  This paper presents an unsupervised deep-learning framework named Local
Deep-Feature Alignment (LDFA) for dimension reduction. We construct
neighbourhood for each data sample and learn a local Stacked Contractive
Auto-encoder (SCAE) from the neighbourhood to extract the local deep features.
Next, we exploit an affine transformation to align the local deep features of
each neighbourhood with the global features. Moreover, we derive an approach
from LDFA to map explicitly a new data sample into the learned low-dimensional
subspace. The advantage of the LDFA method is that it learns both local and
global characteristics of the data sample set: the local SCAEs capture local
characteristics contained in the data set, while the global alignment
procedures encode the interdependencies between neighbourhoods into the final
low-dimensional feature representations. Experimental results on data
visualization, clustering and classification show that the LDFA method is
competitive with several well-known dimension reduction techniques, and
exploiting locality in deep learning is a research topic worth further
exploring.
