Label embedded dictionary learning for image classification

Abstract

Recently, label consistent k-svd (LC-KSVD) algorithm has been successfully applied in image classification. The objective function of LC-KSVD is consisted of reconstruction error, classification error and discriminative sparse codes error with 0 -norm sparse regularization term. The 0 -norm, however, leads to NP-hard problem. Despite some methods such as orthogonal matching pursuit can help solve this problem to some extent, it is quite difficult to find the optimum sparse solution. To overcome this limitation, we propose a label embedded dictionary learning (LEDL) method to utilise the 1 -norm as the sparse regularization term so that we can avoid the hard-to-optimize problem by solving the convex optimization problem. Alternating direction method of multipliers and blockwise coordinate descent algorithm are then exploited to optimize the corresponding objective function. Extensive experimental results on six benchmark datasets illustrate that the proposed algorithm has achieved superior performance compared to some conventional classification algorithms. Figure 1:The scheme of LEDL is on the right while the LC-KSVD is on the left. The difference between the two methods is the sparse regularization term which LEDL use the 1 -norm regularization term and LC-KSVD use the 0 -norm regularization term. Compared with 0 -norm, the sparsity constraint factor of 1 -norm is unfixed so that the basis vectors can be selected freely for linear fitting. Thus, our proposed LEDL method can get smaller errors than LC-KSVD.

Class-Specific Sparse Principal Component Analysis for Visual Classification

“…In addition, to eliminate the randomness, we randomly (repeatable) split the dataset into the train set and test set for 8 times and the average accuracy is recorded. We compare the CS-SPCA approach with several popular visual classification approaches such as SVM [40], SRC [41], CRC [42], SLRC [43], NRC [44], LC-KSVD [2], CSDL-SRC [6], LEDL [3], and LC-PDL [45]. In our experiments, all the comparison methods are completed under the same experimental conditions, and all the methods are implemented by ourselves and adjusted to the optimal results.…”

“…Then, for the CMU-PIE dataset, there are 41, 368 pieces of images of 68 individuals in total, captured under 43 different Methods\Dataset Fifteen Scene MIT Indoor-67 SVM [40] 83.9 53.2 SRC [41] 81.5 52.9 CRC [42] 83.8 54.4 SLRC [43] 83.8 54.8 NRC [44] 80.5 52.3 LC-PDL [44] 84.7 53.6 LC-KSVD [2] 76.7 41.8 CSDL-SRC [6] 81.3 52.7 LEDL [3] 82. TABLE 3 validates the superiority of the CS-SPCA approach compared with other image classification methods.…”

“…FIGURE 8 shows several sample images from this dataset. [40] 67.5 80.5 SRC [41] 67.1 80.4 CRC [42] 67.7 80.7 SLRC [43] 66.4 80.9 NRC [44] 65.5 79.6 LC-PDL [45] 69.7 81.2 LC-KSVD [2] 68.0 79.4 CSDL-SRC [6] 66.6 80.5 LEDL [3] 67.9 80.7…”

“…TABLE 8 and TABLE 9 show the classification rate on two face recognition datasets with increasing the training size. For the Extend YaleB dataset, the CS-SPCA approach 69.8 77.9 79.8 82.0 CRC [42] 68.3 76.6 78.8 81.4 SLRC [43] 66.5 75.1 77.5 79.6 NRC [44] 68.5 77.0 79.4 81.4 LC-PDL [45] 62.6 72.2 74.5 75.7 LC-KSVD [2] 62.1 69.0 75.0 80.0 CSDL-SRC [6] 69.8 78.6 81.0 82.9 LEDL [3] 69.8 77.1 79.9 81.5…”

“…It could only find the suboptimal sparse solution due that the 0 -norm regularized objective function was a non-convex problem. Shao et al [3] proposed label embedded dictionary learning method to replace the 0 -norm regularization term with 1 -norm regularization term. In robust flexible discriminative dictionary learning (RFDDL) [4], the labels are utilized flexibly to enhance the robust property to sparse errors and encoding the locality, reconstruction error, and label consistency more accurately.…”