Enhancing hyperspectral remote sensing image classification using robust learning technique

2.1 Indian Pines

The Indian Pines dataset was obtained through the use of an airborne sensor named Airborne Visible/Infrared Imaging Spectrometer (AVIRIS). With dimensions of 145 × 145 pixels and a total of 220 spectral bands, this dataset is a valuable resource for hyperspectral imaging analysis. The wavelength range of the bands spans from 0.4 to 2.5 μm, providing comprehensive spectral information that can be utilized to identify different areas and substances with great precision. The absorption bands are removed for this study, and the remaining 200 bands are used. It consists of sixteen different land cover classes.

2.2 University of Pavia

The University of Pavia dataset encompasses an urban area within the city of Pavia, Italy, and was collected through the application of a Reflective Optics System Imaging Spectrometer (ROSIS-3). It comprises 115 spectral bands with a wavelength range of 0.43–0.86 μm and a spatial resolution of 1.3 m/pixel, represented by 610 × 340 pixels. Despite its high spatial resolution, the dataset contained some noisy channels that were subsequently removed, remaining only 103 channels to be employed in this study for the purpose of classification. It consists of nine land-cover classes.

3.1 BPVAM algorithm

To take full advantage of the momentum term, an optimal value of momentum should be selected. A small value may not help take the model out of local minima and a large value can make the model fluctuate around the optimal value. To overcome these issues, an adaptive momentum ( $\alpha$ ) term is introduced in the weight update step in the BP algorithm by (Hameed et al., 2019). The new algorithm is termed BPVAM. This adaptive momentum dynamically adjusts $\alpha$ during training, promoting convergence without getting stuck in local minima. The BPVAM algorithm ensures that momentum effectively guides the optimization process. By fine-tuning $\alpha$ , it strikes a balance between stability and progress, making it a valuable addition to the field of neural network training techniques. In practical applications, BPVAM has demonstrated improved convergence and optimization performance, offering a promising solution for training deep neural networks more efficiently.

3.2 Principal component analysis (PCA)

PCA, also referred to as Karhunen-Loeve transform, was first proposed by Pearson (Pearson, 1901). The method is a multivariate statistical analysis technique, which effectively reduces the dimensionality of the data through reduction. Its work is started by receiving d-dimensional input vectors. The objective of PCA is to represent these d-dimensional vectors using k-dimensional vectors, where k≪d. It first calculates the mean vector (μ) and covariance matrix Σ using the d-dimensional space. The computation and arrangement of the eigenvalues and their corresponding eigenvectors are performed to allocate the dimensional space with maximal variance. The original data is then transformed using the newly generated Eigenvectors.

3.3 BPVAM-PCA HSS classification

The input data consists of a high number of channels. Before applying the BPVAM algorithm, the utilization of PCA was employed to reduce the dimensional magnitude of the input features. The robustness of the system was improved when highly redundant features with low variance were discarded using PCA. This improved the likelihood of the model reaching convergence early in the training process without affecting its performance.

The original data set for the Indian Pines data consisted of 220 bands, while The University of Pavia consisted of 115 bands. PCA was applied to select the most suitable number of bands to obtain highly discriminative features. We experimented with three different feature sizes for the University of Pavia (5, 10, and 20). Increasing the dimensional beyond 20 did not improve accuracy. Moreover, reducing features below ten also decreased the performance of the model. Similarly, for the Indian pines dataset, we empirically selected feature sizes of 10, 40, and 80. The features that have been selected were then taken as input to the BPVAM model for the classification of each pixel into one of the categories. We observed that the BPVAM reached a low steady-state error faster during training using features with high variance and low autocorrelation.

The workflow of the proposed BPVAM-PCA model will whole steps is illustrated in Fig. 1. The initiation of the learning process involves the random initialization of the weight vectors and other learning parameters of the model. The input data is passed to the PCA algorithm first and then fed it BPVAM model for classification. The training process is iterative over several epochs to obtain optimal values for both weights and biases. Two possibilities are used to stop the training process: maximum number of iterations and stopping criteria. The training will continue until the error reaches the acceptable threshold value or reach the maximum number of iterations. After training is completed, the optimized weights and biases will be stored and taken into consideration for the subsequent stage of processing. Finally, the test data is passed to the trained/optimized model which will then produce the final class labels for each pixel.

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Fig. 1

Block diagram of the BPVAM-PCA method.

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4.1 Indian Pines dataset

Table 1 summarizes the quantitative results obtained for the Indian Pines dataset. The best feature sizes used in this dataset for PCA are 10, 40, and 80. It can be seen that the BPVAM-PCA algorithm produced relatively better performance compared to BP-PCA for all three sizes of extracted features. Data with 80 features produced better results with an accuracy of 98.83 % and SSE of 1.1233 for the training dataset, while the accuracy of 97.30 % and SSE of 1.0665 for the testing dataset. The performance of BP-PCA was relatively similar to BPVAM-PCA which achieved accuracy = 0.9869 and error = 1.2350 in training, and accuracy = 96.71 % and SSE = 1.19 in the testing. BPVAM-PCA produces on average 2 % better accuracy for other feature sizes than the BP-PCA algorithm.

Initially, all models produced higher SSE due to random initialization. As the iterations proceeded, all models started to gradually converge.

In Table 2, Pre, Rec, Spe, and F1 results for two methods, BP-PCA and BPVAM-PCA, are compared across different feature sizes for the Indian Pines dataset with 16 distinct classes. BPVAM-PCA consistently exhibits superior performance over BP-PCA in terms of Pre, Rec, and F1 across most classes and feature sizes. This suggests that BPVAM-PCA not only minimizes false positives and maximizes true positives more effectively but also strikes a better balance between Pre and Rec. Both methods demonstrate high Spe, indicating their proficiency in identifying true negatives among actual negative instances. The overall trend in the results indicates that BPVAM-PCA is better suited for the Indian Pines dataset, delivering more accurate and reliable predictions than BP-PCA.

Fig. 2 shows the convergence behavior of BP-PCA and BPVAM-PCA methods for different feature sizes on the Indian Pines dataset. The visual results confirm the performance of the proposed model shown in Tables 1, and 2 by providing significant performance enhancement for BPVAM-PCA over BP-PCA. The data extracted with 80 features give better results by achieving less error and faster convergence. The improved performance also demonstrates that learning of BPVAM-PCA is robust by dealing with different size and feature characteristics.

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Fig. 2

Convergence behavior of BP-PCA and BPVAM-PCA methods using different features on sthe Indian Pines dataset.

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It can be seen from Fig. 2 that both models resulted in relatively higher SSE when the feature size was set to 10. This indicates that dimensionality reduction from large dimensional space to very low dimensional space resulted in the loss of important information. In addition, this also leads the models to converge slowly to reach a steady-error state. Especially, BPVAM-PCA took almost 180 iterations to reach a stable error state. For features sizes of 40 and 80, the overall behavior of the models was similar. It can be noticed that BPVAM-PCA not only converged faster but also resulted in lower SSE from the very beginning till the end of iterations.

The following Fig. 3 shows the behavior of each experiment conducted on the Indian Pines dataset and the effect of each experiment under some conditions and hyperparameters. Where, we notice some models give better results than others depending on the type of features extracted, as well as their impact on the model during learning. Some models are weak in finding all classes, but we note the best result obtained by BPVAM-PCA with 80 features.

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Fig. 3

Predicted classes by BP-PCA and BPVAM-PCA methods using different features for Indian Pines dataset. a) BP-PCA with 10 features. b) BPVAM-PCA with 10 features. c) BP-PCA with 40 features. d) BPVAM-PCA with 40 features. e) BP-PCA with 80 features. f) BPVAM-PCA with 80 features.

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4.2 Pavia University dataset

The second experiment is performed using The University of Pavia hyperspectral dataset. Since the number of bands in The University of Pavia dataset was relatively less (103) than the Indian Pines dataset (200), a set of smaller features was selected. Three different combinations were tested for different feature sizes: 5, 10 and 20. As mentioned earlier, these sizes were empirically calculated by running the experiment several times. The dataset was split into training (75 %) and testing (30 %) subsets.

Table 3 summarizes the results obtained for BP-PCA and BPVAM-PCA models for the Pavia University dataset with varying size of features. It is clearly seen from the table that the proposed BPVAM-PCA model outperformed BP-PCA by improving the classification accuracies with all three different feature sizes. BPVAM-PCA for feature size of 20 produced more accurate results with accuracy = 99.71 % and error = 2.16 for training and accuracy = 99.11 % and SSE = 2.15 for testing dataset. Compared with BPVAM, BP-PCA achieved relatively low performance with accuracy = 99.64 % and SSE = 2.73 for training, and accuracy = 98.88 % and SSE = 2.72 for the test datasets. For features size 5, BP-PCA produced the lowest testing accuracy (99.53 %) with high SSE (3.5). In contrast, the performance of BPVAM-PCA was relatively better in terms of accuracy (99.54 %) and SSE (3.2). Similarly, for feature size 10, both models exhibited similar behavior, yet BPVAM-PCA proved to be more accurate for both test and training. This shows that BPVAM-PCA maintains its robustness by iteratively adapting itself using variable momentum, then gives better results than other models when tested with varying sizes of features.

Table 4 presents Pre, Rec, Spe, and F1 results for two classification methods, BP-PCA and BPVAM-PCA, evaluated across three distinct feature sizes (5, 10, and 20) using the University of Pavia dataset, which comprises nine land cover classes. BPVAM-PCA demonstrates slightly higher precision, recall, and specificity values across most classes and feature sizes, indicating its proficiency in classifying land cover types. The performance comparison between BP-PCA and BPVAM-PCA, as shown in the presented results, reveals that BPVAM-PCA consistently achieves F1-scores close to 1, suggesting a well-balanced trade-off between precision and recall.

Fig. 4 shows that the BPVAM-PCA model maintained the best performance in terms of low error and speed of convergence for all three extracted features. This indicates that the variable adaptive momentum provided significant performance enhancement for BPVAM-PCA over BP-PCA. Fig. 5 confirms the results shown in Tables 3, and 4 where the experiment was tested on the University of Pavia dataset in 6 different cases under different conditions and hyperparameters. It is clear that the best result was obtained by BPVAM-PCA with 20 features, where the extracted features and selected hyperparameters have a very large impact on the learning model and can also outperform the weaknesses challenges of other comparable models in finding all classes.

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Fig. 4

Convergence behavior of BP-PCA and BPVAM-PCA methods using different features on The University of Pavia dataset.

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Fig. 5

Predicted classes by BP-PCA and BPVAM-PCA methods using different features for Pavia University dataset. a) BP-PCA with 5 features. b) BPVAM-PCA with 5 features. c) BP-PCA with 10 features. d) BPVAM-PCA with 10 features. e) BP-PCA with 20 features. f) BPVAM-PCA with 20 features.

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When the performance of the two models are compared for both Indian Pines and Pavia University datasets, the best classification results are obtained by the proposed method. In case of the Indian Pines dataset, the feature size of 80 produced the best result, while for the University of Pavia dataset the best performance was obtained for BPVAM-PCA with 20 features. It can be concluded that selecting a few number of features may not be useful as most of the features that carry most significant information are lost. This lead to a suboptimal performance of model in understanding the true patterns of the data. It is worth noting that the dataset had some class imbalance issues, yet the BPVAM-PCA was able to overcome this issue and adapt to learn more about the input patterns with few samples. Generally, when models are trained with imbalance data, their performance may be severely degraded. However, the proposed model's performance remain intact even with imbalance data. This is a highly desirable feature as many multi-class classification problems may have class imbalance issues. Special techniques need to be implemented to deal with it. BPCAM-PCA was able to deal with class imbalance to some extend with ease.