4.5 Multidimensional Analyzer
5.1.3 Application and Evaluation
Scatter plot navigation with decision trees has been implemented within MDA, see Section 4.5. MDA supports loading a decision tree from file, the core elements of decision tree navigation (i.e., the decision tree itself and the link scatter plot views) and, additionally, further coordinated data views, which may be application-dependent.
Additionally the scatter plot indicates which points belong to the training set by a small white dot and displays false classifications by a large triangle. Now the approach is illustrated for two typical application scenarios.
Figure 5.2: Trajectories superimposed on an image. The 7 colors denote differently classified trajectories.
Understanding Decision Trees
The first example is an application of data analysis in computer vision. This application was used to evaluate decision tree navigation in a qualitative study with a domain expert. She was interested in classifying trajectories of people walking into a given room (see Figure 5.2). A semi-automatically labeled set of trajectories each belonging to one of 7 classes was taken as input. The 321 trajectories were sampled at 250 positions and transformed to a feature vector representation consisting of the final x and y screen coordinates (x end andy end), a standard deviation of position in x and y screen directions (x std devand y std dev) calculated at every 10th position using a local window of 21 positions on the path and a local direction (angle) based on the direction between 21 samples calculated at the same positions. The resulting feature space was ((250-20)/10)*2+2=48 dimensional. Matlab’s classregtree method was used to create the classifier with supervised learning, which uses Breiman’s Classification and Regression Trees method [BFSO84]. The resulting classifier is a binary decision tree, where each branching node is split based on the values of a coordinate of the input vector. The trained decision tree used 10 data dimensions and consisted of 12 inner nodes, see Figure 5.3. The domain expert was interested in analyzing the resulting decision tree. She was used to Matlab decision tree plots similar to the plot in the
“Decision Tree” widget in Figure 5.3. She regularly plotted trajectories over an input
5.1. Scatter Plot Navigation with Decision Trees 63
Figure 5.3: Screenshot of MDA showing a scatter plot in the main part of the window (left). In the center-right, a decision tree is presented; inner nodes are drawn as circles labeled with the dimension considered, leaf nodes are drawn as squares labeled with the classifier result. In the upper-right corner, the values for the different data dimension of the selected data item (marked with a black ring in the scatter plot) are printed. Colors represent the classification. Points of the scatter plot (left) that were not part of the training set are marked with white dots inside; classifier errors are marked by gray triangles. In the bottom-right, the trajectories are rendered in their 3D spatial context.
All four views are linked, propagating the selection of data items between the views.
See the accompanying video (decTree.avi).
image like in Figure 5.2 in order to analyze the trajectories. However, she had no prior experience with multidimensional analysis tools like GGobi. Since there is a high density of trajectories in the image, she typically plotted just one or a small group of trajectories during analysis. This was cumbersome because each trajectory had to be examined together with additional information like the features used by the decision tree. The objective of this process was to identify incorrectly labeled trajectories.
With MDA, the domain expert investigated if the classifier performed as expected and, if not, she tried to find incorrectly labeled and incorrectly classified trajectories. The following interaction modes were explained to the expert:
• Within the scatter plot: zooming and panning by mouse navigation.
• Switching color coding between labeling and showing decision tree results.
• Selecting a trajectory in the scatter plot with the mouse.
A different data set consisting of 241 trajectories had 9 clusters. A high-dimensional feature vector using all 250 x and y positions in addition to the features described above was used. A decision tree was trained which used 15 data dimensions and consisted of 17 inner nodes. Figure 5.4 shows the tool during the evaluation session. The first subfigure (top left) shows the scatter plot corresponding to the root of the decision tree, with the data dimensions (8, 12) mapped to the (x,y) axes. The user chooses to descend to the right child of the node; the application grays out and minimizes the points of the scatter plot that are not on the right side of the node (subfigure 2). While descending to the child node, the application needs to change the axis mapping to (8, 5). This looks like a 3D rigid body rotation presented as snapshots from the animation (subfigures 2–7). At the child node, the user selects the left child (data dimension 4) and the other points of the scatter plot are grayed out by the system (subfigure 8).
The expert reported that she had gained insight related to the labeling of the trajecto-ries that had significant errors and thereby degraded the decision tree obtained by the learning algorithm. She found the application and the decision tree navigation intuitive.
Even without previous exposure to similar systems, there was no steep learning curve. In summary, the domain expert found decision tree navigation useful.
Understanding Multidimensional Data
Scatter plot navigation with decision trees is not only useful to understand decision trees, but also to get insight into multidimensional data. The key observation is that decision trees use the dimensions of the data that are most suited to separate differently labeled data points. This property can be utilized to guide the exploration of multidimensional data sets. The process consists of two stages: first, a decision tree is trained from the input data; second, the navigation technique is applied for interactive data analysis.
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Figure 5.4: Navigation with a decision tree in a video trajectory data set. Subfigures are ordered counterclockwise. The red-green box indicates the rotation and the grayed out subset of points. See the accompanying video (decTree.avi) for an animated presentation.
Figure 5.5: Scatter plot navigation using the regions of the “olive oil” data set. Regions:
A: Region 1 (south), B: Region 2 (Sardinia), C: Region 3 (north).
Data analysis is illustrated for the well-known “olive oil” data set [FALT83], briefly used in Section 4.4.2. This benchmark data set consists of olive oils coming from nine different areas of Italy given their composition with respect to eight fatty acids. The areas are grouped in three regions. Using regions as class attribute results in a small tree with only three leaf nodes and two inner nodes. Therefore, a single 2D scatter plot is sufficient to separate the three regions as shown in Figure 5.5. Note that these two dimensions can be found automatically, and no user interaction is required.
A decision tree can also be trained using areas as class attribute. Then, the nine areas cannot be separated as easily, see Figure 5.6. The root node separates the areas North-Apulia, Calabria, South-Apulia, and Sicily from the other five areas. The left branch consisting of six inner nodes separates the other five areas from each other. The right branch, however, requires 15 inner nodes to separate the four regions. By ignoring Sicilian oils—similar to Caragea et al. [CCH01], who analyzed the “olive oil” data set using SVM classifiers—the remaining three regions can be separated by just four inner nodes.