Nonlinear Discrimination Research Articles

Locally linear discriminant analysis for multimodally distributed classes for face recognition with a single model image

We present a novel method of nonlinear discriminant analysis involving a set of locally linear transformations called "Locally Linear Discriminant Analysis (LLDA)." The underlying idea is that global nonlinear data structures are locally linear and local structures can be linearly aligned. Input vectors are projected into each local feature space by linear transformations found to yield locally linearly transformed classes that maximize the between-class covariance while minimizing the within-class covariance. In face recognition, linear discriminant analysis (LDA) has been widely adopted owing to its efficiency, but it does not capture nonlinear manifolds of faces which exhibit pose variations. Conventional nonlinear classification methods based on kernels such as generalized discriminant analysis (GDA) and support vector machine (SVM) have been developed to overcome the shortcomings of the linear method, but they have the drawback of high computational cost of classification and overfitting. Our method is for multiclass nonlinear discrimination and it is computationally highly efficient as compared to GDA. The method does not suffer from overfitting by virtue of the linear base structure of the solution. A novel gradient-based learning algorithm is proposed for finding the optimal set of local linear bases. The optimization does not exhibit a local-maxima problem. The transformation functions facilitate robust face recognition in a low-dimensional subspace, under pose variations, using a single model image. The classification results are given for both synthetic and real face data.

Four-user, 2.5-Gb/s, spectrally coded OCDMA system demonstration using low-power nonlinear processing

This paper describes the demonstration of 2.5-Gb/s four-user optical-code-division-multiple-access (OCDMA) system operating at bit-error rate /spl les/10/sup -11/ utilizing programmable spectral phase encoding, an ultrasensitive (/spl sim/200 fJ/b) periodically poled lithium-niobate-waveguide nonlinear waveform discriminator and 10G Ethernet receiver. A comprehensive description of this ultra-short-pulse spectral phase-coded OCDMA system is presented. On the subsystem level, two key component technologies, namely, femtosecond encoding/decoding and low-power high-contrast nonlinear discrimination, have been developed and characterized. At the system level, data for the four-user OCDMA system operating at 2.5 Gb/s for binary as well as multilevel code families are described.

Non-Linear Discrimination of Days After Planting of Lettuce by Using Image Information

This research is a fundamental analysis of a growth monitoring method for plant production control. Two varieties of lettuce, Telme lettuce and Tango lettuce, were made into the object in this research. The number of days after planting of the lettuce was determined by image analysis and the neural network. For Telme lettuce, the 10th, 20th and 30th days after planting were set as the target dates to note. For Tango lettuce, the 7th, 14th and 21st days were fixed as objectives. In the previous analysis, the number of days was recognized by linear discriminant analysis. The error rate of the recognition by the linear method was 2.5% for Telme lettuce and 20% for Tango lettuce. The Tango lettuce showed a large individual difference in the image features. Thus, the features were distributed widely in the feature space and there were many intersections among the three groups. It was difficult to separate the space into three parts by the discriminant planes. Therefore, the non-linear method was adopted. The accuracy of the discrimination was improved by the neural network. The error rate decreased down to 1.00% for Telme lettuce and 14.7% for Tango lettuce. These results show the high feasibility of incorporating the discriminant algorithm into the monitoring instrumentation for the growth control system.

An Improved Training Algorithm for Nonlinear Kernel Discriminants

A simple method to derive nonlinear discriminants is to map the samples into a high-dimensional feature space F using a nonlinear function and then to perform a linear discriminant analysis in F. Clearly, if F is a very high, or even infinitely, dimensional space, designing such a receiver may be a computationally intractable problem. However, using Mercer kernels, this problem can be solved without explicitly mapping the data to F. Recently, a powerful method of obtaining nonlinear kernel Fisher discriminants (KFDs) has been proposed, and very promising results were reported when compared with the other state-of-the-art classification techniques. In this paper, we present an extension of the KFD method that is also based on Mercer kernels. Our approach, which is called the nonlinear kernel second-order discriminant (KSOD), consists of determining a nonlinear receiver via optimization of a general form of second-order measures of performance. We also propose a complexity control procedure in order to improve the performance of these classifiers when few training data are available. Finally, simulations compare our approach with the KFD method.

Low-Power High-Contrast Coded Waveform Discrimination at 10 GHz Via Nonlinear Processing

We demonstrate ultrafast optical code-division multiple-access nonlinear waveform discrimination at 10 GHz with less than 1 mW coupled into a nonlinear periodically poled lithium niobate waveguide and greater than 20-dB contrast ratio between coded and uncoded waveforms. Excellent signal-to-noise is observed at the system receiver, pointing toward the practicability of nonlinear waveform discrimination in a system environment.

Nonlinear price discrimination with a finite number of consumers and constrained recontracting

In the monopoly nonlinear pricing problem with unobservable consumer types, we study mechanisms in which the firm makes the set of consumer options conditional on the aggregate reports of consumer types it receives. Previous mechanisms that exploit knowledge of the true type distribution often have multiple equilibria or use noncredible contracts off the equilibrium path. When the monopolist can replace contracts after initial reports subject to the constraint that truthful consumers are not made worse off, the outcome is essentially the same as when the monopolist has full information. This holds whether or not the monopolist can make offers to consumers who reject all original contract offers. When the monopolist must guarantee nonnegative surplus to all truthful consumers in all contingencies, the equilibrium outcome has undistorted contracts but lower profits for the monopolist.

Spectrally coded O-CDMA system with four users at 2.5 Gbit/s using low power nonlinear processing

A four-user 2.5 Gbit/s optical code-division multiple-access (O-CDMA) system is demonstrated at ≤10−11 BER utilising programmable spectral phase encoding, an ultrasensitive (<0.4 pJ/bit) PPLN-waveguide nonlinear waveform discriminator, and a 10G Ethernet receiver.

Pattern recognition of weld defects detected by radiographic test

In recent years there has been a marked advance in the research for the development of an automatized system to analyze weld defects detected by radiographs. This work describes a study of nonlinear pattern classifiers, implemented by artificial neural networks, to classify weld defects existent in radiographic weld beads, aiming principally to increase the percentage of defect recognition success obtained with the linear classifiers. Radiographic patterns from International Institute of Welding (IIW) were used. Geometric features of defect classes were used as input data of the classifiers. Using a novel approach for this area of research, a criterion of neural relevance was applied to evaluate the discrimination capacity of the classes studied by the features used, aiming to prove that the quality of the features is more important than the quantity of features used. Well known for other applications, but still not exploited in weld defect recognition, the analytical techniques of the principal nonlinear discrimination components, also developed by neural networks, are presented to show the classification problem in two dimensions, as well as evaluating the classification performance obtained with these techniques. The results prove the efficiency of the techniques for the data used.

Stimulus generalization in two associative learning processes.

Recent studies involving nonlinear discrimination problems suggest that stimuli in human associative learning are represented configurally with narrow generalization, such that presentation of stimuli that are even slightly dissimilar to stored configurations weakly activate these configurations. The authors note that another well-known set of findings in human associative learning, cue-interaction phenomena, suggest relatively broad generalization. Three experiments show that current models of human associative learning, which try to model both nonlinear discrimination and cue interaction as the result of 1 process, fail because they cannot simultaneously account for narrow and broad generalization. Results suggest that human associative learning involves (a) an exemplar-based process with configural stimulus representation and narrow generalization and (b) an adaptive learning process characterized by broad generalization and cue interaction.

Second-Order Measures of Quality for Binary Classification: A Critical Overview and their Use for Nonlinear Receiver Design

When deriving a detector, we are often led to consider design criteria such as second-order measures of quality. The aim of this paper is to provide a critical overview of these criteria. We first consider the case of deriving unconstrained detectors. We show that second-order criteria must satisfy a non-trivial condition to yield Bayes-optimal receivers, to be considered as relevant criteria for detector design. Next, we address the case where constraints are imposed on the detection structure, leading us to consider some set ${\cal {D}} of admissible detectors. In these conditions we prove that even if there exists a monotonic function of the likelihood ratio in ${\cal {D}} obtaining this statistic via the optimization of a second-order criterion, relevant or not, is not guaranteed. Results are illustrated by simulation examples. Finally, in order to derive nonlinear discriminants via optimization of second-order criteria, we propose a method based on the kernel trick used in the implementation of the w...

Reduction of the error floor of binary fsk by nonlinear frequency discriminators

We consider the error floor of binary frequency-shift keying (FSK) due to intersymbol interference in time-dispersive mobile radio channels, with a limiter-discriminator-integrator detector. The errors are caused by bursts in the instantaneous frequency. We propose and verify that a nonlinear frequency discriminator can achieve zero error floor for pure FSK by clipping off these bursts. For filtered FSK, the error floor is not completely removed, but strongly reduced - typically by one or two orders of magnitude. The tighter the filtering, the less effective this nonlinearity is. The nonlinear discriminator can also be used in conjunction with adaptive sampling.

Toxicity Mode‐of‐action: Discrimination via Infrared Spectra And Eigenvalues of the Modified Adjacency Matrix

AbstractAquatic toxicity can be partitioned into a number of mechanisms of action, the allocation of a given chemical to its particular mode being of fundamental importance for the toxicological risk assessment. We investigated the possibility to automatically allocate each chemical to its putative aquatic toxicity mode‐of‐action on the basis of the sole chemical physical information. In this paper, we refer to the four mode‐of‐action classes defined in Hermens' laboratory [1, 2]; the chemical descriptors used were the Infrared spectra and the Burden's Modified Adjacency Matrix Eigenvalues. At odds with Infrared spectrum, the Eigenvalues were able to allocate the chemicals into the different mechanism of action classes via a nonlinear discrimination method (K‐nearest neighbours classifier).

EXTRACTING FEATURE SUBSPACE FOR KERNEL BASED LINEAR PROGRAMMING SUPPORT VECTOR MACHINES

We propose linear programming formulations of support vector machines (SVM). Unlike standard SVMs which use quadratic programs, our approach explores a fairly small dimensional subspace of a feature space to construct the nonlinear discriminator. This allows us to obtain the discriminator by solving a smaller sized linear program. We demonstrate that an orthonormal basis of the subspace can be implicitly treated by eigenvectors of the Gram matrix defined by the associated kernel function. When the number of given data points is very large, we construct a subspace by random sampling of data points. Numerical experiments indicate that the subspace generated by less than 2% of the entire training data points achieves reasonable performance for a fairly large instance with 60000 data points.

Maximum margin equalizers trained with the Adatron algorithm

In this paper we apply the structural risk minimization principle as an appropriate criterion to train decision feedback and transversal equalizers. We consider both linear discriminant (optimal hyperplane) and nonlinear discriminant (support vector machine) classifiers as an alternative to the linear minimum mean-square error (MMSE) equalizer and radial basis function (RBF) networks, respectively. A fast and simple adaptive algorithm called the Adatron is applied to obtain the linear or nonlinear classifier. In this way we avoid the high computational cost of quadratic programming. Moreover, the use of soft margin (regularized) classifiers is proposed as a simple way to consider “noisy” channel states: this alternative improves the bit error rate, mainly at low SNR's. Furthermore, an adaptive implementation is discussed. Some simulation examples show the advantages of the proposed linear and nonlinear equalizers: a better performance in comparison to the linear MMSE and a simpler structure in comparison to the RBF (Bayesian).

Evidence for the utilization of distinctive features in nonlinear discrimination problems

There is evidence that in human Pavlovian conditioning positive patterning (A−, B−, AB+) as well as negative patterning (A+, B+, AB−) are solved by applying abstract rules. In the present report we further investigated how humans solve patterning discriminations by conducting two Go/NoGo reaction time experiments that utilized the stimulus probability effect: stimuli presented with a low probability of occurrence elicit larger pupil dilations than those presented with a high frequency. In decreasing the ratio of compound and elemental trials from 1/1 (24 A, 24 B, 48 AB) in Experiment 1 to 1/2 (32 A, 32 B, 32 AB) in Experiment 2 we manipulated stimulus probability. The results of both experiments indicate that humans utilize distinctive features such as number information in order to classify the stimuli.

Diamond potential estimation based on kimberlite major element chemistry

A strong correlation between the chemical composition of kimberlites and their diamond grade has been established using statistical methods. The investigation is based upon major element analyses of kimberlite samples, from which xenoliths have been removed. The samples represent highly diamondiferous, moderately diamondiferous, slightly diamondiferous and diamond-free rocks from diatremes of the Yakutian Kimberlite Province. In total, the investigation comprises 3792 whole-rock analyses and 1176 determinations of diamond grade. By means of correlation analysis, the kimberlite chemical analyses were subdivided into 113 clusters. Regression analysis was carried out between mean major element oxide concentrations of the clusters and the corresponding average values of diamond contents. The combined use of the regression method with a break-point and generalized nonlinear discrimination analysis has allowed to correctly estimate the average diamond grade of kimberlite clusters in more than 85–90% of the cases. The established statistical relations are convincingly justified from a petrological point of view. The reliable petrochemical description of kimberlite variety, based on averaging 25–30 whole-rock analyses or on analyzing of a sample obtained as a result of sequential quartering of a much larger sample, allows to estimate safely its diamond grade using major oxide contents. The method has worldwide application potential.

Probing the Time Course of Nonlinear Discriminations during Human Electrodermal Conditioning

Animal-based theories of Pavlovian conditioning propose that patterning discriminations are solved using unique cues or immediate configuring. Recent studies with humans, however, provided evidence that in positive and negative patterning two different rules are utilized. The present experiment was designed to provide further support for this proposal by tracking the time course of the allocation of cognitive resources. One group was trained in a positive patterning schedule (A−, B−, AB+) and a second in a negative patterning schedule (A+, B+, AB−). Electrodermal responses and secondary task probe reaction time were measured. In negative patterning, reaction times were slower during reinforced stimuli than during nonreinforced stimuli at both probe positions while there were no differences in positive patterning. These results support the assumption that negative patterning is solved using a rule that is more complex and requires more resources than does the rule employed to solve positive patterning.

Independent task Fourier filters

Since the early 1960s, a major part of optical computing systems has been Fourier pattern recognition, which takes advantage of high speed filter changes to enable powerful nonlinear discrimination in real time.'' Because filter has a task quite independent of the tasks of the other filters, they can be applied and evaluated in parallel or, in a simple approach I describe, in sequence very rapidly. Thus I use the name ITFF (independent task Fourier filter). These filters can also break very complex discrimination tasks into easily handled parts, so the wonderful space invariance properties of Fourier filtering need not be sacrificed to achieve high discrimination and good generalizability even for ultracomplex discrimination problems. The training procedure proceeds sequentially, as the task for a given filter is defined a posteriori by declaring it to be the discrimination of particular members of set A from all members of set B with sufficient margin. That is, we set the threshold to achieve the desired margin and note the A members discriminated by that threshold. Discriminating those A members from all members of B becomes the task of that filter. Those A members are then removed from the set A, so no other filter will be asked to perform that already accomplished task.

Synchronously mode-locked fiber laser based on parametric gain modulation and soliton shaping

A novel synchronously mode-locked fiber laser is demonstrated by combining the parametric gain modulation in a pulse-pumped nonlinear optical loop mirror (NOLM) with the soliton shaping property of a nonlinear amplifying loop mirror (NALM). Parametric gain modulation induced by the synchronous pump pulses within the NOLM starts and defines the timing of the mode-locked signal pulses, while the nonlinear intensity discrimination in the NALM stabilizes the mode-locked pulses and optimizes their shapes. A stream of 1.3 ps transform-limited soliton pulses is generated when the NOLM is pumped by a mode-locked fiber laser. Moreover, we find that the timing jitter of the synchronously mode-locked pulse train is suppressed by more than 10 dB when compared to the pumping laser.

Discrimination of anesthetic states using mid-latency auditory evoked potential and artificial neural networks.

This study was undertaken to determine whether artificial neural network (ANN) processing of mid-latency auditory evoked potentials (MLAEPs) can identify different anesthetic states during propofol anesthesia, and to determine those parameters that are most useful in the identification process. Twenty-one patients undergoing elective abdominal surgery were studied. To maintain general anesthesia, the patients received propofol (3-5 mgkg(-1) h(-1) intravenously). Epidural analgesia at the level of T4-5 blocked painful stimuli. MLAEP was recorded continuously with patients awake, during induction, during maintenance of general anesthesia, and during emergence until the patients were recovered from anesthesia. Latencies of the 5 MLAEP peaks and three peak to peak amplitudes were measured, along with hemodynamic parameters (heart rate, systolic, and diastolic arterial blood pressure). Four-layer ANNs were used to model the relationship between the parameters of the MLAEP and the four different states (awake, adequate anesthesia, during/before intraoperative movement, and emergence from anesthesia). The best identification accuracy was obtained using only the five latencies. The combination of five latencies and three amplitudes did not improve the identification accuracy. Use of the only the three hemodynamic parameters produced a much poorer identification. This study suggests that the MLAEP has useful information for identifying different anesthetic states, especially in its latencies. A nonlinear discrimination approach, such as the ANN, can effectively capture the relation between the MLAEP patterns and the different states of anesthesia.