Noncompact uniform universal approximation

The universal approximation theorem is generalised to uniform convergence on the (noncompact) input space $\mathbb R^n$. All continuous functions that vanish at infinity can be uniformly approximated by neural networks with one hidden layer, for all continuous activation functions $\varphi\neq0$ with asymptotically linear behaviour at $\pm\infty$. When $\varphi$ is moreover bounded, we exactly determine which functions can be uniformly approximated by neural networks, with the following unexpected results. Let $\overline{\mathcal{N}_\varphi^l(\mathbb R^n)}$ denote the vector space of functions that are uniformly approximable by neural networks with $l$ hidden layers and $n$ inputs. For all $n$ and all $l\geq2$, $\overline{\mathcal{N}_\varphi^l(\mathbb R^n)}$ turns out to be an algebra under the pointwise product. If the left limit of $\varphi$ differs from its right limit (for instance, when $\varphi$ is sigmoidal) the algebra $\overline{\mathcal{N}_\varphi^l(\mathbb R^n)}$ ($l\geq2$) is independent of $\varphi$ and $l$, and equals the closed span of products of sigmoids composed with one-dimensional projections. If the left limit of $\varphi$ equals its right limit, $\overline{\mathcal{N}_\varphi^l(\mathbb R^n)}$ ($l\geq1$) equals the (real part of the) commutative resolvent algebra, a C*-algebra which is used in mathematical approaches to quantum theory. In the latter case, the algebra is independent of $l\geq1$, whereas in the former case $\overline{\mathcal{N}_\varphi^2(\mathbb R^n)}$ is strictly bigger than $\overline{\mathcal{N}_\varphi^1(\mathbb R^n)}$.Comment: 9 pages, 2 figure

Combined forecast model involving wavelet-group methods of data handling for drought forecasting

Vigorous efforts to improve the effectiveness of drought forecasting models has yet to yield accurate result. The situation gives room on the use of robust forecasting methods that could effectively improve existing methods. The complex nature of time series data does not enable one single method that is suitable in all situations. Thus, a combined model that will provide a better result is then proposed. This study introduces a wavelet and group methods of data handling (GMDH) by integrating discrete wavelet transform (DWT) and GMDH with transfer functions such as sigmoid and radial basis function (RBF) to form three wavelet-GMDH models known as modified W-GMDH (MW-GMDH), sigmoid W-GMDH (SW-GMDH) and RBF W-GMDH. To assess the effectiveness of this approach, these models were applied to rainfall data at four study stations namely Arau and Kuala Krai in Malaysia as well as Badeggi and Duku-Lade in Nigeria. These data were transformed into four Standardized Precipitation Index (SPI) known as SPI3, SPI6, SPI9 and SPI12. The result shows that the integration of DWT improved the performance of the conventional GMDH model. The combination of these models further improved the performance of each model. The proposed model provides efficient, simple, and reliable accuracy when compared with other models. The incorporation of wavelet to the study results in improving performance for all four stations with the Combined W-GMDH (CW-GMDH) and Combined Regression W-GMDH (CRW-GMDH) models. The results show that Duku-Lade station produced the lowest value of 0.0239 and 0.0211 for RMSE and MAE and highest value of 0.9858 for R respectively. In addition, CRW-GMDH model produce the lowest value of 0.0168 and 0.0117, and the highest value of 0.9870 for RMSE MAE, and R respectively. On the percentage improvement, Duku-Lade station shows improvement over other models with the reductions in RMSE and MAE by 42.3% and 80.3% respectively. This indicates that the model is most suitable for the drought forecasting in this station. The results of the comparison among the four stations indicate that the CW-GMDH and CRW-GMDH models are more accurate and perform better than MW-GMDH, SW-GMDH and RBFW-GMDH models. However, the overall performance of the CRW-GMDH model outweigh that of the CW-GMDH model. In conclusion, CRW-GMDH model performs better than other models for drought forecasting and capable of providing a promising alternative to drought forecasting technique

CASM-AMFMNet: A Network based on Coordinate Attention Shuffle Mechanism and Asymmetric Multi-Scale Fusion Module for Classification of Grape Leaf Diseases

Grape disease is a significant contributory factor to the decline in grape yield, typically affecting the leaves first. Efficient identification of grape leaf diseases remains a critical unmet need. To mitigate background interference in grape leaf feature extraction and improve the ability to extract small disease spots, by combining the characteristic features of grape leaf diseases, we developed a novel method for disease recognition and classification in this study. First, Gaussian filters Sobel smooth de-noising Laplace operator (GSSL) was employed to reduce image noise and enhance the texture of grape leaves. A novel network designated coordinated attention shuffle mechanism-asymmetric multi-scale fusion module net (CASM-AMFMNet) was subsequently applied for grape leaf disease identification. CoAtNet was employed as the network backbone to improve model learning and generalization capabilities, which alleviated the problem of gradient explosion to a certain extent. The CASM-AMFMNet was further utilized to capture and target grape leaf disease areas, therefore reducing background interference. Finally, Asymmetric multi-scale fusion module (AMFM) was employed to extract multi-scale features from small disease spots on grape leaves for accurate identification of small target diseases. The experimental results based on our self-made grape leaf image dataset showed that, compared to existing methods, CASM-AMFMNet achieved an accuracy of 95.95%, F1 score of 95.78%, and mAP of 90.27%. Overall, the model and methods proposed in this report could successfully identify different diseases of grape leaves and provide a feasible scheme for deep learning to correctly recognize grape diseases during agricultural production that may be used as a reference for other crops diseases

CASM-AMFMNet: A Network based on Coordinate Attention Shuffle Mechanism and Asymmetric Multi-Scale Fusion Module for Classification of Grape Leaf Diseases

Grape disease is a significant contributory factor to the decline in grape yield, typically affecting the leaves first. Efficient identification of grape leaf diseases remains a critical unmet need. To mitigate background interference in grape leaf feature extraction and improve the ability to extract small disease spots, by combining the characteristic features of grape leaf diseases, we developed a novel method for disease recognition and classification in this study. First, Gaussian filters Sobel smooth de-noising Laplace operator (GSSL) was employed to reduce image noise and enhance the texture of grape leaves. A novel network designated coordinated attention shuffle mechanism-asymmetric multi-scale fusion module net (CASM-AMFMNet) was subsequently applied for grape leaf disease identification. CoAtNet was employed as the network backbone to improve model learning and generalization capabilities, which alleviated the problem of gradient explosion to a certain extent. The CASM-AMFMNet was further utilized to capture and target grape leaf disease areas, therefore reducing background interference. Finally, Asymmetric multi-scale fusion module (AMFM) was employed to extract multi-scale features from small disease spots on grape leaves for accurate identification of small target diseases. The experimental results based on our self-made grape leaf image dataset showed that, compared to existing methods, CASM-AMFMNet achieved an accuracy of 95.95%, F1 score of 95.78%, and mAP of 90.27%. Overall, the model and methods proposed in this report could successfully identify different diseases of grape leaves and provide a feasible scheme for deep learning to correctly recognize grape diseases during agricultural production that may be used as a reference for other crops diseases

Pole -mounted sonar vibration prediction using CMAC neural networks

The efficiency and accuracy of pole-mounted sonar systems are severely affected by pole vibration, Traditional signal processing techniques are not appropriate for the pole vibration problem due to the nonlinearity of the pole vibration and the lack of a priori knowledge about the statistics of the data to be processed. A novel approach of predicting the pole-mounted sonar vibration using CMAC neural networks is presented. The feasibility of this approach is studied in theory, evaluated by simulation and verified with a real-time laboratory prototype, Analytical bounds of the learning rate of a CMAC neural network are derived which guarantee convergence of the weight vector in the mean. Both simulation and experimental results indicate the CMAC neural network is an effective tool for this vibration prediction problem

模糊SOP神經網路之模式參考自適應控制系統設計及其應用研究

[[abstract]]In this study, we present a novel neural network called fuzzy sum-of- product neural network (FSOPNN). The architecture of FSOPNN modifies the conventional sum-of-product neural network (SOPNN) by means of fuzzy logic and cerebellar model articulation controller (CMAC) for improving the learning capability in the situation that requests the ability to model input/output differential characteristics of a plant. In order to show the applicability of FSOPNN, two FSOPNNs are utilized in a model reference adaptive control (MRAC) system, one as a neuroidentifier called FSPNI and the other as a neurocontroller called FSPNC. The FSPNI is used on-line to identify the input-output behavior of the controlled plant, as well as estimate the sensitivity information of the controlled plant. Using the resulting identification model, the parameters (i.e. the content of weights) of the controller FSPNC are adjusted by the output error and the plant sensitivity, such that the output of the controlled plant approaches the output of the reference model asymptotically. Finally one simulation for induction motor servo system using proposed controller has performed to demonstrate the feasibility and performance of the proposed controller.