Plotting results with many features

I need an advice for plotting my results. I got different classification results by including different features and different k values. So, I got different results for each of them:

My features: alphaRaw16-1, alphaRaw16-2, alphaRaw16-3, grad-x, grad-y, grad-z.
The range of k value: 1 to 21

And, the results look like:

True_Positive   False_Negative  k  Feature
89%              4%          1   alphaRaw16-1
91%              5%          1   alphaRaw16-2
93%              8%          1   alphaRaw16-3
97%              1%          1   grad-x
66%              3%          1   grad-y
77%              42%         1   grad-z
91%              2%          1   grad-x, alphaRaw16-1

..               ..          ..  ..
94%              7%          1   alphaRaw16-1,alphaRaw16-2,alphaRaw16-3,grad-x,grad-y,grad-x
92%              9%          2   alphaRaw16-1

...              ..          ..   ..
90%              12%         21   alphaRaw16-1,alphaRaw16-2,alphaRaw16-3,grad-x,grad-y,grad-x


How to best display these results in a meaningful way? Could you please advise me?

1 Answer

Your Feature variable with 64 different feature combinations (or 63 if you don't count the empty one) is equivalent to 6 independent binary variables. So, adding k, you have 7 factors and 2 responses. If you model your problem that way, your software should provide some useful output display.

The amazing insightfulness of data visualization falls off quickly as we show more than a handful of variables. However, if you focus on a few aspects at a time, you can get some benefit.

You can look at the two responses by each of the 7 factors independently.

More options are available if you restrict yourself to one response at a time. You can see two-way interactions with a scatterplot matrix.

Dots are jittered for the binary factors and color represents the response.

A heatmap is one way to see the entire structure, though some patterns are stand out better than others, and you should experiment with the ordering/hierarchy (informed by the model output).

In this case, You might notice a couple feature:

1. Every other group of 4 columns is darker near the top, which suggests a X4*K interaction.
2. The right half is darker, which suggest X1 may be significant.

If you estimate those and subtract them out, other patterns may become evident, but it's quite iffy already.

To re-emphasize the first point, analytical methods will almost always be more effective for data with this many dimensions. Here is part of the model output for my fake data, which identifies the main effects right away.

Parameter Estimates

Term               Estimate  Std Error  t Ratio   Prob>|t|
X4                -1.093515   0.054667   -20.00    <.0001
X1                -0.88112    0.054667   -16.12    <.0001
Intercept          1.531147   0.11336     13.51    <.0001
X3                -0.615258   0.054667   -11.25    <.0001
K                  0.100797   0.009028    11.17    <.0001
X4*K              -0.089554   0.009028    -9.92    <.0001
X2                -0.460676   0.054667    -8.43    <.0001
X2*X5              0.3937876  0.054667     7.20    <.0001
X1*X2*X5          -0.377805   0.054667    -6.91    <.0001
X1*X2              0.3277955  0.054667     6.00    <.0001
X2*X3              0.3087438  0.054667     5.65    <.0001
X5                -0.282575   0.054667    -5.17    <.0001
X1*X5              0.2798842  0.054667     5.12    <.0001
X1*X4*X6*K         0.0307494  0.009028     3.41    0.0007
X2*X5*X6           0.1657399  0.054667     3.03    0.0025
X4*X6*K            0.0232485  0.009028     2.58    0.0101
X5*K               0.0213684  0.009028     2.37    0.0181
X3*X5             -0.125324   0.054667    -2.29    0.0220
X1*X2*X3*K        -0.018911   0.009028    -2.09    0.0364
X2*X4*K           -0.017889   0.009028    -1.98    0.0478
X4*X6              0.1036833  0.054667     1.90    0.0581
X1*X6             -0.097084   0.054667    -1.78    0.0760
X1*X4*X5           0.0768364  0.054667     1.41    0.1601
X3*X4*X6*K         0.0124664  0.009028     1.38    0.1676
X2*X3*X6          -0.075022   0.054667    -1.37    0.1702
X1*X3*X4           0.0680795  0.054667     1.25    0.2132
...