Twinned principal curves.

Principal Curves are extensions of Principal Component Analysis and are smooth curves, which pass through the middle of a data set. We extend the method so that, on pairs of data sets which have underlying non-linear correlations, we have pairs of curves which go through the 'centre' of data sets in such a way that the non-linear correlations between the data sets are captured. The core of the method is to iteratively average the current local projections of the data points which produces an increasingly sparsified set of nodes. The Twinned Principal Curves are generated in three ways: by joining up the nodes in order, by performing Local Canonical Correlation Analysis and by performing Local Exploratory Correlation Analysis (Koetsier et al., 2002). The latter two are shown to improve the forecasting capability of the method but at an increased computational load. We show that it is crucial to terminate the algorithm after a small number of iterations for the first method and investigate several criteria for doing so.     

Semiblind spatial ICA of fMRI using spatial constraints

Independent component analysis (ICA) utilizing prior information, also called semiblind ICA, has demonstrated considerable promise in the analysis of functional magnetic resonance imaging (fMRI). So far, temporal information about fMRI has been used in temporal ICA or spatial ICA as additional constraints to improve estimation of task‐related components. Considering that prior information about spatial patterns is also available, a semiblind spatial ICA algorithm utilizing the spatial information was proposed within the framework of constrained ICA with fixed‐point learning. The proposed approach was first tested with synthetic fMRI‐like data, and then was applied to real fMRI data from 11 subjects performing a visuomotor task. Three components of interest including two task‐related components and the “default mode” component were automatically extracted, and atlas‐defined masks were used as the spatial constraints. The default mode network, a set of regions that appear correlated in particular in the absence of tasks or external stimuli and is of increasing interest in fMRI studies, was found to be greatly improved when incorporating spatial prior information. Results from simulation and real fMRI data demonstrate that the proposed algorithm can improve ICA performance compared to a different semiblind ICA algorithm and a standard blind ICA algorithm. Hum Brain Mapp, 2010. © 2009 Wiley‐Liss, Inc.     

A neural implementation of canonical correlation analysis

We derive a new method of performing Canonical Correlation Analysis with Artificial Neural Networks. We demonstrate the network's capabilities on artificial data and then compare its effectiveness with that of a standard statistical method on real data. We demonstrate the capabilities of the network in two situations where standard statistical techniques are not effective: where we have correlations stretching over three data sets and where the maximum nonlinear correlation is greater than any linear correlation. The network is also applied to Becker's (Network: Computation in Neural Systems, 1996, 7:7–31) random dot stereogram data and shown to be extremely effective at detecting shift information.     

Interval data clustering using self-organizing maps based on adaptive Mahalanobis distances

The self-organizing map is a kind of artificial neural network used to map high dimensional data into a low dimensional space. This paper presents a self-organizing map for interval-valued data based on adaptive Mahalanobis distances in order to do clustering of interval data with topology preservation. Two methods based on the batch training algorithm for the self-organizing maps are proposed. The first method uses a common Mahalanobis distance for all clusters. In the second method, the algorithm starts with a common Mahalanobis distance per cluster and then switches to use a different distance per cluster. This process allows a more adapted clustering for the given data set. The performances of the proposed methods are compared and discussed using artificial and real interval data sets.     

Max–min distance nonnegative matrix factorization

Nonnegative Matrix Factorization (NMF) has been a popular representation method for pattern classification problems. It tries to decompose a nonnegative matrix of data samples as the product of a nonnegative basis matrix and a nonnegative coefficient matrix. The columns of the coefficient matrix can be used as new representations of these data samples. However, traditional NMF methods ignore class labels of the data samples. In this paper, we propose a novel supervised NMF algorithm to improve the discriminative ability of the new representation by using the class labels. Using the class labels, we separate all the data sample pairs into within-class pairs and between-class pairs. To improve the discriminative ability of the new NMF representations, we propose to minimize the maximum distance of the within-class pairs in the new NMF space, and meanwhile to maximize the minimum distance of the between-class pairs. With this criterion, we construct an objective function and optimize it with regard to basis and coefficient matrices, and slack variables alternatively, resulting in an iterative algorithm. The proposed algorithm is evaluated on three pattern classification problems and experiment results show that it outperforms the state-of-the-art supervised NMF methods.     

Method for bias field correction of brain T1-weighted magnetic resonance images minimizing segmentation error

This work presents a new algorithm (nonuniform intensity correction; NIC) for correction of intensity inhomogeneities in T1-weighted magnetic resonance (MR) images. The bias field and a bias-free image are obtained through an iterative process that uses brain tissue segmentation. The algorithm was validated by means of realistic phantom images and a set of 24 real images. The first evaluation phase was based on a public domain phantom dataset, used previously to assess bias field correction algorithms. NIC performed similar to previously described methods in removing the bias field from phantom images, without introduction of degradation in the absence of intensity inhomogeneity. The real image dataset was used to compare the performance of this new algorithm to that of other widely used methods (N3, SPM'99, and SPM2). This dataset included both low and high bias field images from two different MR scanners of low (0.5 T) and medium (1.5 T) static fields. Using standard quality criteria for determining the goodness of the different methods, NIC achieved the best results, correcting the images of the real MR dataset, enabling its systematic use in images from both low and medium static field MR scanners. A limitation of our method is that it might fail if the bias field is so high that the initial histogram does not show bimodal distribution for white and gray matter.     

POPFNN: A Pseudo Outer-product Based Fuzzy Neural Network

A novel fuzzy neural network, called the pseudo outer-product based fuzzy neural network (POPFNN), is proposed in this paper. The functions performed by each layer in the proposed POPFNN strictly correspond to the inference steps in the truth value restriction method in fuzzy logic [Mantaras (1990) Approximate reasoning models, Ellis Horwood]. This correspondence gives it a strong theoretical basis. Similar to most of the existing fuzzy neural networks, the proposed POPFNN uses a self-organizing algorithm (Kohonen, 1988, Self-organization and associative memories, Springer) to learn and initialize the membership functions of the input and output variables from a set of training data. However, instead of employing the popularly used competitive learning [Kosko (1990) IEEE Trans. Neural Networks, 3(5), 801], this paper proposes a novel pseudo outer-product (POP) learning algorithm to identify the fuzzy rules that are supported by the training data. The proposed POP learning algorithm is fast, reliable, and highly intuitive. Extensive experimental results and comparisons are presented at the end of the paper for discussion. Copyright © 1996 Elsevier Science Ltd.     

On mixtures of three normal populations caused by monogenic inheritance: application to desipramine metabolism.

For a mixture of three normal distributions, which represent genotypes AA, Aa and aa, a method of estimation of the seven unknown parameters is proposed which works well whenever the phenotype (aa) is sufficiently well separated from the phenotype (AA, Aa). It is based on p-values of Kolmogorov's test of goodness of fit to normality. Initial parameter values for this iterative algorithm can be found by visual check and/or by using the EM algorithm. In an example of a data set of size 59 from a study of the metabolic rate of desipramine, the usefulness of this method is demonstrated. Extensions to more complex situations are feasible and are indicated at the end.     

Snap-drift neural network for self-organisation and sequence learning

This paper presents two novel neural networks based on snap-drift in the context of self-organisation and sequence learning. The snap-drift neural network employs modal learning that is a combination of two modes; fuzzy AND learning (snap), and Learning Vector Quantisation (drift). We present the snap-drift self-organising map (SDSOM) and the recurrent snap-drift neural network (RSDNN). The SDSOM uses the standard SOM architecture, where a layer of input nodes connects to the self-organising map layer and the weight update consists of either snap (min of input and weight) or drift (LVQ, as in SOM). The RSDNN uses a simple recurrent network (SRN) architecture, with the hidden layer values copied back to the input layer. A form of reinforcement learning is deployed in which the mode is swapped between the snap and drift when performance drops, and in which adaptation is probabilistic, whereby the probability of a neuron being adapted is reduced as performance increases. The algorithms are evaluated on several well known data sets, and it is found that these exhibit effective learning that is faster than alternative neural network methods.     

Distributed semi-supervised support vector machines

The semi-supervised support vector machine (S${}^3$VM) is a well-known algorithm for performing semi-supervised inference under the large margin principle. In this paper, we are interested in the problem of training a S${}^3$VM when the labeled and unlabeled samples are distributed over a network of interconnected agents. In particular, the aim is to design a distributed training protocol over networks, where communication is restricted only to neighboring agents and no coordinating authority is present. Using a standard relaxation of the original S${}^3$VM, we formulate the training problem as the distributed minimization of a non-convex social cost function. To find a (stationary) solution in a distributed manner, we employ two different strategies: (i) a distributed gradient descent algorithm; (ii) a recently developed framework for In-Network Nonconvex Optimization (NEXT), which is based on successive convexifications of the original problem, interleaved by state diffusion steps. Our experimental results show that the proposed distributed algorithms have comparable performance with respect to a centralized implementation, while highlighting the pros and cons of the proposed solutions. To the date, this is the first work that paves the way toward the broad field of distributed semi-supervised learning over networks.     

A canonical correlation neural network for multicollinearity and functional data.

We review a recent neural implementation of Canonical Correlation Analysis and show, using ideas suggested by Ridge Regression, how to make the algorithm robust. The network is shown to operate on data sets which exhibit multicollinearity. We develop a second model which not only performs as well on multicollinear data but also on general data sets. This model allows us to vary a single parameter so that the network is capable of performing Partial Least Squares regression (at one extreme) to Canonical Correlation Analysis (at the other)and every intermediate operation between the two. On multicollinear data, the parameter setting is shown to be important but on more general data no particular parameter setting is required. Finally, we develop a second penalty term which acts on such data as a smoother in that the resulting weight vectors are much smoother and more interpretable than the weights without the robustification term. We illustrate our algorithms on both artificial and real data.     

RKF-PCA: Robust kernel fuzzy PCA

Principal component analysis (PCA) is a mathematical method that reduces the dimensionality of the data while retaining most of the variation in the data. Although PCA has been applied in many areas successfully, it suffers from sensitivity to noise and is limited to linear principal components. The noise sensitivity problem comes from the least-squares measure used in PCA and the limitation to linear components originates from the fact that PCA uses an affine transform defined by eigenvectors of the covariance matrix and the mean of the data.In this paper, a robust kernel PCA method that extends the kernel PCA and uses fuzzy memberships is introduced to tackle the two problems simultaneously. We first introduce an iterative method to find robust principal components, called Robust Fuzzy PCA (RF-PCA), which has a connection with robust statistics and entropy regularization. The RF-PCA method is then extended to a non-linear one, Robust Kernel Fuzzy PCA (RKF-PCA), using kernels. The modified kernel used in the RKF-PCA satisfies the Mercer’s condition, which means that the derivation of the K-PCA is also valid for the RKF-PCA. Formal analyses and experimental results suggest that the RKF-PCA is an efficient non-linear dimension reduction method and is more noise-robust than the original kernel PCA.     

Pharmacokinetics and Pharmacodynamics of Valproate Analogues in Rats. IV. Anticonvulsant Action and Neurotoxocity of Octanoic Acid, Cyclohexanecarboxylic Acid, and 1-Methyl-1 -Cyclohexanecarboxylic Acid

Summary: We examined the pharmacodynamics of valproate (VPA) and three structural analogues, octanoic acid (OA), cyclohexanecarboxylic acid (CCA), and 1-methyl-1-cyclohexanecarboxylic acid (MCCA) in rats. A pentylenetetrazol (PTZ) infusion seizure model was used to determine threshold convulsive doses of PTZ; the increase in PTZ threshold dose after administration of test compound was taken as an index of anticonvulsant activity. Each of the compounds investigated antagonized PTZ-induced seizures, with MCCA evidencing the highest potency. Both CCA and MCCA appeared to have an approximate twofold advantage relative to VPA in protective index (i.e., the ratio of concentrations that produce toxicity to concentrations that produce anticonvulsant effect), based on a rotorod assay of neurotoxicity. Examination of the time course of PTZ antagonism indicated that there was significant dissociation between pharmacokinetics and pharmacodynamics of VPA, with a marked delay in production of maximal anticonvulsant activity. In contrast, only a slight delay in production of maximal protection against PTZ-induced seizures was observed for MCCA, and no delay was evident for CCA. The data indicate that the dynamics of anticonvulsant action differ between these low-molecular-weight carboxylic acids despite their similar chemical structures.     

S-TREE: self-organizing trees for data clustering and online vector quantization.

This paper introduces S-TREE (Self-Organizing Tree), a family of models that use unsupervised learning to construct hierarchical representations of data and online tree-structured vector quantizers. The S-TREE1 model, which features a new tree-building algorithm, can be implemented with various cost functions. An alternative implementation, S-TREE2, which uses a new double-path search procedure, is also developed. The performance of the S-TREE algorithms is illustrated with data clustering and vector quantization examples, including a Gauss-Markov source benchmark and an image compression application. S-TREE performance on these tasks is compared with the standard tree-structured vector quantizer (TSVQ) and the generalized Lloyd algorithm (GLA). The image reconstruction quality with S-TREE2 approaches that of GLA while taking less than 10% of computer time. S-TREE1 and S-TREE2 also compare favorably with the standard TSVQ in both the time needed to create the codebook and the quality of image reconstruction.     

Hybrid extreme rotation forest

This paper proposes the Hybrid Extreme Rotation Forest (HERF), an innovative ensemble learning algorithm for classification problems, combining classical Decision Trees with the recently proposed Extreme Learning Machines (ELM) training of Neural Networks. In the HERF algorithm, training of each individual classifier involves two steps: first computing a randomized data rotation transformation of the training data, second, training the individual classifier on the rotated data. The testing data is subjected to the same transformation as the training data, which is specific for each classifier in the ensemble. Experimental design in this paper involves (a) the comparison of factorization approaches to compute the randomized rotation matrix: the Principal Component Analysis (PCA) and the Quartimax, (b) assessing the effect of data normalization and bootstrapping training data selection, (c) all variants of single and combined ELM and decision trees, including Regularized ELM. This experimental design effectively includes other state-of-the-art ensemble approaches in the comparison, such as Voting ELM and Random Forest. We report extensive results over a collection of machine learning benchmark databases. Ranking the cross-validation results per experimental dataset and classifier tested concludes that HERF significantly improves over the other state-of-the-art ensemble classifier. Besides, we find some other results such as that the data rotation with Quartimax improves over PCA, and the relative insensitivity of the approach to regularization which may be attributable to the de facto regularization performed by the ensemble approach.     

SOM-based algorithms for qualitative variables.

It is well known that the SOM algorithm achieves a clustering of data which can be interpreted as an extension of Principal Component Analysis, because of its topology-preserving property. But the SOM algorithm can only process real-valued data. In previous papers, we have proposed several methods based on the SOM algorithm to analyze categorical data, which is the case in survey data. In this paper, we present these methods in a unified manner. The first one (Kohonen Multiple Correspondence Analysis, KMCA) deals only with the modalities, while the two others (Kohonen Multiple Correspondence Analysis with individuals, KMCA_ind, Kohonen algorithm on DISJonctive table, KDISJ) can take into account the individuals, and the modalities simultaneously.     

Functional gut disorders or disordered gut function? Small bowel dysmotility evidenced by an original technique

Background This study aimed to determine the proportion of cases with abnormal intestinal motility among patients with functional bowel disorders. To this end, we applied an original method, previously developed in our laboratory, for analysis of endoluminal images obtained by capsule endoscopy. This novel technology is based on computer vision and machine learning techniques. Methods The endoscopic capsule (Pillcam SB1; Given Imaging, Yokneam, Israel) was administered to 80 patients with functional bowel disorders and 70 healthy subjects. Endoluminal image analysis was performed with a computer vision program developed for the evaluation of contractile events (luminal occlusions and radial wrinkles), non‐contractile patterns (open tunnel and smooth wall patterns), type of content (secretions, chyme) and motion of wall and contents. Normality range and discrimination of abnormal cases were established by a machine learning technique. Specifically, an iterative classifier (one‐class support vector machine) was applied in a random population of 50 healthy subjects as a training set and the remaining subjects (20 healthy subjects and 80 patients) as a test set. Key Results The classifier identified as abnormal 29% of patients with functional diseases of the bowel (23 of 80), and as normal 97% of healthy subjects (68 of 70) (P < 0.05 by chi‐squared test). Patients identified as abnormal clustered in two groups, which exhibited either a hyper‐ or a hypodynamic motility pattern. The motor behavior was unrelated to clinical features. Conclusions & Inferences With appropriate methodology, abnormal intestinal motility can be demonstrated in a significant proportion of patients with functional bowel disorders, implying a pathologic disturbance of gut physiology.     

Psychometric analysis of the Willoughby Personality Schedule

The Willoughby Personality Schedule (WPS) was subjected to Item Analysis, Coefficient Alpha Reliability Analysis, Factor Analysis and parametric tests for sex and age differences to assess its psychometric qualities. A set of norms for adult neurotics was also developed. The WPS items were all shown to be significantly related to total WPS score and to converge into a unitary construct: hypersensitivity to interpersonal situations. The potential clinical and research uses for the WPS in assertion and social skills training are discussed.     

A proposed dosing algorithm for the individualized dosing of human immunoglobulin in chronic inflammatory neuropathies

Dosing guidelines for immunoglobulin (Ig) treatment in neurological disorders do not consider variations in Ig half‐life or between patients. Individualization of therapy could optimize clinical outcomes and help control costs. We developed an algorithm to optimize Ig dose based on patient's response and present this here as an example of how dosing might be individualized in a pharmacokinetically rational way and how this achieves potential dose and cost savings. Patients are “normalized” with no more than two initial doses of 2 g/kg, identifying responders. A third dose is not administered until the patient's condition deteriorates, allowing a “dose interval” to be set. The dose is then reduced until relapse allowing dose optimization. Using this algorithm, we have individualized Ig doses for 71 chronic inflammatory neuropathy patients. The majority of patients had chronic inflammatory demyelinating polyradiculoneuropathy (n = 39) or multifocal motor neuropathy (n = 24). The mean (standard deviation) dose of Ig administered was 1.4 (0.6) g/kg, with a mean dosing interval of 4.3 weeks (median 4 weeks, range 0.5–10). Use of our standardized algorithm has allowed us to quickly optimize Ig dosing.