  This paper proposes a novel deep subspace clustering approach which uses
convolutional autoencoders to transform input images into new representations
lying on a union of linear subspaces. The first contribution of our work is to
insert multiple fully-connected linear layers between the encoder layers and
their corresponding decoder layers to promote learning more favorable
representations for subspace clustering. These connection layers facilitate the
feature learning procedure by combining low-level and high-level information
for generating multiple sets of self-expressive and informative representations
at different levels of the encoder. Moreover, we introduce a novel loss
minimization problem which leverages an initial clustering of the samples to
effectively fuse the multi-level representations and recover the underlying
subspaces more accurately. The loss function is then minimized through an
iterative scheme which alternatively updates the network parameters and
produces new clusterings of the samples. Experiments on four real-world
datasets demonstrate that our approach exhibits superior performance compared
to the state-of-the-art methods on most of the subspace clustering problems.
