Discriminative Nonlinear Analysis Operator Learning: When Cosparse Model Meets Image Classification

Abstract

A linear synthesis model-based dictionary learning framework has achieved remarkable performances in image classification in the last decade. Behaved as a generative feature model, it, however, suffers from some intrinsic deficiencies. In this paper, we propose a novel parametric nonlinear analysis cosparse model (NACM) with which a unique feature vector will be much more efficiently extracted. Additionally, we derive a deep insight to demonstrate that NACM is capable of simultaneously learning the task-adapted feature transformation and regularization to encode our preferences, domain prior knowledge, and task-oriented supervised information into the features. The proposed NACM is devoted to the classification task as a discriminative feature model and yield a novel discriminative nonlinear analysis operator learning framework (DNAOL). The theoretical analysis and experimental performances clearly demonstrate that DNAOL will not only achieve the better or at least competitive classification accuracies than the state-of-the-art algorithms, but it can also dramatically reduce the time complexities in both training and testing phases.

Classification-Friendly Sparse Encoder and Classifier Learning

“…We mainly evaluate our CF-SECL method for pattern classification. The performance of our method is compared with that of some related state-of-the-art methods: KSVD [33], D-KSVD [12], LC-KSVD2 [13], FDDL [7], [8], DPL [9], JEDL [14], SRC [1], DADCL [19], DCADL [16], TL-FC [17], and DNAOL [18]. Our training model has three parameters i.e., α, β, and γ ) to estimate.…”

“…In addition, DPL, FDDL learn dictionary for sparse coding of training samples; DSRC and JNPDL jointly learn projection and dictionary for discriminative sparse coding of training samples; while SRC and our method use the training sample as synthesis dictionary for sparse coding of training samples. Similar to D-KSVD [12], LC-KSVD [13], JEDL [14], DCADL [16], TL-FC [17], DNAOL [18], our method applies the learnt linear classifier to the sparse feature to obtain the label of a test sample. However, there are differences in the training models.…”

“…In these methods, the linear classifier is directly applied to the sparse codes to map the sparse feature into labels. The method DNAOL [18] is a discriminative nonlinear analysis operator learning framework, in which a nonlinear operation is applied to the sparse features before input them to the classifier.…”

Fast DDL Classification for SAR Images With ${l}_{1,\infty}$ Constraint

“…However, with only a simple analysis operator, this model cannot capture the nonlinear structure of data points. Moreover, the linear operator P will not increase the separability of training samples and indices corresponding to zero feature response will be sensitive to slight variations [21]. To tackle this problem, a nonlinear operator f η is introduced.…”

“…2) Nonlinear sparse model As addressing optimization of (3) is time-consuming, our method generates a nonlinear co-sparse feature vector f η (PX) [21], where P is a linear feature selector, f η is a nonlinear operator and serves as a nonlinear feature extractor. So, this model performs feature extraction and selection via merely two explicit feed-forward operations, and it remarkably reduces computational complexity than conventional sparse recovery iterative algorithms.…”