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In many pattern recognition problems, it is desirable to reduce the number of input features by extracting important features related to the problems. By focusing on only the problem-relevant features, the dimension of features can be greatly reduced and thereby can result in a better generalization performance with less computational complexity. In this paper, we propose a feature extraction method for handling classification problems. The proposed algorithm is used to search for a set of linear combinations of the original features, whose mutual information with the output class can be maximized. The mutual information between the extracted features and the output class is calculated by using the probability density estimation based on the Parzen window method. A greedy algorithm using the gradient descent method is used to determine the new features. The computational load is proportional to the square of the number of samples. The proposed method was applied to several classification problems, which showed better or comparable performances than the conventional feature extraction methods.

To solve the problem of low accuracy in the traditional FunkSVD recommendation algorithm, an improved FunkSVD algorithm (RM-FS) is proposed. RM-FS is an improvement of the traditional FunkSVD algorithm, using RMSProp, a deep learning optimization algorithm. The RM-FS algorithm can not only solve the problem of reduced accuracy of the traditional FunkSVD algorithm because of iterative oscillations but also alleviate the impact of data sparseness on the accuracy of the algorithm, achieving the effect of improving the accuracy of the traditional algorithm. The experimental results show that the RM-FS algorithm proposed in this paper effectively improves the accuracy of the recommendation algorithm, which is better than the traditional FunkSVD recommendation algorithm and other improved FunkSVD algorithms.

In this paper we consider the problem of estimating the parameters of a nonlinear dynamical system given a finite time series of observations that are contaminated by observational noise. The least squares method is a standard method for parameter estimation, but for nonlinear dynamical systems it is well known that the least squares method can result in biased estimates, especially when the noise is significant relative to the nonlinearity. In this paper, it is demonstrated that by combining nonlinear noise reduction and least squares parameter fitting it is possible to obtain more accurate parameter estimates.

In this paper, we present the application of the gradient descent of indeterminism (GDI) shadowing filter to a chaotic system, that is the ski-slope model. The paper focuses on the quality of the estimated states and their usability for forecasting. One main problem is that the existing GDI shadowing filter fails to provide stability to the convergence of the root mean square error and the last point error of the ski-slope model. Furthermore, there are unexpected cases in which the better state estimates give worse forecasts than the worse state estimates. We investigate these unexpected cases in particular and show how the presence of the humps contributes to them. However, the results show that the GDI shadowing filter can successfully be applied to the ski-slope model with only slight modification, that is, by introducing the adaptive step-size to ensure the convergence of indeterminism. We investigate its advantages over fixed step-size and how it can improve the performance of our shadowing filter.

Cross-project defect prediction (CPDP) has recently become very popular in the field of software defect prediction. It was generally treated as a binary classification problem or a regression problem in most of previous studies. However, these existing CPDP methods may be not suitable for those software projects that have limited manpower and budget. To address the issue of priority estimation for buggy software entities, in this paper CPDP is formulated as a ranking problem. Inspired by the idea of the pointwise approach to learning to rank, we propose a ranking-oriented CPDP approach called ROCPDP. A case study conducted on the datasets collected from AEEEM and PROMISE shows that ROCPDP outperforms the eight baseline methods in two CPDP scenarios, namely one-to-one and many-to-one. Besides, in the many-to-one scenario ROCPDP is, by and large, comparable to the best baseline method performed in a specific within-project defect prediction scenario.

A general technique for representing quasi-periodic oscillations, typical of biomedical signals, is described. Using energy thresholding and Gaussian kernels, in conjunction with a nonlinear gradient descent optimization, it is shown that significant noise reduction, compression and turning point location is possible. As such, the signal representation model can be considered a form of correlated source separation. Applications to filtering, modelling and robust ECG QT-analysis are described.

Given a fuzzy logic system, how can we determine the membership functions that will result in the best performance? If we constrain the membership functions to a certain shape (e.g., triangles or trapezoids) then each membership function can be parameterized by a small number of variables and the membership optimization problem can be reduced to a parameter optimization problem. This is the approach that is typically taken, but it results in membership functions that are not (in general) sum normal. That is, the resulting membership function values do not add up to one at each point in the domain. This optimization approach is modified in this paper so that the resulting membership functions are sum normal. Sum normality is desirable not only for its intuitive appeal but also for computational reasons in the real time implementation of fuzzy logic systems. The sum normal constraint is applied in this paper to both gradient descent optimization and Kalman filter optimization of fuzzy membership functions. The methods are illustrated on a fuzzy automotive cruise controller.

There are well established methods for fuzzy clustering especially for the cases where the feature values are numerical of ratio or interval scale. Not so well established are methods to be applied when the feature values are ordinal or nominal. In that case there is no one best method it seems. This paper discusses a method where unknown numeric variables are assigned to the ordinal values. Part of minimizing an objective function for the clustering is to find numeric values for these variables. Thus real numbers of interval scale and even ratio scale for that matter are assigned to the original ordinal values. The method uses the same objective function as used in fuzzy c-means clustering but both the membership function and the ordinal to real mapping are determined by gradient descent. Since the ordinal to real mapping is not known it cannot be verified for its legitimacy. However the ordinal to real mapping that is found is best in terms of the clustering produced. Simulations show the method to be quite effective.

In the complex and changeable macro-economy, the sustainable development of enterprises is closely related to their ability to resist risks. To analyze the influencing factors of listed enterprises’ anti risk ability, this study constructs an indicator system of influencing variables through principal component analysis. The financial risk early warning method based on improved RBF neural network is constructed. Afterwards, the relevance of the indicator system was confirmed by the Kaiser-Meyer–Olkin (KMO) test. And in simulation experiments, it compared the classification performance of the BP neural network and the improved RBF model combined with the clustering algorithm. In the training dataset, the classification accuracy of the BP neural network was 79.6% while that of the improved RBF model was as high as 93.6%. In the 30 test datasets, the BP neural network appeared to have seven false positives. In the 30 test datasets, the BP neural network produced seven false judgments, while the proposed method only had three judgment errors. Several experiments showed that the BGD-RBF financial risk early warning model effectively maintained a high performance in the classification accuracy of enterprise financial status. It is more reliable than the traditional BP neural network method.

In this paper, a Wavelet Neuro-Fuzzy model has been proposed. The proposed work caters an application of wavelet network used in fuzzy systems for forecasting of dynamic systems. A wavelet network approximates the consequent part of each fuzzy rule. The wavelet network is a feed-forward neural network with one hidden layer that uses a combination of Wavelet and Sigmoid Activation Function. A hybrid learning method composed of genetic algorithm and gradient descent is proposed to tune the learning parameters of the proposed Wavelet Neuro-Fuzzy model. Further, an analysis regarding the convergence and stability of gradient descent learning is presented for the proposed Wavelet Neuro-Fuzzy model. To evaluate the effectiveness of proposed model and learning strategy, three different classes of benchmark problems have been considered.

In linear regression, outliers have a serious effect on the estimation of regression model parameters and the prediction of final results, so outlier detection is one of the key steps in data analysis. In this paper, we use a mean shift model and then we apply the penalty function to penalize the mean shift parameters, which is conducive to get a sparse parameter vector. We choose Sorted L1 regularization (SLOPE), which provides a convex loss function, and shows good statistical properties in parameter selection. We apply an iterative process which using gradient descent method and parameter selection at each step. Our algorithm has higher computational efficiency since the calculation of inverse matrix is avoided. Finally, we use Cross-Validation rules (CV) and Bayesian Information Criterion (BIC) criteria to fine tune the parameters, which helps our program identify outliers and obtain more robust regression coefficients. Compared with other methods, the experimental results show that our program has a fantastic performance in all aspects of outlier detection.

This paper addresses the issue of obtaining the optimal rotation to match two functions on the sphere by minimizing the squared error norm and the Kullback–Leibler information criteria. In addition, the accuracy in terms of the band-limited approximations in both cases are also discussed. Algorithms for fast and accurate rotational matching play a significant role in many fields ranging from computational biology to spacecraft attitude estimation. In electron microscopy, peaks in the so-called "rotation function" determine correlations in orientation between density maps of macromolecular structures when the correspondence between the coordinates of the structures is not known. In X-ray crystallography, the rotational matching of Patterson functions in Fourier space is an important step in the determination of protein structures. In spacecraft attitude estimation, a star tracker compares observed patterns of stars with rotated versions of a template that is stored in its memory. Many algorithms for computing and sampling the rotation function have been proposed over the years. These methods usually expand the rotation function in a bandlimited Fourier series on the rotation group. In some contexts the highest peak of this function is interpreted as the optimal rotation of one structure into the other, and in other contexts multiple peaks describe symmetries in the functions being compared. Prior works on rotational matching seek to maximize the correlation between two functions on the sphere. We also consider the use of the Kullback–Leibler information criteria. A gradient descent algorithm is proposed for obtaining the optimal rotation, and a measure is defined to compare the convergence of this procedure applied to the maximal correlation and Kullback–Leibler information criteria.

Despite being widely used in the practical problems around the world, Gradient Descent Back-propagation algorithm comes with problems like slow convergence and convergence to local minima. Previous researchers have suggested certain modifications to improve the convergence in gradient Descent Back-propagation algorithm such as careful selection of input weights and biases, learning rate, momentum, network topology, activation function and value for 'gain' in the activation function. This research proposed an algorithm for improving the working performance of back-propagation algorithm which is 'Gradient Descent with Adaptive Momentum (GDAM)' by keeping the gain value fixed during all network trials. The performance of GDAM is compared with 'Gradient Descent with fixed Momentum (GDM)' and 'Gradient Descent Method with Adaptive Gain (GDM-AG)'. The learning rate is fixed to 0.4 and maximum epochs are set to 3000 while sigmoid activation function is used for the experimentation. The results show that GDAM is a better approach than previous methods with an accuracy ratio of 1.0 for classification problems like Wine Quality, Mushroom and Thyroid disease.

Yaw control is significant to the attitude control of small unmanned helicopters (SUHs). Since the existing robust control method cannot be applied to the SUH with unknown dynamics and disturbances, this paper proposes an improved active disturbance rejection control (IADRC) to solve the problem. The IADRC obtains the optimal solution of the actuator gain ($b_0$) by gradient descent. Besides, this paper summarizes some experiences during the tuning process of ADRC, which significantly reduces the difficulty of designing ADRC. Finally, the experimental results show that the proposed method is better than the traditional PID in robust and tracking control performance.