We use the Haxby's data set and perform classification
We use only logistic regression as the classifier. In this table, we just need to decide if what choice of lanbda we should use. And the result shows that lambda = 0.1 is probably the best.
We then proceed to pick voxels with V>=V_thres to do classification.
The plot of V versus the accuracy (averaged, min, max) and the ratio of voxels used
This is the version 1, using only training set to train the model
Raw output
V: 0.00 min: 75.00% avg: 87.50% max: 100.00% std: 8.33% #voxel: 577
V: 0.04 min: 75.00% avg: 90.00% max: 100.00% std: 7.91% #voxel: 559
V: 0.07 min: 75.00% avg: 87.50% max: 100.00% std: 8.33% #voxel: 542
V: 0.11 min: 75.00% avg: 91.25% max: 100.00% std: 8.44% #voxel: 511
V: 0.14 min: 87.50% avg: 93.75% max: 100.00% std: 6.59% #voxel: 480
V: 0.18 min: 87.50% avg: 91.25% max: 100.00% std: 6.04% #voxel: 453
V: 0.21 min: 87.50% avg: 92.50% max: 100.00% std: 6.45% #voxel: 422
V: 0.25 min: 87.50% avg: 93.75% max: 100.00% std: 6.59% #voxel: 381
V: 0.29 min: 87.50% avg: 93.75% max: 100.00% std: 6.59% #voxel: 322
V: 0.32 min: 87.50% avg: 93.75% max: 100.00% std: 6.59% #voxel: 273
V: 0.36 min: 87.50% avg: 93.75% max: 100.00% std: 6.59% #voxel: 231
V: 0.39 min: 87.50% avg: 93.75% max: 100.00% std: 6.59% #voxel: 186
V: 0.43 min: 75.00% avg: 90.00% max: 100.00% std: 7.91% #voxel: 151
V: 0.46 min: 75.00% avg: 93.75% max: 100.00% std: 8.84% #voxel: 121
V: 0.50 min: 75.00% avg: 91.25% max: 100.00% std: 8.44% #voxel: 88
V: 0.54 min: 75.00% avg: 90.00% max: 100.00% std: 7.91% #voxel: 64
V: 0.57 min: 75.00% avg: 88.75% max: 100.00% std: 9.22% #voxel: 47
V: 0.61 min: 50.00% avg: 85.00% max: 100.00% std: 16.46% #voxel: 32
V: 0.64 min: 62.50% avg: 81.25% max: 100.00% std: 12.15% #voxel: 20
V: 0.68 min: 50.00% avg: 78.75% max: 100.00% std: 13.24% #voxel: 13
V: 0.71 min: 37.50% avg: 62.50% max: 75.00% std: 13.18% #voxel: 7
V: 0.79 min: 12.50% avg: 45.00% max: 75.00% std: 20.58% #voxel: 5
V: 0.82 min: 12.50% avg: 31.25% max: 50.00% std: 12.15% #voxel: 3
V: 0.86 min: 12.50% avg: 40.00% max: 62.50% std: 14.19% #voxel: 2
V: 0.89 min: 25.00% avg: 41.25% max: 62.50% std: 11.86% #voxel: 1
This is version 2, using both training and cv set to train the model
V: 0.00 min: 75.00% avg: 87.50% max: 100.00% std: 10.21% #voxel: 577
V: 0.04 min: 87.50% avg: 95.00% max: 100.00% std: 6.45% #voxel: 559
V: 0.07 min: 75.00% avg: 91.25% max: 100.00% std: 8.44% #voxel: 542
V: 0.11 min: 75.00% avg: 93.75% max: 100.00% std: 10.62% #voxel: 511
V: 0.14 min: 87.50% avg: 90.00% max: 100.00% std: 5.27% #voxel: 480
V: 0.18 min: 75.00% avg: 91.25% max: 100.00% std: 8.44% #voxel: 453
V: 0.21 min: 87.50% avg: 92.50% max: 100.00% std: 6.45% #voxel: 422
V: 0.25 min: 87.50% avg: 95.00% max: 100.00% std: 6.45% #voxel: 381
V: 0.29 min: 87.50% avg: 93.75% max: 100.00% std: 6.59% #voxel: 322
V: 0.32 min: 87.50% avg: 93.75% max: 100.00% std: 6.59% #voxel: 273
V: 0.36 min: 87.50% avg: 96.25% max: 100.00% std: 6.04% #voxel: 231
V: 0.39 min: 87.50% avg: 96.25% max: 100.00% std: 6.04% #voxel: 186
V: 0.43 min: 87.50% avg: 96.25% max: 100.00% std: 6.04% #voxel: 151
V: 0.46 min: 87.50% avg: 96.25% max: 100.00% std: 6.04% #voxel: 121
V: 0.50 min: 75.00% avg: 92.50% max: 100.00% std: 10.54% #voxel: 88
V: 0.54 min: 87.50% avg: 95.00% max: 100.00% std: 6.45% #voxel: 64
V: 0.57 min: 75.00% avg: 88.75% max: 100.00% std: 7.10% #voxel: 47
V: 0.61 min: 62.50% avg: 88.75% max: 100.00% std: 13.76% #voxel: 32
V: 0.64 min: 62.50% avg: 78.75% max: 87.50% std: 10.29% #voxel: 20
V: 0.68 min: 62.50% avg: 77.50% max: 100.00% std: 11.49% #voxel: 13
V: 0.71 min: 25.00% avg: 60.00% max: 87.50% std: 17.48% #voxel: 7
V: 0.79 min: 0.00% avg: 47.50% max: 87.50% std: 26.22% #voxel: 5
V: 0.82 min: 0.00% avg: 35.00% max: 50.00% std: 15.37% #voxel: 3
V: 0.86 min: 25.00% avg: 41.25% max: 50.00% std: 8.44% #voxel: 2
V: 0.89 min: 25.00% avg: 42.50% max: 62.50% std: 10.54% #voxel: 1
Again, this is a "peek-type" classification though--namely, I calculate the distinguishability for all the voxels in the brain using all the samples available regardless of they are in the train or test set. It makes sense for now because this experiment does not aim for the highest classification accuracy, but just to see how much the classification accuracy can be improved when the non-informative voxels are gradually removed step by step. So, from this curve we can say the following:
Now, the whole brain version1
The raw output
V: 0.00 min: 12.50% avg: 37.50% max: 62.50% std: 17.68% #voxel: 43193
V: 0.04 min: 37.50% avg: 57.50% max: 87.50% std: 16.87% #voxel: 27899
V: 0.07 min: 50.00% avg: 63.75% max: 87.50% std: 12.43% #voxel: 19595
V: 0.11 min: 50.00% avg: 76.25% max: 87.50% std: 12.43% #voxel: 13718
V: 0.14 min: 62.50% avg: 78.75% max: 100.00% std: 11.86% #voxel: 9354
V: 0.18 min: 62.50% avg: 77.50% max: 100.00% std: 14.19% #voxel: 6280
V: 0.21 min: 62.50% avg: 82.50% max: 87.50% std: 8.74% #voxel: 4206
V: 0.25 min: 75.00% avg: 90.00% max: 100.00% std: 7.91% #voxel: 2787
V: 0.29 min: 75.00% avg: 88.75% max: 100.00% std: 7.10% #voxel: 1839
V: 0.32 min: 75.00% avg: 90.00% max: 100.00% std: 7.91% #voxel: 1275
V: 0.36 min: 87.50% avg: 93.75% max: 100.00% std: 6.59% #voxel: 886
V: 0.39 min: 75.00% avg: 92.50% max: 100.00% std: 8.74% #voxel: 653
V: 0.43 min: 75.00% avg: 93.75% max: 100.00% std: 8.84% #voxel: 461
V: 0.46 min: 75.00% avg: 96.25% max: 100.00% std: 8.44% #voxel: 317
V: 0.50 min: 75.00% avg: 96.25% max: 100.00% std: 8.44% #voxel: 221
V: 0.54 min: 75.00% avg: 93.75% max: 100.00% std: 8.84% #voxel: 160
V: 0.57 min: 75.00% avg: 93.75% max: 100.00% std: 8.84% #voxel: 107
V: 0.61 min: 75.00% avg: 93.75% max: 100.00% std: 10.62% #voxel: 69
V: 0.64 min: 75.00% avg: 92.50% max: 100.00% std: 8.74% #voxel: 40
V: 0.68 min: 75.00% avg: 88.75% max: 100.00% std: 10.94% #voxel: 22
V: 0.71 min: 50.00% avg: 71.25% max: 87.50% std: 13.24% #voxel: 10
V: 0.79 min: 12.50% avg: 45.00% max: 75.00% std: 20.58% #voxel: 5
V: 0.82 min: 12.50% avg: 31.25% max: 50.00% std: 12.15% #voxel: 3
V: 0.86 min: 12.50% avg: 40.00% max: 62.50% std: 14.19% #voxel: 2
V: 0.89 min: 25.00% avg: 41.25% max: 62.50% std: 11.86% #voxel: 1
Now, whole brain version 2
V: 0.00 min: 12.50% avg: 37.50% max: 75.00% std: 20.41% #voxel: 43193
V: 0.04 min: 37.50% avg: 55.00% max: 75.00% std: 14.67% #voxel: 27899
V: 0.07 min: 50.00% avg: 66.25% max: 87.50% std: 13.24% #voxel: 19595
V: 0.11 min: 75.00% avg: 80.00% max: 100.00% std: 8.74% #voxel: 13718
V: 0.14 min: 62.50% avg: 80.00% max: 100.00% std: 12.08% #voxel: 9354
V: 0.18 min: 75.00% avg: 86.25% max: 100.00% std: 7.10% #voxel: 6280
V: 0.21 min: 75.00% avg: 86.25% max: 100.00% std: 9.22% #voxel: 4206
V: 0.25 min: 62.50% avg: 83.75% max: 100.00% std: 14.49% #voxel: 2787
V: 0.29 min: 50.00% avg: 78.75% max: 87.50% std: 13.24% #voxel: 1839
V: 0.32 min: 62.50% avg: 82.50% max: 100.00% std: 10.54% #voxel: 1275
V: 0.36 min: 75.00% avg: 92.50% max: 100.00% std: 8.74% #voxel: 886
V: 0.39 min: 87.50% avg: 97.50% max: 100.00% std: 5.27% #voxel: 653
V: 0.43 min: 87.50% avg: 96.25% max: 100.00% std: 6.04% #voxel: 461
V: 0.46 min: 75.00% avg: 97.50% max: 100.00% std: 7.91% #voxel: 317
V: 0.50 min: 75.00% avg: 96.25% max: 100.00% std: 8.44% #voxel: 221
V: 0.54 min: 75.00% avg: 97.50% max: 100.00% std: 7.91% #voxel: 160
V: 0.57 min: 75.00% avg: 97.50% max: 100.00% std: 7.91% #voxel: 107
V: 0.61 min: 87.50% avg: 97.50% max: 100.00% std: 5.27% #voxel: 69
V: 0.64 min: 87.50% avg: 96.25% max: 100.00% std: 6.04% #voxel: 40
V: 0.68 min: 75.00% avg: 90.00% max: 100.00% std: 9.86% #voxel: 22
V: 0.71 min: 62.50% avg: 73.75% max: 87.50% std: 10.94% #voxel: 10
V: 0.79 min: 0.00% avg: 47.50% max: 87.50% std: 26.22% #voxel: 5
V: 0.82 min: 0.00% avg: 35.00% max: 50.00% std: 15.37% #voxel: 3
V: 0.86 min: 25.00% avg: 41.25% max: 50.00% std: 8.44% #voxel: 2
V: 0.89 min: 25.00% avg: 42.50% max: 62.50% std: 10.54% #voxel: 1
Comparison of the accuracy from all the methods
Things I should do: