Learning Prototype Models for Tangent Distance

true: 2 true proj. pred. proj. (0) true: 5 true proj. pred. proj. (8) true: 2 true proj. pred. proj. (0) true: 9 true proj. pred. proj. (4) true: 4 true proj. pred. proj. (7) Figure 2: Some of the errors for the test set corresponding to line (3) of table 4. Each case is displayed a s a c olumn of three images. The top is the true image, the middle the tangent projection of the true image onto the subspace m o del of its class, the bottom image the tangent projection of the image onto the winning class. The models are suuciently rich to allow distortions that can fool Euclidean distance. tangent subspace per class and the tangent distance is enough to outperform clas-siication using 1000 prototypes per class and the Euclidean distance (4:1% versus 5:5% on the test data). Table 1: Test errors for a variety of situations. In all cases the test data the 2007 USPS test digits. Each entry describes the model used i n e ach class, so for example in row 5 there a r e 5 m o dels per class, hence 5 0 i n a l l .