  How does the machine classify styles in art? And how does it relate to art
historians' methods for analyzing style? Several studies have shown the ability
of the machine to learn and predict style categories, such as Renaissance,
Baroque, Impressionism, etc., from images of paintings. This implies that the
machine can learn an internal representation encoding discriminative features
through its visual analysis. However, such a representation is not necessarily
interpretable. We conducted a comprehensive study of several of the
state-of-the-art convolutional neural networks applied to the task of style
classification on 77K images of paintings, and analyzed the learned
representation through correlation analysis with concepts derived from art
history. Surprisingly, the networks could place the works of art in a smooth
temporal arrangement mainly based on learning style labels, without any a
priori knowledge of time of creation, the historical time and context of
styles, or relations between styles. The learned representations showed that
there are few underlying factors that explain the visual variations of style in
art. Some of these factors were found to correlate with style patterns
suggested by Heinrich W\"olfflin (1846-1945). The learned representations also
consistently highlighted certain artists as the extreme distinctive
representative of their styles, which quantitatively confirms art historian
observations.
