Sparse Representation-based Object Recognition - Sparse Representations and Compressive Sensing for Imaging and Vision - page 73

Tabl e 5. 4 Classification accuracy ( % ) for the University of Pavia dataset [41]

Class SVM SVMCK KLR KLRCK OMP KOMP SOMP KSOMP

1 84.30 79.85 82.96 74.40 68.23 76.09 59.33 94.23

2 67.01 84.86 83.34 85.91 67.04 69.61 78.15 76.74

3 68.43 81.87 64.13 61.71 65.45 72.12 83.53 79.23

4 97.80 96.36 96.33 96.22 97.29 98.11 96.91 95.12

5 99.37 99.37 99.19 99.10 99.73 99.73 99.46 100

6 92.45 93.55 80.05 84.45 73.27 87.66 77.41 99.50

7 89.91 90.21 84.51 85.32 87.26 88.07 98.57 99.80

8 92.42 92.81 83.17 93.37 81.87 89.51 89.09 98.78

9 97.23 95.35 89.81 96.48 95.97 93.96 91.95 29.06

Overall 79.15 87.18 83.56 84.77 73.30 78.33 79.00 85.67

Average 87.66 90.47 84.83 86.33 81.79 86.10 86.04 85.83

The class label for the sample x 1 is then given by

( )= ( ) .

class x 1 arg min

m =

,···, L r m

x 1

1

This framework for classification was successfully applied to the hyperspectral
classification problem in [41]. We highlight some of the results on the University
of Pavia image using the non-linear sparse coding methods. The image consists of
1096

492 pixels, each having 102 spectral bands. About 5% of the labeled data are
used as training samples. The classification results are summarized in Table 5.4 .As
can be seen from this table, that operating in the feature space significantly improves
the accuracy of sparse coding methods on this dataset.
The ideas presented in this section can be extended to the case of multi-
modal multivariate sparse representation which is covered in the next section.
For simplicity, we present the multivariate sparse representation framework in
terms of multimodal biometrics recognition [130], however, it can be used for any
multimodal or multichannel classification problem [97].

×

5.4 Multimodal Multivariate Sparse Representation

Consider a multimodal C -class classification problem with D different biometric
traits. Suppose there are p i training samples in each biometric trait. For each
biometric trait i = 1 ,..., D , we denote

X i X i 1 , X i 2 ,..., X i C ] =[

p i dictionary of training samples consisting of C sub-dictionaries X i k 's
corresponding to C different classes. Each sub-dictionary

as an n i ×

X i j =[ x i j , 1 , x i j , 2 ,..., x i j , p j ] ∈ R

n × p j