A new classifier based on information theoretic learning with unlabeled data.

Supervised learning is conventionally performed with pairwise input-output labeled data. After the training procedure, the adaptive system's weights are fixed while the testing procedure with unlabeled data is performed. Recently, in an attempt to improve classification performance unlabeled data has been exploited in the machine learning community. In this paper, we present an information theoretic learning (ITL) approach based on density divergence minimization to obtain an extended training algorithm using unlabeled data during the testing. The method uses a boosting-like algorithm with an ITL based cost function. Preliminary simulations suggest that the method has the potential to improve the performance of classifiers in the application phase.     

Dolphin Swarm Extreme Learning Machine

As a novel learning algorithm for a single hidden-layer feedforward neural network, the extreme learning machine has attracted much research attention for its fast training speed and good generalization performances. Instead of iteratively tuning the parameters, the extreme machine can be seen as a linear optimization problem by randomly generating the input weights and hidden biases. However, the random determination of the input weights and hidden biases may bring non-optimal parameters, which have a negative impact on the final results or need more hidden nodes for the neural network. To overcome the above drawbacks caused by the non-optimal input weights and hidden biases, we propose a new hybrid learning algorithm named dolphin swarm algorithm extreme learning machine adopting the dolphin swarm algorithm to optimize the input weights and hidden biases efficiently. Each set of input weights and hidden biases is encoded into one vector, namely the dolphin. The dolphins are evaluated by root mean squared error and updated by the four pivotal phases of the dolphin swarm algorithm. Eventually, we will obtain an optimal set of input weights and hidden biases. To evaluate the effectiveness of our method, we compare the proposed algorithm with the standard extreme learning machine and three state-of-the-art methods, which are the particle swarm optimization extreme learning machine, evolutionary extreme learning machine, and self-adaptive evolutionary extreme learning machine, under 13 benchmark datasets obtained from the University of California Irvine Machine Learning Repository. The experimental results demonstrate that the proposed method can achieve superior generalization performances than all the compared algorithms.     

Epileptic EEG classification based on extreme learning machine and nonlinear features

The automatic detection and classification of epileptic EEG are significant in the evaluation of patients with epilepsy. This paper presents a new EEG classification approach based on the extreme learning machine (ELM) and nonlinear dynamical features. The theory of nonlinear dynamics has been a powerful tool for understanding brain electrical activities. Nonlinear features extracted from EEG signals such as approximate entropy (ApEn), Hurst exponent and scaling exponent obtained with detrended fluctuation analysis (DFA) are employed to characterize interictal and ictal EEGs. The statistics indicate that the differences of those nonlinear features between interictal and ictal EEGs are statistically significant. The ELM algorithm is employed to train a single hidden layer feedforward neural network (SLFN) with EEG nonlinear features. The experiments demonstrate that compared with the backpropagation (BP) algorithm and support vector machine (SVM), the performance of the ELM is better in terms of training time and classification accuracy which achieves a satisfying recognition accuracy of 96.5% for interictal and ictal EEG signals.     

Self-adaptive Extreme Learning Machine Optimized by Rough Set Theory and Affinity Propagation Clustering

Recently, a simple and efficient learning algorithm for single hidden layer feedforward networks (SLFNs) called extreme learning machine (ELM) has been developed by G.-B. Huang et al. One key strength of ELM algorithm is that there is only one parameter, the number of hidden nodes, to be determined while it has the significantly low computational time required for training new classifiers and good generalization performance. However, there is no effective method for finding the proper and universal number of hidden nodes. In order to address this problem, we propose a self-adaptive extreme learning machine (SELM) algorithm. SELM algorithm determines self-adaptively the number of hidden nodes and constructs Gaussian function as activation functions of hidden nodes. And in this algorithm, rough set theory acts as the pre-treatment cell to eliminate the redundant attributes of data sets. Then, affinity propagation clustering (AP Clustering) is used to self-adaptively determine the number of hidden nodes, while the centers and widths of AP clustering are utilized to construct a Gaussian function in the hidden layer of SLFNs. Empirical study of SELM algorithm on several commonly used classification benchmark problems shows that the proposed algorithm can find the proper number of hidden nodes and construct compact network classifiers, comparing with traditional ELM algorithm.     

Dynamic evolving spiking neural networks for on-line spatio- and spectro-temporal pattern recognition

On-line learning and recognition of spatio- and spectro-temporal data (SSTD) is a very challenging task and an important one for the future development of autonomous machine learning systems with broad applications. Models based on spiking neural networks (SNN) have already proved their potential in capturing spatial and temporal data. One class of them, the evolving SNN (eSNN), uses a one-pass rank-order learning mechanism and a strategy to evolve a new spiking neuron and new connections to learn new patterns from incoming data. So far these networks have been mainly used for fast image and speech frame-based recognition. Alternative spike-time learning methods, such as Spike-Timing Dependent Plasticity (STDP) and its variant Spike Driven Synaptic Plasticity (SDSP), can also be used to learn spatio-temporal representations, but they usually require many iterations in an unsupervised or semi-supervised mode of learning. This paper introduces a new class of eSNN, dynamic eSNN, that utilise both rank-order learning and dynamic synapses to learn SSTD in a fast, on-line mode. The paper also introduces a new model called deSNN, that utilises rank-order learning and SDSP spike-time learning in unsupervised, supervised, or semi-supervised modes. The SDSP learning is used to evolve dynamically the network changing connection weights that capture spatio-temporal spike data clusters both during training and during recall. The new deSNN model is first illustrated on simple examples and then applied on two case study applications: (1) moving object recognition using address-event representation (AER) with data collected using a silicon retina device; (2) EEG SSTD recognition for brain–computer interfaces. The deSNN models resulted in a superior performance in terms of accuracy and speed when compared with other SNN models that use either rank-order or STDP learning. The reason is that the deSNN makes use of both the information contained in the order of the first input spikes (which information is explicitly present in input data streams and would be crucial to consider in some tasks) and of the information contained in the timing of the following spikes that is learned by the dynamic synapses as a whole spatio-temporal pattern.     

Common Subspace Learning via Cross-Domain Extreme Learning Machine

Extreme learning machine (ELM) is proposed for solving a single-layer feed-forward network (SLFN) with fast learning speed and has been confirmed to be effective and efficient for pattern classification and regression in different fields. ELM originally focuses on the supervised, semi-supervised, and unsupervised learning problems, but just in the single domain. To our best knowledge, ELM with cross-domain learning capability in subspace learning has not been exploited very well. Inspired by a cognitive-based extreme learning machine technique (Cognit Comput. 6:376–390, 1; Cognit Comput. 7:263–278, 2.), this paper proposes a unified subspace transfer framework called cross-domain extreme learning machine (CdELM), which aims at learning a common (shared) subspace across domains. Three merits of the proposed CdELM are included: (1) A cross-domain subspace shared by source and target domains is achieved based on domain adaptation; (2) ELM is well exploited in the cross-domain shared subspace learning framework, and a new perspective is brought for ELM theory in heterogeneous data analysis; (3) the proposed method is a subspace learning framework and can be combined with different classifiers in recognition phase, such as ELM, SVM, nearest neighbor, etc. Experiments on our electronic nose olfaction datasets demonstrate that the proposed CdELM method significantly outperforms other compared methods.     

Detecting and preventing error propagation via competitive learning

Semisupervised learning is a machine learning approach which is able to employ both labeled and unlabeled samples in the training process. It is an important mechanism for autonomous systems due to the ability of exploiting the already acquired information and for exploring the new knowledge in the learning space at the same time. In these cases, the reliability of the labels is a crucial factor, because mislabeled samples may propagate wrong labels to a portion of or even the entire data set. This paper has the objective of addressing the error propagation problem originated by these mislabeled samples by presenting a mechanism embedded in a network-based (graph-based) semisupervised learning method. Such a procedure is based on a combined random-preferential walk of particles in a network constructed from the input data set. The particles of the same class cooperate among them, while the particles of different classes compete with each other to propagate class labels to the whole network. Computer simulations conducted on synthetic and real-world data sets reveal the effectiveness of the model.     

A general soft label based Linear Discriminant Analysis for semi-supervised dimensionality reduction

Dealing with high-dimensional data has always been a major problem in research of pattern recognition and machine learning, and Linear Discriminant Analysis (LDA) is one of the most popular methods for dimension reduction. However, it only uses labeled samples while neglecting unlabeled samples, which are abundant and can be easily obtained in the real world. In this paper, we propose a new dimension reduction method, called “SL-LDA”, by using unlabeled samples to enhance the performance of LDA. The new method first propagates label information from the labeled set to the unlabeled set via a label propagation process, where the predicted labels of unlabeled samples, called “soft labels”, can be obtained. It then incorporates the soft labels into the construction of scatter matrixes to find a transformed matrix for dimension reduction. In this way, the proposed method can preserve more discriminative information, which is preferable when solving the classification problem. We further propose an efficient approach for solving SL-LDA under a least squares framework, and a flexible method of SL-LDA (FSL-LDA) to better cope with datasets sampled from a nonlinear manifold. Extensive simulations are carried out on several datasets, and the results show the effectiveness of the proposed method.     

Incremental multi-class semi-supervised clustering regularized by Kalman filtering

This paper introduces an on-line semi-supervised learning algorithm formulated as a regularized kernel spectral clustering (KSC) approach. We consider the case where new data arrive sequentially but only a small fraction of it is labeled. The available labeled data act as prototypes and help to improve the performance of the algorithm to estimate the labels of the unlabeled data points. We adopt a recently proposed multi-class semi-supervised KSC based algorithm (MSS-KSC) and make it applicable for on-line data clustering. Given a few user-labeled data points the initial model is learned and then the class membership of the remaining data points in the current and subsequent time instants are estimated and propagated in an on-line fashion. The update of the memberships is carried out mainly using the out-of-sample extension property of the model. Initially the algorithm is tested on computer-generated data sets, then we show that video segmentation can be cast as a semi-supervised learning problem. Furthermore we show how the tracking capabilities of the Kalman filter can be used to provide the labels of objects in motion and thus regularizing the solution obtained by the MSS-KSC algorithm. In the experiments, we demonstrate the performance of the proposed method on synthetic data sets and real-life videos where the clusters evolve in a smooth fashion over time.     

The constraint based decomposition (CBD) training architecture.

The Constraint Based Decomposition (CBD) is a constructive neural network technique that builds a three or four layer network, has guaranteed convergence and can deal with binary, n-ary, class labeled and real-value problems. CBD is shown to be able to solve complicated problems in a simple, fast and reliable manner. The technique is further enhanced by two modifications (locking detection and redundancy elimination) which address the training speed and the efficiency of the internal representation built by the network. The redundancy elimination aims at building more compact architectures while the locking detection aims at improving the training speed. The computational cost of the redundancy elimination is negligible and this enhancement can be used for any problem. However, the computational cost of the locking detection is exponential in the number of dimensions and should only be used in low dimensional spaces. The experimental results show the performance of the algorithm presented in a series of classical benchmark problems including the 2-spiral problem and the Iris, Wine, Glass, Lenses, Ionosphere, Lung cancer, Pima Indians, Bupa, TicTacToe, Balance and Zoo data sets from the UCI machine learning repository. CBD's generalization accuracy is compared with that of C4.5, C4.5 with rules, incremental decision trees, oblique classifiers, linear machine decision trees, CN2, learning vector quantization (LVQ), backpropagation, nearest neighbor, Q* and radial basis functions (RBFs). CBD provides the second best average accuracy on the problems tested as well as the best reliability (the lowest standard deviation).     

Human Semi‐Supervised Learning

Most empirical work in human categorization has studied learning in either fully supervised or fully unsupervised scenarios. Most real‐world learning scenarios, however, are semi‐supervised: Learners receive a great deal of unlabeled information from the world, coupled with occasional experiences in which items are directly labeled by a knowledgeable source. A large body of work in machine learning has investigated how learning can exploit both labeled and unlabeled data provided to a learner. Using equivalences between models found in human categorization and machine learning research, we explain how these semi‐supervised techniques can be applied to human learning. A series of experiments are described which show that semi‐supervised learning models prove useful for explaining human behavior when exposed to both labeled and unlabeled data. We then discuss some machine learning models that do not have familiar human categorization counterparts. Finally, we discuss some challenges yet to be addressed in the use of semi‐supervised models for modeling human categorization.     

Self-supervised ARTMAP

Computational models of learning typically train on labeled input patterns (supervised learning), unlabeled input patterns (unsupervised learning), or a combination of the two (semi-supervised learning). In each case input patterns have a fixed number of features throughout training and testing. Human and machine learning contexts present additional opportunities for expanding incomplete knowledge from formal training, via self-directed learning that incorporates features not previously experienced. This article defines a new self-supervised learning paradigm to address these richer learning contexts, introducing a neural network called self-supervised ARTMAP. Self-supervised learning integrates knowledge from a teacher (labeled patterns with some features), knowledge from the environment (unlabeled patterns with more features), and knowledge from internal model activation (self-labeled patterns). Self-supervised ARTMAP learns about novel features from unlabeled patterns without destroying partial knowledge previously acquired from labeled patterns. A category selection function bases system predictions on known features, and distributed network activation scales unlabeled learning to prediction confidence. Slow distributed learning on unlabeled patterns focuses on novel features and confident predictions, defining classification boundaries that were ambiguous in the labeled patterns. Self-supervised ARTMAP improves test accuracy on illustrative low-dimensional problems and on high-dimensional benchmarks. Model code and benchmark data are available from: http://techlab.eu.edu/SSART/.     

Rank-Adaptive Non-Negative Matrix Factorization

Dimension reduction is a challenge task in data processing, especially in high-dimensional data processing area. Non-negative matrix factorization (NMF), as a classical dimension reduction method, has a contribution to the parts-based representation for the characteristics of non-negative constraints in the NMF algorithm. In this paper, the NMF algorithm is introduced to extract local features for dimension reduction. Considering the problem of which NMF is required to define the number of the decomposition rank manually, we proposed a rank-adaptive NMF algorithm, in which the affinity propagation (AP) clustering algorithm is introduced to determine adaptively the number of the decomposition rank of NMF. Then, the rank-adaptive NMF algorithm is used to extract features for the original image. After that, a low-dimensional representation of the original image is obtained through the projection from the original images to the feature space. Finally, we used extreme learning machine (ELM) and k-nearest neighbor (KNN) as the classifier to classify those low-dimensional feature representations. The experimental results demonstrate that the decomposition rank determined by the AP clustering algorithm can reflect the characteristics of the original data. When it is combined with the classification algorithm ELM or KNN and applied to handwritten character recognition, the proposed method not only reduces the dimension of original images but also performs well in terms of classification accuracy and time consumption. A new rank-adaptive NMF algorithm is proposed based on the AP clustering algorithm and the original NMF algorithm. According to this algorithm, the low-dimensional representation of the original data can be obtained without any prior knowledge. In addition, the proposed rank-adaptive NMF algorithm combined with the ELM and KNN classification algorithms performs well.     

An Online Sequential Learning Non-parametric Value-at-Risk Model for High-Dimensional Time Series

Online Value-at-Risk (VaR) analysis in high-dimensional space remains a challenge in the era of big data. In this paper, we propose an online sequential learning non-parametric VaR model called OS-GELM which is an autonomous cognitive system. This model uses a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) process and an online sequential extreme learning machine (OS-ELM) to cognitively calculate VaR, which can be used for online risk analysis. The proposed model not only learns the data one-by-one or chunk-by-chunk but also calculates VaR in real time by extending OS-ELM from machine learning to the non-parametric GARCH process. The GARCH process is also extended to one-by-one and chunk-by-chunk mode. In OS-GELM, the parameters of hidden nodes are randomly selected. The output weights are analytically determined based on the sequentially arriving data. In addition, the generalization performance of the OS-GELM model attains a small training error and generates the smallest norm of weights. Experimentally obtained VaRs are compared with those given by GARCH-type models and conventional OS-ELM. The computational results demonstrate that the OS-GELM model obtains more accurate results and is better at forecasting the online VaR. OS-GELM model is an autonomous cognitive system to dynamically calculate Value-at-Risk, which can be used for online financial risk assessment about human being’s behavior. The OS-GELM model can calculate VaR in real time, which can be used as a tool for online risk management. OS-GELM can handle any bounded, non-constant, piecewise-continuous membership function to realize real-time VaR monitoring.     

NeuCube: A spiking neural network architecture for mapping,learning and understanding of spatio-temporal brain data

The brain functions as a spatio-temporal information processing machine. Spatio- and spectro-temporal brain data (STBD) are the most commonly collected data for measuring brain response to external stimuli. An enormous amount of such data has been already collected, including brain structural and functional data under different conditions, molecular and genetic data, in an attempt to make a progress in medicine, health, cognitive science, engineering, education, neuro-economics, Brain–Computer Interfaces (BCI), and games. Yet, there is no unifying computational framework to deal with all these types of data in order to better understand this data and the processes that generated it. Standard machine learning techniques only partially succeeded and they were not designed in the first instance to deal with such complex data. Therefore, there is a need for a new paradigm to deal with STBD. This paper reviews some methods of spiking neural networks (SNN) and argues that SNN are suitable for the creation of a unifying computational framework for learning and understanding of various STBD, such as EEG, fMRI, genetic, DTI, MEG, and NIRS, in their integration and interaction. One of the reasons is that SNN use the same computational principle that generates STBD, namely spiking information processing. This paper introduces a new SNN architecture, called NeuCube, for the creation of concrete models to map, learn and understand STBD. A NeuCube model is based on a 3D evolving SNN that is an approximate map of structural and functional areas of interest of the brain related to the modeling STBD. Gene information is included optionally in the form of gene regulatory networks (GRN) if this is relevant to the problem and the data. A NeuCube model learns from STBD and creates connections between clusters of neurons that manifest chains (trajectories) of neuronal activity. Once learning is applied, a NeuCube model can reproduce these trajectories, even if only part of the input STBD or the stimuli data is presented, thus acting as an associative memory. The NeuCube framework can be used not only to discover functional pathways from data, but also as a predictive system of brain activities, to predict and possibly, prevent certain events. Analysis of the internal structure of a model after training can reveal important spatio-temporal relationships ‘hidden’ in the data. NeuCube will allow the integration in one model of various brain data, information and knowledge, related to a single subject (personalized modeling) or to a population of subjects. The use of NeuCube for classification of STBD is illustrated in a case study problem of EEG data. NeuCube models result in a better accuracy of STBD classification than standard machine learning techniques. They are robust to noise (so typical in brain data) and facilitate a better interpretation of the results and understanding of the STBD and the brain conditions under which data was collected. Future directions for the use of SNN for STBD are discussed.     

SLT-Based ELM for Big Social Data Analysis

Recently, social networks and other forms of media communication have been gathering the interest of both the scientific and the business world, leading to the increasing development of the science of opinion and sentiment analysis. Facing the huge amount of information present on the Web represents a crucial task and leads to the study and creation of efficient models able to tackle the task. To this end, current research proposes an efficient approach to support emotion recognition and polarity detection in natural language text. In this paper, we show how the most recent advances in statistical learning theory (SLT) can support the development of an efficient extreme learning machine (ELM) and the assessment of the resultant model’s performance when applied to big social data analysis. ELM, developed to overcome some issues in back-propagation networks, represents a powerful learning tool. However, the main problem is represented by the necessity to cope with a large number of available samples, and the generalization performance has to be carefully assessed. For this reason, we propose an ELM implementation that exploits the Spark distributed in memory technology and show how to take advantage of SLT results in order to select ELM hyperparameters able to provide the best generalization performance.     

Supervised Learning and Codebook Optimization for Bag-of-Words Models

In this paper, we present a novel approach for supervised codebook learning and optimization for bag-of-words models. This type of models is frequently used in visual recognition tasks like object class recognition or human action recognition. An entity is represented as a histogram of codewords, which are traditionally clustered with unsupervised methods like k-means or random forests and then classified in a supervised way. We propose a new supervised method for joint codebook creation and class learning, which learns the cluster centers of the codebook in a goal-directed way using the class labels of the training set. As a result, the codebook is highly correlated to the recognition problem, leading to a more discriminative codebook. We propose two different learning algorithms, one based on error backpropagation and the other based on cluster label reassignment. We apply the proposed method to human action recognition from video sequences and evaluate it on the KTH data set, reporting very promising results. The proposed technique allows us to improve the discriminative power of an unsupervised learned codebook or to keep the discriminative power while decreasing the size of the learned codebook, thus decreasing the computational complexity due to the nearest neighbor search.     

A Twin Multi-Class Classification Support Vector Machine

Twin support vector machine (TSVM) is a novel machine learning algorithm, which aims at finding two nonparallel planes for each class. In order to do so, one needs to resolve a pair of smaller-sized quadratic programming problems rather than a single large one. Classical TSVM is proposed for the binary classification problem. However, multi-class classification problem is often met in our real world. For this problem, a new multi-class classification algorithm, called Twin-KSVC, is proposed in this paper. It takes the advantages of both TSVM and K-SVCR (support vector classification-regression machine for k-class classification) and evaluates all the training points into a “1-versus-1-versus-rest” structure, so it generates ternary outputs { ?1, 0, +1}. As all the samples are utilized in constructing the classification hyper-plane, our proposed algorithm yields higher classification accuracy in comparison with other two algorithms. Experimental results on eleven benchmark datasets demonstrate the feasibility and validity of our proposed algorithm.     

Semi-supervised Learning for Affective Common-Sense Reasoning

Background

Big social data analysis is the area of research focusing on collecting, examining, and processing large multi-modal and multi-source datasets in order to discover patterns/correlations and extract information from the Social Web. This is usually accomplished through the use of supervised and unsupervised machine learning algorithms that learn from the available data. However, these are usually highly computationally expensive, either in the training or in the prediction phase, as they are often not able to handle current data volumes. Parallel approaches have been proposed in order to boost processing speeds, but this clearly requires technologies that support distributed computations.

Methods

Extreme learning machines (ELMs) are an emerging learning paradigm, presenting an efficient unified solution to generalized feed-forward neural networks. ELM offers significant advantages such as fast learning speed, ease of implementation, and minimal human intervention. However, ELM cannot be easily parallelized, due to the presence of a pseudo-inverse calculation. Therefore, this paper aims to find a reliable method to realize a parallel implementation of ELM that can be applied to large datasets typical of Big Data problems with the employment of the most recent technology for parallel in-memory computation, i.e., Spark, designed to efficiently deal with iterative procedures that recursively perform operations over the same data. Moreover, this paper shows how to take advantage of the most recent advances in statistical learning theory (SLT) in order to address the issue of selecting ELM hyperparameters that give the best generalization performance. This involves assessing the performance of such algorithms (i.e., resampling methods and in-sample methods) by exploiting the most recent results in SLT and adapting them to the Big Data framework. The proposed approach has been tested on two affective analogical reasoning datasets. Affective analogical reasoning can be defined as the intrinsically human capacity to interpret the cognitive and affective information associated with natural language. In particular, we employed two benchmarks, each one composed by 21,743 common-sense concepts; each concept is represented according to two models of a semantic network in which common-sense concepts are linked to a hierarchy of affective domain labels.

Results

The labeled data have been split into two sets: The first 20,000 samples have been used for building the model with the ELM with the different SLT strategies, while the rest of the labeled samples, numbering 1743, have been kept apart as reference set in order to test the performance of the learned model. The splitting process has been repeated 30 times in order to obtain statistically relevant results. We ran the experiments through the use of the Google Cloud Platform, in particular, the Google Compute Engine. We employed the Google Compute Engine Platform with NM = 4 machines with two cores and 1.8 GB of RAM (machine type n1-highcpu-2) and an HDD of 30 GB equipped with Spark. Results on the affective dataset both show the effectiveness of the proposed parallel approach and underline the most suitable SLT strategies for the specific Big Data problem.

Conclusion

In this paper we showed how to build an ELM model with a novel scalable approach and to carefully assess the performance, with the use of the most recent results from SLT, for a sentiment analysis problem. Thanks to recent technologies and methods, the computational requirements of these methods have been improved to allow for the scaling to large datasets, which are typical of Big Data applications.

     

Fast Face Recognition Via Sparse Coding and Extreme Learning Machine

Most face recognition approaches developed so far regard the sparse coding as one of the essential means, while the sparse coding models have been hampered by the extremely expensive computational cost in the implementation. In this paper, a novel scheme for the fast face recognition is presented via extreme learning machine (ELM) and sparse coding. The common feature hypothesis is first introduced to extract the basis function from the local universal images, and then the single hidden layer feedforward network (SLFN) is established to simulate the sparse coding process for the face images by ELM algorithm. Some developments have been done to maintain the efficient inherent information embedding in the ELM learning. The resulting local sparse coding coefficient will then be grouped into the global representation and further fed into the ELM ensemble which is composed of a number of SLFNs for face recognition. The simulation results have shown the good performance in the proposed approach that could be comparable to the state-of-the-art techniques at a much higher speed.