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The core idea behind the NovoSpark's visualization technique is to present each multidimensional observation as a single observation curve. With this approach if two data observations are close, the observation curves will have very similar shapes, whereas if the records are different, the curves will look significantly different as well.

 

Let us illustrate this by an example. Suppose we have two 10-dimensional observations A and B as shown below.

A: {53.78, 1, 17.56, 2.54, 6.36, 0.16, 4.63, 8.1, 3.28, 1.9} B: {50.53, 1.4, 19.05, 2.34, 5.95, 1.53, 3.63, 7.82, 2.98, 2.48}

The observation curves below are the visual representations of observations A and B.

Figure 1. Observation curve A

Figure 2. Observation curve B

Let us now put these two images together. As you may have noticed, the observation curves A and B look very similar. It means that the original observations are very much alike too.

The more indistinguishable the observation curves are from each other, the more identical the original data observations are.

 

Figure 3. Observation curves A and B

The approach establishes a one-to-one correspondence between data records and observation curves.

The order of observation parameters, or data columns, is significant for the shapes of observation curves. For instance, if we swap the first three parameters in observations A and B, the shapes of the observation curves will change too, as shown on Figure 4.

A (new): {17.56, 53.78, 1, 2.54, 6.36, 0.16, 4.63, 8.1, 3.28, 1.9}

B (new): {19.05, 50.53, 1.4, 2.34, 5.95, 1.53, 3.63, 7.82, 2.98, 2.48}

 

Figure 4. Observation curves A and B with swapped parameters

An observation curve is a two-dimensional image of a multidimensional data observation.

When the curves are rendered in three-dimensional space, with the third dimension, also called "Z-dimension" , representing either a distance in multidimensional space or time span between two observations, a lot of interesting data properties can be seen.

 

Figure 5. Observation curves A and B shown in 3D space

A straight path between observation A and observation in multidimensional space can be represented as a surface connecting two observation curves. Any observation with intermediate data values like the one highlighted in red on Figure 6, will lie on this surface.

The image on Figure 7 below was obtained as a result of connecting 38 individual observation curves in an ordered dataset.

 

Figure 6. The shortest path between observations A and B

 

Figure 7. Dynamic process on a 3D view

Three-dimensional visualization space provides an opportunity to look at the same image from different angles. For instance, the below image represents a "left side" 2D projection view of the above dataset.

Figure 8. Dynamic process on a 2D view

Let us get back to observations A and B . If we were to see the differences between them in more detail, one of the techniques that could be used for this purpose is the transformation of the original data.

The original data can be normalized to have data values lie within the [0, 1] range. For instance, here is the result of applying the normalization to observations A and B:

 

The original data with max values in each column highlighted in bold:

A: { 53.78, 1.0, 17.56, 2.54, 6.36, 0.16, 4.63, 8.10, 3.28, 1.90 }

B: { 50.53, 1.4, 19.05, 2.34, 5.95, 1.53, 3.63, 7.82, 2.98, 2.48 }

 

The normalized data:

A: {1, 0, 0, 1, 1, 0, 1, 1, 1, 0}

B: {0, 1, 1, 0, 0, 1, 0, 0, 0, 1}

Figure 9. Observation curves A and B after normalization

In the cases when different observation parameters are measured in different units or scale, the shapes of observation curves may get obscured by the nibs appearing on both sides of the curves. To eliminate them and enhance the general appearance of the curves a filter can be applied as shown on Figure 10.

Figure 10. Observation curves A and B after normalization and filter

To see the differences between observation curves in even greater detail a color palette can be used to identify curves' levels based on the colors they are rendered with on the image. By imaginarily stretching the curves along the Z-axis and looking at the resulting color bars from the top you can obtain a spectrum view of each observation.

 

The below images show the spectrum bars of observations A and B . You can see that they look very similar, which is an indication that the original data observations are very similar as well.

Figure 11. Observation curve A and its spectrum bar

Figure 12. Observation curve B and its spectrum bar


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