you can make your selections in one view and see which samples appear in the cloaked view.

Decision Diagrams Facilitate Understanding

Most Pirouette algorithms offer outlier diagnostics to help you optimize the training set and corresponding model. You can view these diagnostics as a table or graphically. Plotting one diagnostic against another allows quick evaluation of outliers by comparing a sample point to the thresholds for each metric. SIMCA also presents the Class Distances as a decision diagram in which the distances of the samples to a class model are shown for 2 classes at a time. In each of these cases, the multiple thresholds divide the plot space into subregions of membership and not.

Outlier Diagnostics Emphasize Unusual Samples

To optimize a multivariate model, three things need to be evaluated: model complexity, variables used, and appropriateness of samples. Pirouette offers various outlier diagnostics to help with sample evaluation, which include “in-model” and “out-of-model” metrics. These diagnostics are displayed in a single plot so you can quickly proceed with your evaluation. And, if you decide one or more samples should not be included in the data set, quickly create a new set by excluding the offending players.

HCA Dendrogram Illustrates Similarities Among Samples

A dendrogram is a practical and common means to present the results of a cluster analysis. Pirouette’s dendrogram can be easily navigated: double-click on a branch to zoom just those samples. If there are many samples in the data set, this navigation is crucial to see the relationships among similar groups of samples. Drag a similarity line to cut the tree into sub-trees, expressed by a color scheme; then, easily create a new category variable that reflects this cluster grouping.

SIMCA Class Projections Show Category Relationships

Included in the SIMCA results is a graphic called Class Projections. This presents the scores for every sample projected into a 3-dimensional factor space based on PCA of the whole set. Also shown is a 3-D confidence ellipse for each category. Plots like this are often shown in the literature when describing the SIMCA algorithm. The Pirouette Class Projections are unique in that the are offered as an interactive 3-D plot. You should keep in mind, however, that this plot has drawbacks. First, the projections show only the “in-model” information while membership is based on “out-of-model” information, the residuals. Also, 3 PCA factors of the whole data set do not account for all information in every category; much is left out and cannot realistically be shown in such a view.

Run Configuration Dialog Allows Flexible Batch Setup

All algorithms in Pirouette are accessed in a common dialog box. Each algorithm, however, offers unique parameters. On the other hand, transformations such as derivatives and scatter correction are applied before algorithm pretreatment and can thus be set globally. What-if analyses are possible by setting up a batch of runs: compare different algorithms (e.g., PCR and PLS) when run with different pretreatments and different transformations, all in a single batch setup.

Show All Computed Results in a Single Compact View

When an algorithm run has completed, all computed results are gathered into a single group, shown in the Object Manager as a folder. You can pull out individual results, for example the PCA Scores, for display in its own window. Or you can drag out the folder containing all results into an array of subplots, one for each computed result. The subplots can be expanded to fill the window where interactions are enabled. Because the views are “sticky” when you return to the array view, you can create customized graphics for later presentation.

View Multiple Scatter Plots in a Single Multiplot

A scatter plot is an efficient way to see the effects of two variables simultaneously. However, if your data include many variables, to interpret all of their behaviors with 2D scatter plots would be tedious at best. A multiplot is a convenient way to present information from several variables in one view. In addition, Pirouette makes it easy to change which variables are included in the plot array. The limit to the number of variables in one multiplot depends only on the screen size and resolution.