  The goal of compressive sensing is efficient reconstruction of data from few
measurements, sometimes leading to a categorical decision. If only
classification is required, reconstruction can be circumvented and the
measurements needed are orders-of-magnitude sparser still. We define enhanced
sparsity as the reduction in number of measurements required for classification
over reconstruction. In this work, we exploit enhanced sparsity and learn
spatial sensor locations that optimally inform a categorical decision. The
algorithm solves an l1-minimization to find the fewest entries of the full
measurement vector that exactly reconstruct the discriminant vector in feature
space. Once the sensor locations have been identified from the training data,
subsequent test samples are classified with remarkable efficiency, achieving
performance comparable to that obtained by discrimination using the full image.
Sensor locations may be learned from full images, or from a random subsample of
pixels. For classification between more than two categories, we introduce a
coupling parameter whose value tunes the number of sensors selected, trading
accuracy for economy. We demonstrate the algorithm on example datasets from
image recognition using PCA for feature extraction and LDA for discrimination;
however, the method can be broadly applied to non-image data and adapted to
work with other methods for feature extraction and discrimination.
