An integrated chaotic time series prediction model based on efficient extreme learning machine and differential evolution

The paper aims to develop an effective method to identify, detect and classify power quality disturbances using the efficient Extreme learning machine (ELM). It's important to evaluate the learning time while designing any kind of computational algorithms, which used for classification. ELM comprises of a single hidden layer Feed Forward Neural Network (SFNN) with better generalization ability and extreme fast learning. The efficient Fast S-transform(FST) is imposed to extract discriminating features of different power quality disturbances wave form and that correspondence feature will be given as input of the ELM classifier and further proceed for classification. By this process performance of FST based ELM classifier is compared with the ST based ELM classifier with distinctive features of different PQ disturbances. FST signal analysis is done by using different classifier and corresponding result is found out. Ten varieties of PQ disturbances have been chosen for the proposed classification task. The proposed FST based ELM classification is feasible and promising for a real time application as evidenced from our results.

Extreme learning machine (ELM) was extended from the generalized single hidden layer feedforward networks where the input weights of the hidden layer nodes can be assigned randomly. It has been widely used for its much faster learning speed and less manual works. Considering the field of multi-label text classification, in this paper, we propose an ELM based algorithm combined with \(L_{21}\)-norm minimization of the output weights matrix called \(L_{21}\)-norm Minimization ELM, which not only fully inherits the merits of ELM but also facilitates group sparsity and reduces complexity of the learning model. Extensive experiments on several benchmark data sets show a more desirable performance compared with other common multi-label classification algorithms.

Manifold learning in local tangent space via extreme learning machine

Radar Emitter Identification (REI) has been a long-standing topic in military and civil fields. In this paper, we present a novel REI based on the local binary pattern (LBP) feature extracted from bispectrum of radar signal and the extreme learning machine (LBP+ELM). Comparing with conventional radar features, the high-order spectral analysis method is robust and effective in handling the issues of increasing electromagnetism signal density and system complexity in recent REI. But the bispectrum of radar signals suffers from high feature dimensionality. To address this issue, we extract the local binary pattern based on the bispectrum image. Then, the efficient extreme learning machine (ELM) is applied for classifier training. Experiments on six most frequent radar signals recognition are carried out in this paper for performance validation. Comparisons with the original bispectrum based REI are provided to show the superiority of our proposed algorithm.

Long-term prediction of chaotic time series is very difficult, for the chaos restricts predictability. In this paper a new method is studied to model and predict chaotic time series based on minimax probability machine regression (MPMR). Since the positive global Lyapunov exponents lead the errors to increase exponentially in modelling the chaotic time series, a weighted term is introduced to compensate a cost function. Using mean square error (MSE) and absolute error (AE) as a criterion, simulation results show that the proposed method is more effective and accurate for multistep prediction. It can identify the system characteristics quite well and provide a new way to make long-term predictions of the chaotic time series.

Since real-world data sets usually contain large instances, it is meaningful to develop efficient and effective multiple instance learning (MIL) algorithm. As a learning paradigm, MIL is different from traditional supervised learning that handles the classification of bags comprising unlabeled instances. In this paper, a novel efficient method based on extreme learning machine (ELM) is proposed to address MIL problem. First, the most qualified instance is selected in each bag through a single hidden layer feedforward network (SLFN) whose input and output weights are both initialed randomly, and the single selected instance is used to represent every bag. Second, the modified ELM model is trained by using the selected instances to update the output weights. Experiments on several benchmark data sets and multiple instance regression data sets show that the ELM-MIL achieves good performance; moreover, it runs several times or even hundreds of times faster than other similar MIL algorithms.

In this work, we address some issues in the classification of varying length patterns of speech represented as sets of continuous-valued feature vectors using kernel methods. Kernels designed for varying length patterns are called as dynamic kernels. We propose two dynamic kernels namely segment-level pyramid match kernel (SLPMK) and segment-level probabilistic sequence kernel (SLPSK) for classification of long duration speech, represented as varying length sets of feature vectors using extreme learning machine (ELM). SLPMK and SLPSK are designed by partitioning the speech signal into increasingly finer segments and matching the corresponding segments. SLPSK is built upon a set of Gaussian basis functions, where half of the basis functions contain class-specific information while the other half implicates the common characteristics of all the speech utterances of all classes. The computational complexity of SVM training algorithms is usually intensive, which is at least quadratic with respect to the number of training examples. It is difficult to deal with the immense amount of data using traditional SVMs. For reducing the training time of classifier we propose to use a simple algorithm namely ELM. ELM refers to a wider type of generalized single hidden layer feedforward networks (SLFNs) whose hidden layer need not be tuned. In our work, we proposed to explore kernel based ELM to exploit dynamic kernels. We study the performance of the ELM-based classifiers using the proposed SLPSK and SLPMK for speech emotion recognition and speaker identification tasks and compare with other kernels for varying length patterns. Experimental studies showed that proposed ELM-based approach offer a 10–12% of relative improvement over baseline approach, and a 3–9% relative improvement over ELMs/SVMs using other state-of-the-art dynamic kernels.

With multiple antennas’ transmission, multiple-input multiple-output (MIMO) technique is able to utilize the space diversity to obtain high spectrum efficiency. In this study, we propose a single hidden layer feedforward network trained with extreme learning machine (ELM) to estimate channel performances in MIMO system. Bit error rate (BER) and signal-to-noise ratio (SNR) performance of back-propagation (BP) algorithm are also compared with our proposed neural network. The simulation results show that ELM has got much better time efficiency than BP in MIMO modeling. Furthermore, MIMO modeling based on ELM doesn’t need to send pilot, which reduce the waste of spectrum resources.

Recently, there has been an ever-increasing interest in the study of data-driven analytics to predict hidden dangers in the cloud service-based coal mine production, with the purpose of the prevention of possible accidents. In this paper, to achieve the above prediction, a machine learning algorithm based on the single-hidden layer feed forward network (SLFN) using timeliness managing extreme learning machine (TMELM) is utilized. Compared with those traditional learning algorithms, extreme learning machine (ELM) has its unique feature of a higher generalization capability at a much faster learning speed. In addition, the timeliness managing ELM has been proposed by incorporating timeliness management scheme into ELM approach. Under the timeliness managing ELM scheme used to predict the hidden dangers, the newly incremental data could be prior to the historical data while maximizing the contribution of the newly increasing training data, since it may be more feasible that the incremental data can contribute reasonable weights to represent the current production situation in accordance with the practical analysis for accidents in coal mine production. The experimental results on the coal mines of Beijing show that by using timeliness managing ELM, the prediction accuracy of hidden danger can be improved with better stability compared with other similar machine learning methods.

Extreme Learning Machine (ELM) is a learning algorithm proposed recently to train single hidden layer feed forward networks (SLFN). It has many attractive properties that include better generalization performance and very fast learning. ELM starts by assigning random values to the input weights and hidden biases and then in one step it determines the output weights using Moore-Penrose generalized inverse. Despite the aforementioned advantages, ELM performance might be affected by the random initialization of weights and biases or by the large generated network which might contain unnecessary number of neurons. In order to increase the generalization performance and to produce more compact networks, a hybrid model that combines ELM with competitive swarm optimizer (CSO) is proposed in this paper. The proposed model (CSONN-ELM) optimizes the weights and biases and dynamically determines the most appropriate number of neurons. To evaluate the effectiveness of the CSONN-ELM, it is experimented using 23 benchmark datasets, and compared to a set of static rules extracted from literature that are used to determine the number of neurons of SLFN. Moreover, it is compared to two dynamic methods that are used to enhance the performance of ELM, that are Optimally pruned ELM (OP-ELM) and metaheuristic based ELMs (Particle Swarm Optimization-ELM and Differential Evolution-ELM). The obtained results show that the proposed method enhances the generalization performance of ELM and overcomes the static and dynamic methods.

We attempt to quantify the significance of increasing the number of neurons in the hidden layer of a feedforward neural network architecture using the singular value decomposition (SVD). Through this, we extend some well-known properties of the SVD in evaluating the generalizability of single hidden layer feedforward networks (SLFNs) with respect to the number of hidden neurons. The generalization capability of the SLFN is measured by the degree of linear independency of the patterns in hidden layer space, which can be indirectly quantified from the singular values obtained from the SVD, in a post-learning step.

The prediction accuracy and generalization ability of neural/neurofuzzy models for chaotic time series prediction highly depends on employed network model as well as learning algorithm. In this study, several neural and neurofuzzy models with different learning algorithms are examined for prediction of several benchmark chaotic systems and time series. The prediction performance of locally linear neurofuzzy models with recently developed Locally Linear Model Tree (LoLiMoT) learning algorithm is compared with that of Radial Basis Function (RBF) neural network with Orthogonal Least Squares (OLS) learning algorithm, MultiLayer Perceptron neural network with error back-propagation learning algorithm, and Adaptive Network based Fuzzy Inference System. Particularly, cross validation techniques based on the evaluation of error indices on multiple validation sets is utilized to optimize the number of neurons and to prevent over fitting in the incremental learning algorithms. To make a fair comparison between neural and neurofuzzy models, they are compared at their best structure based on their prediction accuracy, generalization, and computational complexity. The experiments are basically designed to analyze the generalization capability and accuracy of the learning techniques when dealing with limited number of training samples from deterministic chaotic time series, but the effect of noise on the performance of the techniques is also considered. Various chaotic systems and time series including Lorenz system, Mackey-Glass chaotic equation, Henon map, AE geomagnetic activity index, and sunspot numbers are examined as case studies. The obtained results indicate the superior performance of incremental learning algorithms and their respective networks, such as, OLS for RBF network and LoLiMoT for locally linear neurofuzzy model.

The theory and implementation of an extreme learning machine (ELM) have proved that it is a simple, efficient, and accurate machine learning methodology. In an ELM, the hidden nodes are randomly initiated and fixed without iterative tuning. However, the optimal hidden layer neuron number ($L_{opt})$ is the key to ELM generalization performance where initializing this number by trial and error is not reasonably satisfied. Optimizing the hidden layer size using the leave-one-out cross validation method is a costly approach. In this paper, a fast and reliable statistical approach called optimum ELM (OELM) was developed to determine the minimum hidden layer size that yields an optimum performance. Another improvement that exploits the advantages of orthogonal projections with singular value decomposition was proposed in order to tackle the problem of randomness and correlated features in the input data. This approach, named projected ELM (PELM), achieves more than 2{\%} advance in average accuracy. The final contribution of this paper was implementing Tikhonov regularization in the form of the L$_{2}$-penalty with ELM (TRELM), which regularizes and improves the matrix computations utilizing the L-curve criterion and SVD. The L-curve, unlike iterative methods, can estimate the optimum regularization parameter by illustrating a curve with few points that represents the tradeoff between minimizing the training error and the residual of output weight. The proposed TRELM was tested in 3 different scenarios of data sizes: small, moderate, and big datasets. Due to the simplicity, robustness, and less time consumption of OELM and PELM, it is recommended to use them with small and even moderate amounts of data. TRELM demonstrated that when enhancing the ELM performance it is necessary to enlarge the size of hidden nodes $(L)$. As a result, in big data, increasing $L$ in TRELM is necessary, which concurrently leads to a better accuracy. Various well-known datasets and state-of-the-art learning approaches were compared with the proposed approaches.

Two-stage extreme learning machine for regression

Image receptive fields for artificial neural networks