Quadratic Networks Excel in Extracting Features Compared to Conventional Networks

Table of Links

Abstract and 1. Introduction

2. Preliminaries and 2.1. Blind deconvolution

2.2. Quadratic neural networks

3. Methodology

3.1. Time domain quadratic convolutional filter

3.2. Superiority of cyclic features extraction by QCNN

3.3. Frequency domain linear filter with envelope spectrum objective function

3.4. Integral optimization with uncertainty-aware weighing scheme

4. Computational experiments

4.1. Experimental configurations

4.2. Case study 1: PU dataset

4.3. Case study 2: JNU dataset

4.4. Case study 3: HIT dataset

5. Computational experiments

5.1. Comparison of BD methods

5.2. Classification results on various noise conditions

5.3. Employing ClassBD to deep learning classifiers

5.4. Employing ClassBD to machine learning classifiers

5.5. Feature extraction ability of quadratic and conventional networks

5.6. Comparison of ClassBD filters

6. Conclusions

Appendix and References

5.5. Feature extraction ability of quadratic and conventional networks

Previously, we have theoretically demonstrated that quadratic networks possess superior cyclostationary feature extraction ability to conventional networks. It is also necessary to validate the performance in practice. Therefore, we construct two time-domain filters using quadratic convolutional layers and conventional convolutional layers with an identical structure and then evaluate their feature-extraction performance on the JNU dataset subjected to -10 dB noise.

The signals are analyzed using the Fast-SC method [84]. The results, as depicted in Figure 8, clearly demonstrate that the quadratic network outperforms in terms of feature extraction capability. The bright lines in the spectral coherence, highlight the quadratic network can extract cyclic frequency across high and low frequency bands. Despite the severe attenuation of the signal amplitude due to the noise, the quadratic network effectively recovers the cyclic frequency of the signal. Remarkably, the amplitude of the initial few cyclic frequencies is even higher than that of the raw signal.