字典学习supervised-dictionary-learning.pdf

Supervised Dictionary Learning
Julien Mairal Francis Bach
INplete, with a number of basis elements greater
than the dimension of the data. Recent research has shown that sparsity helps to capture higher-order
correlation in data. In [3, 4], sparse decompositions are used with predefined dictionaries for face
and signal recognition. In [5], dictionaries are learned for a reconstruction task, and the correspond-
ing sparse models are used as features in an SVM. In [6], a discriminative method is introduced
for various classification tasks, learning one dictionary per class; the classification process itself is
based on the corresponding reconstruction error, and does not exploit the actual decomposition co-
efficients. In [7], a generative model for documents is learned at the same time as the parameters of
a deep network structure. In [8], multi-task learning is performed by learning features and tasks are
selected using a sparsity criterion. The framework we present in this paper extends these approaches
by learning simultaneously a single shared dictionary as well as models for different signal classes
in a mixed generative and discriminative formulation (see also [9], where a different discriminative
term is added to the classical reconstructive one). Similar joint generative/discriminative frame-
works have