where η is the learning rate, α is the momentum term, and δ_pj is the error signal of the output layer's node j. δ_pj is calculated as follows:

When j is not the output layer nodes, we also used the above weight amendment to connect the hidden layer's node i and the hidden layer's node j. But in this case δ_pj calculation becomes

where δ_pk is the error message between the output with input from node j and node k and w_kj is the weight connecting nodes j and k.

Identified Network and Application of the Results

After testing, we define the structure of the back-propagation network as nine nodes in the input layer, 10 nodes in the hidden layer, and three nodes in the output layer. The error is 0.05; α is 0.8; and η is 0.02.

Figure 3: The result of the multiresolution decomposition for giant foxtail seed FT-IR with CWT.

For the training process, we used nine input layer nodes of back-propagation network structure, followed by normalized nine feature vectors. The output layer nodes were divided into category 1: yellow foxtail seed; category 2: giant foxtail seed; and category 3: green foxtail seed. The trained network was used to verify the 180 different sample data. The input data are the eigenvectors extracted from the wavelet transform of the original FT-IR. The results are shown in Table I.

Figure 4: The result of the multiresolution decomposition for green foxtail seed FT-IR with CWT.

Based upon the results in Table I, the three different types of plant seeds (the yellow foxtail seed, the giant foxtail seed, and the green foxtail seed) are identified correctly. The eigenvectors of the different plant seeds that were extracted from the wavelet transform of the FT-IR have significant difference, so that a high classification accuracy could be achieved. Because the feature values of the green foxtail seed are very different from the ones of the two other seeds, an identification rate of 100% can be obtained.