Several works have shown that deep CNN classifiers can be easily transferred across datasets, e.g. the transfer of a CNN trained to recognize objects on ImageNET to an object detector on Pascal VOC. Less clear, however, is the ability of CNNs to transfer knowledge across tasks. A common example of such transfer is the problem of scene classification that should leverage localized object detections to recognize holistic visual concepts. While this problem is currently addressed with Fisher vector representations, these are now shown ineffective for the high-dimensional and highly non-linear features extracted by modern CNNs. It is argued that this is mostly due to the reliance on a model, the Gaussian mixture of diagonal covariances, which has a very limited ability to capture the second order statistics of CNN features. This problem is addressed by the adoption of a better model, the mixture of factor analyzers (MFA), which approximates the non-linear data manifold by a collection of local subspaces. The Fisher score with respect to the MFA (MFA-FS) is derived and proposed as an image representation for holistic image classifiers. Extensive experiments show that the MFA-FS has state of the art performance for object-to-scene transfer and this transfer actually outperforms the training of a scene CNN from a large scene dataset. The two representations are also shown to be complementary, in the sense that their combination outperforms each of the representations by itself. When combined, they produce a state of the art scene classifier.