Fourier methods have a long and proven track record as an excellent tool in data processing. We propose to integrate Fourier methods into complex recurrent neural network architectures and show accuracy improvements on prediction tasks as well as computational load reductions. We predict synthetic data drawn from synthetic-equations as well as real world power load data.
In machine learning, Fourier analysis is mostly associated with signal-processing heavy domains such as speech recognition @cite_1 , medical imaging @cite_21 and audio-processing @cite_25 @cite_12 . Recently, a comparison @cite_11 of the time versus frequency domain for audio event recognition with neural networks showed the discriminative gains of processing sound in the frequency domain.
@cite_21 @cite_1 @cite_25 @cite_12 @cite_11
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The Fourier domain is used in computer vision and machine learning as image analysis tasks in the Fourier domain are analogous to spatial domain methods but are achieved using different operations. Convolutional Neural Networks (CNNs) use machine learning to achieve state-of-the-art results with respect to many computer vision tasks. One of the main limiting aspects of CNNs is the computational cost of updating a large number of convolution parameters. Further, in the spatial domain, larger images take exponentially longer than smaller image to train on CNNs due to the operations involved in convolution methods. Consequently, CNNs are often not a viable solution for large image computer vision tasks. In this paper a Fourier Convolution Neural Network (FCNN) is proposed whereby training is conducted entirely within the Fourier domain. The advantage offered is that there is a significant speed up in training time without loss of effectiveness. Using the proposed approach larger images can therefore be processed within viable computation time. The FCNN is fully described and evaluated. The evaluation was conducted using the benchmark Cifar10 and MNIST datasets, and a bespoke fundus retina image dataset. The results demonstrate that convolution in the Fourier domain gives a significant speed up without adversely affecting accuracy. For simplicity the proposed FCNN concept is presented in the context of a basic CNN architecture, however, the FCNN concept has the potential to improve the speed of any neural network system involving convolution. Recognizing acoustic events is an intricate problem for a machine and an emerging field of research. Deep neural networks achieve convincing results and are currently the state-of-the-art approach for many tasks. One advantage is their implicit feature learning, opposite to an explicit feature extraction of the input signal. In this work, we analyzed whether more discriminative features can be learned from either the time-domain or the frequency-domain representation of the audio signal. For this purpose, we trained multiple deep networks with different architectures on the Freiburg-106 and ESC-10 datasets. Our results show that feature learning from the frequency domain is superior to the time domain. Moreover, additionally using convolution and pooling layers, to explore local structures of the audio signal, significantly improves the recognition performance and achieves state-of-the-art results. Deep learning has dramatically improved the performance of speech recognition systems through learning hierarchies of features optimized for the task at hand. However, true end-to-end learning, where features are learned directly from waveforms, has only recently reached the performance of hand-tailored representations based on the Fourier transform. In this paper, we detail an approach to use convolutional filters to push past the inherent tradeoff of temporal and frequency resolution that exists for spectral representations. At increased computational cost, we show that increasing temporal resolution via reduced stride and increasing frequency resolution via additional filters delivers significant performance improvements. Further, we find more efficient representations by simultaneously learning at multiple scales, leading to an overall decrease in word error rate on a difficult internal speech test set by 20.7 relative to networks with the same number of parameters trained on spectrograms. In recent years, deep learning has not only permeated the computer vision and speech recognition research fields but also fields such as acoustic event detection (AED). One of the aims of AED is to detect and classify non-speech acoustic events occurring in conversation scenes including those produced by both humans and the objects that surround us. In AED, deep learning has enabled modeling of detail-rich features, and among these, high resolution spectrograms have shown a significant advantage over existing predefined features (e.g., Mel-filter bank) that compress and reduce detail. In this paper, we further asses the importance of feature extraction for deep learning-based acoustic event detection. AED, based on spectrogram-input deep neural networks, exploits the fact that sounds have “global” spectral patterns, but sounds also have “local” properties such as being more transient or smoother in the time-frequency domain. These can be exposed by adjusting the time-frequency resolution used to compute the spectrogram, or by using a model that exploits locality leading us to explore two different feature extraction strategies in the context of deep learning: (1) using multiple resolution spectrograms simultaneously and analyzing the overall and event-wise influence to combine the results, and (2) introducing the use of convolutional neural networks (CNN), a state of the art 2D feature extraction model that exploits local structures, with log power spectrogram input for AED. An experimental evaluation shows that the approaches we describe outperform our state-of-the-art deep learning baseline with a noticeable gain in the CNN case and provides insights regarding CNN-based spectrogram characterization for AED.