Discriminative unsupervised 2D dimensionality reduction with graph embedding

Dimensionality reduction is a great challenge in high dimensional unlabelled data processing. The existing dimensionality reduction methods are prone to employing similarity matrix and spectral clustering algorithm. However, the noises in original data always make the similarity matrix unreliable and degrade the clustering performance. Besides, existing spectral clustering methods just focus on the local structures and ignore the global discriminative information, which may lead to overfitting in some cases. To address these issues, a novel unsupervised 2-dimensional dimensionality reduction method is proposed in this paper, which incorporates the similarity matrix learning and global discriminant information into the procedure of dimensionality reduction. Particularly, the number of the connected components in the learned similarity matrix is equal to cluster number. We compare the proposed method with several 2-dimensional unsupervised dimensionality reduction methods and evaluate the clustering performance by K-means on several benchmark data sets. The experimental results show that the proposed method outperforms the state-of-the-art methods.     

A perceptron network for functional identification and control ofnonlinear systems

Tracking control of a general class of nonlinear systems using a perceptron neural network (PNN) is presented. The basic structure of the PNN and its training law are first derived. A novel discrete-time control strategy is introduced that employs the PNN for direct online estimation of the required feedforward control input. The developed controller can be applied to both discrete- and continuous-time plants. Unlike most of the existing direct adaptive or learning schemes, the nonlinear plant is not assumed to be feedback linearizable. The stability of the neural controller under ideal conditions and its robust stability to inexact modeling information are rigorously analyzed.     

A supervised non-linear dimensionality reduction approach for manifold learning

In this paper we introduce a novel supervised manifold learning technique called Supervised Laplacian Eigenmaps (S-LE), which makes use of class label information to guide the procedure of non-linear dimensionality reduction by adopting the large margin concept. The graph Laplacian is split into two components: within-class graph and between-class graph to better characterize the discriminant property of the data. Our approach has two important characteristics: (i) it adaptively estimates the local neighborhood surrounding each sample based on data density and similarity and (ii) the objective function simultaneously maximizes the local margin between heterogeneous samples and pushes the homogeneous samples closer to each other.Our approach has been tested on several challenging face databases and it has been conveniently compared with other linear and non-linear techniques, demonstrating its superiority. Although we have concentrated in this paper on the face recognition problem, the proposed approach could also be applied to other category of objects characterized by large variations in their appearance (such as hand or body pose, for instance).     

Dynamic structure neural networks for stable adaptive control ofnonlinear systems

An adaptive control technique, using dynamic structure Gaussian radial basis function neural networks, that grow in time according to the location of the system's state in space is presented for the affine class of nonlinear systems having unknown or partially known dynamics. The method results in a network that is "economic" in terms of network size, for cases where the state spans only a small subset of state space, by utilizing less basis functions than would have been the case if basis functions were centered on discrete locations covering the whole, relevant region of state space. Additionally, the system is augmented with sliding control so as to ensure global stability if and when the state moves outside the region of state space spanned by the basis functions, and to ensure robustness to disturbances that arise due to the network inherent approximation errors and to the fact that for limiting the network size, a minimal number of basis functions are actually being used. Adaptation laws and sliding control gains that ensure system stability in a Lyapunov sense are presented, together with techniques for determining which basis functions are to form part of the network structure. The effectiveness of the method is demonstrated by experiment simulations.     

Incremental nonlinear dimensionality reduction by manifold learning

Understanding the structure of multidimensional patterns, especially in unsupervised cases, is of fundamental importance in data mining, pattern recognition, and machine learning. Several algorithms have been proposed to analyze the structure of high-dimensional data based on the notion of manifold learning. These algorithms have been used to extract the intrinsic characteristics of different types of high-dimensional data by performing nonlinear dimensionality reduction. Most of these algorithms operate in a "batch" mode and cannot be efficiently applied when data are collected sequentially. In this paper, we describe an incremental version of ISOMAP, one of the key manifold learning algorithms. Our experiments on synthetic data as well as real world images demonstrate that our modified algorithm can maintain an accurate low-dimensional representation of the data in an efficient manner.     

Optimal, unsupervised learning in invariant object recognition

A means for establishing transformation-invariant representations of objects is proposed and analyzed, in which different views are associated on the basis of the temporal order of the presentation of these views, as well as their spatial similarity. Assuming knowledge of the distribution of presentation times, an optimal linear learning rule is derived. Simulations of a competitive network trained on a character recognition task are then used t highlight the success of this learning rule in relation to simple Hebbian learning and to show that the theory can give accurate quantitative predictions for the optimal parameters for such networks.     

Dimensionality reduction in unsupervised learning of conditionalGaussian networks

This paper introduces a novel enhancement for unsupervised learning of conditional Gaussian networks that benefits from feature selection. Our proposal is based on the assumption that, in the absence of labels reflecting the cluster membership of each case of the database, those features that exhibit low correlation with the rest of the features can be considered irrelevant for the learning process. Thus, we suggest performing this process using only the relevant features. Then, every irrelevant feature is added to the learned model to obtain an explanatory model for the original database which is our primary goal. A simple and, thus, efficient measure to assess the relevance of the features for the learning process is presented. Additionally, the form of this measure allows us to calculate a relevance threshold to automatically identify the relevant features. The experimental results reported for synthetic and real-world databases show the ability of our proposal to distinguish between relevant and irrelevant features and to accelerate learning, while still obtaining good explanatory models for the original database     

On-line tuning of fuzzy-neural network for adaptive control ofnonlinear dynamical systems

The adaptive fuzzy-neural controllers tuned online for a class of unknown nonlinear dynamical systems are proposed. To approximate the unknown nonlinear dynamical systems, the fuzzy-neural approximator is established. Furthermore, the control law and update law to tune on-line both the B-spline membership functions and the weighting factors of the adaptive fuzzy-neural controller are derived. Therefore, the control performance of the controller is improved. Several examples are simulated in order to confirm the effectiveness and applicability of the proposed methods in this paper.     

Fuzzy identification of systems with unsupervised learning

The paper describes a mathematical tool to build a fuzzy model whose membership functions and consequent parameters rely on the estimates of a data set. The proposed method proved to be capable of approximating any real continuous function, also a strongly nonlinear one, on a compact set to arbitrary accuracy. Without resorting to domain experts, the algorithm constructs a model-free, complete function approximation system. Applications to the modeling of several functions among which classical nonlinear ones such as the Rosenbrock and the sine (x, y) functions are reported. The proposed algorithm can find applications in the development of fuzzy logic controllers (FLC).     

Visualizing dimensionality reduction of systems biology data

One of the challenges in analyzing high-dimensional expression data is the detection of important biological signals. A common approach is to apply a dimension reduction method, such as principal component analysis. Typically, after application of such a method the data is projected and visualized in the new coordinate system, using scatter plots or profile plots. These methods provide good results if the data have certain properties which become visible in the new coordinate system but which were hard to detect in the original coordinate system. Often however, the application of only one method does not suffice to capture all important signals. Therefore several methods addressing different aspects of the data need to be applied. We have developed a framework for linear and non-linear dimension reduction methods within our visual analytics pipeline SpRay. This includes measures that assist the interpretation of the factorization result. Different visualizations of these measures can be combined with functional annotations that support the interpretation of the results. We show an application to high-resolution time series microarray data in the antibiotic-producing organism Streptomyces coelicolor as well as to microarray data measuring expression of cells with normal karyotype and cells with trisomies of human chromosomes 13 and 21.     

步进电动机的最佳细分控制

提出按照线性加工弦规律波形对步进电动机绕组电流进行细分,以解决在实际应用中存在的低频振荡、高频出力不足、频率特性差等问题。设计制作了同频脉宽调制细分驱动电路。试验结果表明该方法是正确和可行的。     

Deep reinforcement learning for permanent magnet synchronous motor speed control systems

Neural Computing and Applications - The permanent magnet synchronous motor (PMSM) servo system is widely applied in many industrial fields due to its unique advantages. In this paper, we study the...     

Trace ratio criterion based generalized discriminative learning for semi-supervised dimensionality reduction

Dealing with high-dimensional data has always been a major problem in many pattern recognition and machine learning applications. Trace ratio criterion is a criterion that can be applicable to many dimensionality reduction methods as it directly reflects Euclidean distance between data points of within or between classes. In this paper, we analyze the trace ratio problem and propose a new efficient algorithm to find the optimal solution. Based on the proposed algorithm, we are able to derive an orthogonal constrained semi-supervised learning framework. The new algorithm incorporates unlabeled data into training procedure so that it is able to preserve the discriminative structure as well as geometrical structure embedded in the original dataset. Under such a framework, many existing semi-supervised dimensionality reduction methods such as SDA, Lap-LDA, SSDR, SSMMC, can be improved using our proposed framework, which can also be used to formulate a corresponding kernel framework for handling nonlinear problems. Theoretical analysis indicates that there are certain relationships between linear and nonlinear methods. Finally, extensive simulations on synthetic dataset and real world dataset are presented to show the effectiveness of our algorithms. The results demonstrate that our proposed algorithm can achieve great superiority to other state-of-art algorithms.     

Effective multiplicative updates for non-negative discriminative learning in multimodal dimensionality reduction

Fisher discriminant analysis gives the unsatisfactory results if points in the same class have within-class multimodality and fails to produce the non-negativity of projection vectors. In this paper, we focus on the newly formulated within and between-class scatters based supervised locality preserving dimensionality reduction problem and propose an effective dimensionality reduction algorithm, namely, Multiplicative Updates based non-negative Discriminative Learning (MUNDL), which optimally seeks to obtain two non-negative embedding transformations with high preservation and discrimination powers for two data sets in different classes such that nearby sample pairs in the original space compact in the learned embedding space, under which the projections of the original data in different classes can be appropriately separated from each other. We also show that MUNDL can be easily extended to nonlinear dimensionality reduction scenarios by employing the standard kernel trick. We verify the feasibility and effectiveness of MUNDL by conducting extensive data visualization and classification experiments. Numerical results on some benchmark UCI and real-world datasets show the MUNDL method tends to capture the intrinsic local and multimodal structure characteristics of the given data and outperforms some established dimensionality reduction methods, while being much more efficient.     

Stable model reference adaptive fuzzy control of a class ofnonlinear systems

In this paper, we propose a new adaptive fuzzy control scheme called model reference adaptive fuzzy control (MRAFC). The MRAFC scheme employs a reference model to provide closed-loop performance feedback for generating or modifying a fuzzy controller's knowledge base. The MRAFC scheme grew from ideas in conventional model reference adaptive control (MRAC). The MRAFC scheme is developed to perform adaptive feedback linearization to a class of nonlinear systems. A class of fuzzy controllers, which can be expressed in an explicit form, is used as the primary controller. Based on Lyapunov's second method, we have developed MRAFC schemes and derived fuzzy rule adaptive laws. Hence, not only the stability of the system can be assured but also the performance, such as the issues of robustness and parameter convergence, of the MRAFC system can be analyzed explicitly. We showed that in the case of no modeling error, the state error converges to zero asymptotically. In the case that persistent excitation is satisfied, we showed that the MRAFC system is asymptotically stable. By considering the periodic signal as reference input signal, we showed that the square wave can make the MRAFC system be persistently excited. The feasibility of applying these techniques has been demonstrated by considering the control of an inverted pendulum in following a reference model response     

Quantum speed-up for unsupervised learning

We show how the quantum paradigm can be used to speed up unsupervised learning algorithms. More precisely, we explain how it is possible to accelerate learning algorithms by quantizing some of their subroutines. Quantization refers to the process that partially or totally converts a classical algorithm to its quantum counterpart in order to improve performance. In particular, we give quantized versions of clustering via minimum spanning tree, divisive clustering and k-medians that are faster than their classical analogues. We also describe a distributed version of k-medians that allows the participants to save on the global communication cost of the protocol compared to the classical version. Finally, we design quantum algorithms for the construction of a neighbourhood graph, outlier detection as well as smart initialization of the cluster centres.     

Robust right coprime factorization and robust stabilization ofnonlinear feedback control systems

Robust right coprime factorization and robust stabilization of nonlinear feedback control systems are studied. The concept of robust right coprime factorization of nonlinear operators for feedback control systems is introduced. Some conditions for the robustness of a right coprime factorization of a nonlinear plant under unknown but bounded perturbations are derived. An example with a closed-form solution is included to illustrate the general theory and a step-by-step construction of the robust factorization and the robust stabilization     

Exploring dimensionality reduction of EEG features in motor imagery task classification

A Brain-Computer Interface (BCI) system based on motor imagery (MI) identifies patterns of electrical brain activity to predict the user intention while certain movement imagination tasks are performed. Currently, one of the most important challenges is the adaptive design of a BCI system. For solving it, this work explores dimensionality reduction techniques: once features have been extracted from Electroencephalogram (EEG) signals, the high-dimensional EEG data has to be mapped onto a new reduced feature space to make easier the classification stage. Besides the standard sequential feature selection methods, this paper analyzes two unsupervised transformation-based approaches – Principal Component Analysis and Locality Preserving Projections – and the Local Fisher Discriminant Analysis (LFDA), which works in a supervised manner. The dimensionality in the projected space is chosen following a wrapper-based approach by an efficient leave-one-out estimation. Experiments have been conducted on five novice subjects during their first sessions with MI-based BCI systems in order to show that the appropriate use of dimensionality reduction methods allows increasing the performance. In particular, obtained results show that LFDA gives a significant enhancement in classification terms without increasing the computational complexity and, then, it is a promising technique for designing MI-based BCI system.