  This paper addresses the following questions pertaining to the intrinsic
dimensionality of any given image representation: (i) estimate its intrinsic
dimensionality, (ii) develop a deep neural network based non-linear mapping,
dubbed DeepMDS, that transforms the ambient representation to the minimal
intrinsic space, and (iii) validate the veracity of the mapping through image
matching in the intrinsic space. Experiments on benchmark image datasets (LFW,
IJB-C and ImageNet-100) reveal that the intrinsic dimensionality of deep neural
network representations is significantly lower than the dimensionality of the
ambient features. For instance, SphereFace's 512-dim face representation and
ResNet's 512-dim image representation have an intrinsic dimensionality of 16
and 19 respectively. Further, the DeepMDS mapping is able to obtain a
representation of significantly lower dimensionality while maintaining
discriminative ability to a large extent, 59.75% TAR @ 0.1% FAR in 16-dim vs
71.26% TAR in 512-dim on IJB-C and a Top-1 accuracy of 77.0% at 19-dim vs 83.4%
at 512-dim on ImageNet-100.

Computer Vision and Pattern Recognition;Machine Learning