Piecewise Linear Projection Based on Self-Organizing Map

A piecewise linear projection algorithm, based on kohonen's Self-Organizing Map, is presented. Using this new algorithm, neural network is able to adapt its neural weights to accommodate with input space, while obtaining reduced 2-dimensional subspaces at each neural node. After completion of learning process, first project input data into their corresponding 2-D subspaces, then project all data in the 2-D subspaces into a reference 2-D subspace defined by a reference neural node. By piecewise linear projection, we can more easily deal with large data sets than other projection algorithms like Sammon's nonlinear mapping (NLM). There is no need to re-compute all the input data to interpolate new input data to the 2-D output space.     

Using fuzzy partitions to create fuzzy systems from input-outputdata and set the initial weights in a fuzzy neural network

We create a set of fuzzy rules to model a system from input-output data by dividing the input space into a set of subspaces using fuzzy partitions. We create a fuzzy rule for each subspace as the input space is being divided. These rules are combined to produce a fuzzy rule based model from the input-output data. If more accuracy is required, we use the fuzzy rule-based model to determine the structure and set the initial weights in a fuzzy neural network. This network typically trains in a few hundred iterations. Our method is simple, easy, and reliable and it has worked well when modeling large “real world” systems     

A new approach to radial basis function-based polynomial neural networks: analysis and design

In this study, we introduce a new topology of radial basis function-based polynomial neural networks (RPNNs) that is based on a genetically optimized multi-layer perceptron with radial polynomial neurons (RPNs). This paper offers a comprehensive design methodology involving various mechanisms of optimization, especially fuzzy C-means (FCM) clustering and particle swarm optimization (PSO). In contrast to the typical architectures encountered in polynomial neural networks (PNNs), our main objective is to develop a topology and establish a comprehensive design strategy of RPNNs: (a) The architecture of the proposed network consists of radial polynomial neurons (RPN). These neurons are fully reflective of the structure encountered in numeric data, which are granulated with the aid of FCM clustering. RPN dwells on the concepts of a collection of radial basis function and the function-based nonlinear polynomial processing. (b) The PSO-based design procedure being applied to each layer of the RPNN leads to the selection of preferred nodes of the network whose local parameters (such as the number of input variables, a collection of the specific subset of input variables, the order of the polynomial, the number of clusters of FCM clustering, and a fuzzification coefficient of the FCM method) are properly adjusted. The performance of the RPNN is quantified through a series of experiments where we use several modeling benchmarks, namely a synthetic three-dimensional data and learning machine data (computer hardware data, abalone data, MPG data, and Boston housing data) already used in neuro-fuzzy modeling. A comparative analysis shows that the proposed RPNN exhibits higher accuracy in comparison with some previous models available in the literature.     

稀疏子空间聚类综述

稀疏子空间聚类(Sparse subspace clustering, SSC)是一种基于谱聚类的数据聚类框架. 高维数据通常分布于若干个低维子空间的并上, 因此高维数据在适当字典下的表示具有稀疏性. 稀疏子空间聚类利用高维数据的稀疏表示系数构造相似度矩阵, 然后利用谱聚类方法得到数据的子空间聚类结果. 其核心是设计能够揭示高维数据真实子空间结构的表示模型, 使得到的表示系数及由此构造的相似度矩阵有助于精确的子空间聚类. 稀疏子空间聚类在机器学习、计算机视觉、图像处理和模式识别等领域已经得到了广泛的研究和应用, 但仍有很大的发展空间. 本文对已有稀疏子空间聚类方法的模型、算法和应用等方面进行详细阐述, 并分析存在的不足, 指出进一步研究的方向.     

联机局部自适应模糊C均值聚类算法

基于模糊C均值(FCM)和局部自适应聚类(LAC)提出一种针对高维数据的联机局部自适应模糊C均值聚类算法(OLAFCM).OLAFCM通过为各类属性分别赋以相应的局部权重,使各类属性分布在不同属性组合的张量子空间内,从而有效降低采用全局降维方法造成的信息损失,同时适合聚类数据流.最后,在人工模拟和真实数据集上验证OLAFCM比之现有基于全局降维的划分联机聚类算法具有更好的性能.     

一种可信子空间标志方法*

在D-S证据理论的基础上,给出了可信子空间的定义及能够发现所有可信子空间的贪心算法CSL(creditable subspace labeling)。该方法迭代地发现原始特征空间的信任子空间集Cs。用户根据应用领域的需求, 对Cs中的每个可信子空间调用传统聚类算法发现聚类结果。实验结果表明,CSL具有正确发现原始特征空间的真实子空间的能力,为传统聚类算法处理高维数据空间聚类问题提供了一种新的途径。     

Statistical computations on Grassmann and Stiefel manifolds for image and video-based recognition

In this paper, we examine image and video-based recognition applications where the underlying models have a special structure—the linear subspace structure. We discuss how commonly used parametric models for videos and image sets can be described using the unified framework of Grassmann and Stiefel manifolds. We first show that the parameters of linear dynamic models are finite-dimensional linear subspaces of appropriate dimensions. Unordered image sets as samples from a finite-dimensional linear subspace naturally fall under this framework. We show that an inference over subspaces can be naturally cast as an inference problem on the Grassmann manifold. To perform recognition using subspace-based models, we need tools from the Riemannian geometry of the Grassmann manifold. This involves a study of the geometric properties of the space, appropriate definitions of Riemannian metrics, and definition of geodesics. Further, we derive statistical modeling of inter and intraclass variations that respect the geometry of the space. We apply techniques such as intrinsic and extrinsic statistics to enable maximum-likelihood classification. We also provide algorithms for unsupervised clustering derived from the geometry of the manifold. Finally, we demonstrate the improved performance of these methods in a wide variety of vision applications such as activity recognition, video-based face recognition, object recognition from image sets, and activity-based video clustering.     

基于聚类支持向量机的船用污水处理装置故障诊断

针对船用污水处理装置状态监测与故障诊断问题,提出了一种聚类支持向量机的故障诊断算法模型。该算法模型首先采用神经网络聚类算法将设备监测状态样本空间聚类分析出正常与异常子空间,再对异常子空间构造多分类支持向量机对故障进行诊断识别。该算法模型避免了盲目故障分类,提高了分类性能。通过对某船用污水处理装置实测样本的训练和检验表明,该算法具有较好的泛化性和推广能力。     

Advanced self-organizing polynomial neural network

In this paper, we introduce a concept of advanced self-organizing polynomial neural network (Adv_SOPNN). The SOPNN is a flexible neural architecture whose structure is developed through a modeling process. But the SOPNN has a fatal drawback; it cannot be constructed for nonlinear systems with few input variables. To relax this limitation of the conventional SOPNN, we combine a fuzzy system and neural networks with the SOPNN. Input variables are partitioned into several subspaces by the fuzzy system or neural network, and these subspaces are utilized as new input variables to the SOPNN architecture. Two types of the advanced SOPNN are obtained by combining not only the fuzzy rules of a fuzzy system with SOPNN but also the nodes in a hidden layer of neural networks with SOPNN into one methodology. The proposed method is applied to the nonlinear system with two inputs, which cannot be identified by conventional SOPNN to show the performance of the advanced SOPNN. The results show that the proposed method is efficient for systems with limited data set and a few input variables and much more accurate than other modeling methods with respect to identification error.     

The Hierarchical Fast Learning Artificial Neural Network (HieFLANN)—An Autonomous Platform for Hierarchical Neural Network Construction

The hierarchical fast learning artificial neural network (HieFLANN) is a clustering NN that can be initialized using statistical properties of the data set. This provides the possibility of constructing the entire network autonomously with no manual intervention. This distinguishes it from many existing networks that, though hierarchically plausible, still require manual initialization processes. The unique system of hierarchical networks begins with a reduction of the high-dimensional feature space into smaller and manageable ones. This process involves using the K-iterations fast learning artificial neural network (KFLANN) to systematically cluster a square matrix containing the Mahalanobis distances (MDs) between data set features, into homogeneous feature subspaces (HFSs). The KFLANN is used for its heuristic network initialization capabilities on a given data set and requires no supervision. Through the recurring use of the KFLANN and a second stage involving canonical correlation analysis (CCA), the HieFLANN is developed. Experimental results on several standard benchmark data sets indicate that the autonomous determination of the HFS provides a viable avenue for feasible partitioning of feature subspaces. When coupled with the network transformation process, the HieFLANN yields results showing accuracies comparable with available methods. This provides a new platform by which data sets with high-dimensional feature spaces can be systematically resolved and trained autonomously, alleviating the effects of the curse of dimensionality.     

A fuzzy ensemble of parallel polynomial neural networks with information granules formed by fuzzy clustering

In this paper, we introduce a new category of fuzzy models called a fuzzy ensemble of parallel polynomial neural network (FEP²N²), which consist of a series of polynomial neural networks weighted by activation levels of information granules formed with the use of fuzzy clustering. The two underlying design mechanisms of the proposed networks rely on information granules resulting from the use of fuzzy C-means clustering (FCM) and take advantage of polynomial neural networks (PNNs).The resulting model comes in the form of parallel polynomial neural networks. In the design procedure, in order to estimate the optimal values of the coefficients of polynomial neural networks we use a weighted least square estimation algorithm. We incorporate various types of structures as the consequent part of the fuzzy model when using the learning algorithm. Among the diverse structures being available, we consider polynomial neural networks, which exhibit highly nonlinear characteristics when being viewed as local learning models.We use FCM to form information granules and to overcome the high dimensionality problem. We adopt PNNs to find the optimal local models, which can describe the relationship between the input variables and output variable within some local region of the input space.We show that the generalization capabilities as well as the approximation abilities of the proposed model are improved as a result of using polynomial neural networks. The performance of the network is quantified through experimentation in which we use a number of benchmarks already exploited within the realm of fuzzy or neurofuzzy modeling.     

Conditional fuzzy clustering in the design of radial basis functionneural networks

This paper is concerned with the use of radial basis function (RBF) neural networks aimed at an approximation of nonlinear mappings from R(n) to R. The study is devoted to the design of these networks, especially their layer composed of RBF, using the techniques of fuzzy clustering. Proposed is an idea of conditional clustering whose main objective is to develop clusters (receptive fields) preserving homogeneity of the clustered patterns with regard to their similarity in the input space as well as their respective values assumed in the output space. The detailed clustering algorithm is accompanied by extensive simulation studies.     

Hierarchically clustered adaptive quantization CMAC and its learning convergence.

The cerebellar model articulation controller (CMAC) neural network (NN) is a well-established computational model of the human cerebellum. Nevertheless, there are two major drawbacks associated with the uniform quantization scheme of the CMAC network. They are the following: (1) a constant output resolution associated with the entire input space and (2) the generalization-accuracy dilemma. Moreover, the size of the CMAC network is an exponential function of the number of inputs. Depending on the characteristics of the training data, only a small percentage of the entire set of CMAC memory cells is utilized. Therefore, the efficient utilization of the CMAC memory is a crucial issue. One approach is to quantize the input space nonuniformly. For existing nonuniformly quantized CMAC systems, there is a tradeoff between memory efficiency and computational complexity. Inspired by the underlying organizational mechanism of the human brain, this paper presents a novel CMAC architecture named hierarchically clustered adaptive quantization CMAC (HCAQ-CMAC). HCAQ-CMAC employs hierarchical clustering for the nonuniform quantization of the input space to identify significant input segments and subsequently allocating more memory cells to these regions. The stability of the HCAQ-CMAC network is theoretically guaranteed by the proof of its learning convergence. The performance of the proposed network is subsequently benchmarked against the original CMAC network, as well as two other existing CMAC variants on two real-life applications, namely, automated control of car maneuver and modeling of the human blood glucose dynamics. The experimental results have demonstrated that the HCAQ-CMAC network offers an efficient memory allocation scheme and improves the generalization and accuracy of the network output to achieve better or comparable performances with smaller memory usages. Index Terms-Cerebellar model articulation controller (CMAC), hierarchical clustering, hierarchically clustered adaptive quantization CMAC (HCAQ-CMAC), learning convergence, nonuniform quantization.     

Integrating scattering feature maps with convolutional neural networks for Malayalam handwritten character recognition

Convolutional neural network (CNN)-based deep learning architectures are the state-of-the-art in image-based pattern recognition applications. The receptive filter fields in convolutional layers are learned from training data patterns automatically during classifier learning. There are number of well-defined, well-studied and proven filters in the literature that can extract informative content from the input patterns. This paper focuses on utilizing scattering transform-based wavelet filters as the first-layer convolutional filters in CNN architecture. The scattering networks are generated by a series of scattering transform operations. The scattering coefficients generated in first few layers are effective in capturing the dominant energy contained in the input data patterns. The present work aims at replacing the first-layer convolutional feature maps in CNN architecture with scattering feature maps. This architecture is equivalent to utilizing scattering wavelet filters as the first-layer receptive fields in CNN architecture. The proposed hybrid CNN architecture experiments the Malayalam handwritten character recognition which is one of the challenging multi-class classification problems. The initial studies confirm that the proposed hybrid CNN architecture based on scattering feature maps could perform better than the equivalent self-learning architecture of CNN on handwritten character recognition problems.     

Genetic design of biologically inspired receptive fields for neural pattern recognition

This paper proposes a new method for the design, through simulated evolution, of biologically inspired receptive fields in feedforward neural networks (NNs). The method is intended to enhance pattern recognition performance by creating new neural architectures specifically tuned for a particular pattern recognition problem. It proposes a combined neural architecture composed of two networks in cascade: a feature extraction network (FEN) followed by a neural classifier. The FEN is composed of several layers with receptive fields constructed by additive superposition of excitatory and inhibitory fields. A genetic algorithm (GA) is used to select receptive field parameters to improve classification performance. The parameters are receptive field size, orientation, and bias as well as the number of different receptive fields in each layer. Based on a random initial population where each individual represents a different neural architecture, the GA creates new enhanced individuals. The method is applied to handwritten digit classification and face recognition. In both problems, results show strong dependency between NN classification performance and receptive field architecture. GA selected parameters of the receptive fields produced improvements in the classification performance on the test set up to 90.8% for the problem of handwritten digit classification and up to 84.2% for the face recognition problem. On the same test sets, results were compared advantageously to standard feedforward multilayer perceptron (MLP) NNs where receptive fields are not explicitly defined. The MLP reached a maximum classification performance of 84.9% and 77.5% in both problems, respectively.     

Density Conscious Subspace Clustering for High-Dimensional Data

Instead of finding clusters in the full feature space, subspace clustering is an emergent task which aims at detecting clusters embedded in subspaces. Most of previous works in the literature are density-based approaches, where a cluster is regarded as a high-density region in a subspace. However, the identification of dense regions in previous works lacks of considering a critical problem, called "the density divergence problem” in this paper, which refers to the phenomenon that the region densities vary in different subspace cardinalities. Without considering this problem, previous works utilize a density threshold to discover the dense regions in all subspaces, which incurs the serious loss of clustering accuracy (either recall or precision of the resulting clusters) in different subspace cardinalities. To tackle the density divergence problem, in this paper, we devise a novel subspace clustering model to discover the clusters based on the relative region densities in the subspaces, where the clusters are regarded as regions whose densities are relatively high as compared to the region densities in a subspace. Based on this idea, different density thresholds are adaptively determined to discover the clusters in different subspace cardinalities. Due to the infeasibility of applying previous techniques in this novel clustering model, we also devise an innovative algorithm, referred to as DENCOS (DENsity COnscious Subspace clustering), to adopt a divide-and-conquer scheme to efficiently discover clusters satisfying different density thresholds in different subspace cardinalities. As validated by our extensive experiments on various data sets, DENCOS can discover the clusters in all subspaces with high quality, and the efficiency of DENCOS outperformes previous works.     

Complex cell pooling and the statistics of natural images

In previous work, we presented a statistical model of natural images that produced outputs similar to receptive fields of complex cells in primary visual cortex. However, a weakness of that model was that the structure of the pooling was assumed a priori and not learned from the statistical properties of natural images. Here, we present an extended model in which the pooling nonlinearity and the size of the subspaces are optimized rather than fixed, so we make much fewer assumptions about the pooling. Results on natural images indicate that the best probabilistic representation is formed when the size of the subspaces is relatively large, and that the likelihood is considerably higher than for a simple linear model with no pooling. Further, we show that the optimal nonlinearity for the pooling is squaring. We also highlight the importance of contrast gain control for the performance of the model. Our model is novel in that it is the first to analyze optimal subspace size and how this size is influenced by contrast normalization.     

Prediction of Critical Desalination Parameters Using Radial Basis Functions Networks

Prediction of critical desalination parameters (recovery and salt rejection) of two distinct processes based on real operational data is presented. The proposed method utilizes the radial basis function network using data clustering and histogram equalization. The scheme involves center selection and shape adjustment of the localized receptive fields. This algorithm causes each group of radial basis functions to adapt to regions of the clustered input space. Networks produced by the proposed algorithm have good generalization performance on prediction of non-linear input–output mappings and require a small number of connecting weights. The proposed method was used for the prediction of two different critical parameters for two distinct Reverse Osmosis (RO) plants. The simulation results indeed confirm the effectiveness of the proposed prediction method.     

Properties of Numeric Codes for the Scheme of Random Subspaces RSC

Properties of coarse coding obtained by using the random subspace coding (RSC) scheme with random hyperrectangular receptive fields are considered. Characteristics of codes are provided such as the dimensionality of receptive fields, code density at various points of the input space, code overlapping, and others. The results of theoretical analysis are illustrated by experiments with high-dimensional codes. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 39–52, July–August 2005.     

一种功能分区的BP神经网络结构设计方法

针对全连接BP网络在解决大规模复杂问题时存在的收敛速度缓慢等问题,提出一种功能分区的BP网络结构模式.利用RBF神经元的物理特性对输入样本空间进行分解,并将分解后的样本送给不同的子BP网络学习.与全连接BP网络相比,降低了网络在学习过程中的权值搜索空间,提高了学习速度,改善了网络泛化性能,体现了人脑在学习过程中的知识积累特征.对三维墨西哥草帽函数逼近和双螺旋分类的实验结果表明,该网络能够解决全连接BP网络不能有效解决的问题.