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Otoacoustic emission (OAE) biometrics are inherently robust to replay and falsification attacks. The widely studied transient-evoked OAE (TEOAE) is non-stationary and offers biometric value only in normal-hearing individuals since it is more susceptible to hearing loss. To address these issues, this paper presents a novel yet promising OAE biometric modality-stimulus-frequency OAE (SFOAE). Unlike TEOAE, SFOAE is a highly stationary signal whose fine structures are idiosyncratic to an individual, and relatively stable over time, making it easier to be a biometric without additional complex feature extraction. Moreover, SFOAE is even present in ears with 50 dB HL hearing loss, applicable to hearing-impaired users. In this paper, SFOAE spectra in response to three stimulus levels are fused in the feature level to consolidate different information, followed by a linear discriminant analysis or a multi-kernel convolutional neural network to further reduce the intra-subject variability and increase the inter-subject variability. Tested on a large cohort of subjects containing varying levels of deafness, the SFOAE-based biometric system yields an equal error rate of 0.541% and 1.364% in closed-set and open-set verification scenarios, respectively. In an identification mode, 99.43% and 97.37% accuracies are attained for closed-set and open-set protocols, respectively. In particular, we observe perfect performance in a population restricted to normal hearing in closed-set scenarios. The reason why the system performs well has been examined based on several comparative tests. Although there are implementation issues to be resolved before SFOAE can be applied in the field of biometric, this paper preliminarily demonstrates the basis and excellent potential of SFOAE as a biometric. [ABSTRACT FROM AUTHOR]

This paper presents a simple and effective approach to recognize ultra-high-frequency (UHF) signals of partial discharges (PDs). Six artificial insulation defect models were designed to generate UHF PD signals, which were detected by a Hilbert fractal antenna in a series of experiments. Wavelet packet (WP) decomposition was used to decompose the UHF PD signals into multiple scales. A number of multi-scale fractal dimensions and energy parameters of UHF PD signals were computed and linear discriminant analysis (LDA) was used to reduce the dimensionality of the problem while maximising separation among defected types. The low-dimension data were successfully classified via a simple scheme based on finding the closest class centroid. As a comparison, a back-propagation neural network (BPNN) and a support vector machine (SVM) were also used for recognition of the defects and found to offer no advantage. The recognition experiments were replicated 100 times to establish the robustness of the solutions and the LDA was also found to be superior in this respect. Further results examining the effects of refraction and reflection by transformer components support the conclusion that the proposed approach has potential for the recognition of PDs in practical situations. [ABSTRACT FROM PUBLISHER]

Dimension reduction is a critical technology for high-dimensional data processing, where Linear Discriminant Analysis (LDA) and its variants are effective supervised methods. However, LDA prefers to feature with smaller variance, which causes feature with weak discriminative ability retained. In this paper, we propose a novel Ratio Sum for Linear Discriminant Analysis (RSLDA), which aims at maximizing discriminative ability of each feature in subspace. To be specific, it maximizes the sum of ratio of the between-class distance to the within-class distance in each dimension of subspace. Since the original RSLDA problem is difficult to obtain the closed solution, an equivalent problem is developed which can be solved by an alternative optimization algorithm. For solving the equivalent problem, it is transformed into two sub-problems, one of which can be solved directly, the other is changed into a convex optimization problem, where singular value decomposition is employed instead of matrix inversion. Consequently, performance of algorithm cannot be affected by the non-singularity of covariance matrix. Furthermore, Kernel RSLDA (KRSLDA) is presented to improve the robustness of RSLDA. Additionally, time complexity of RSLDA and KRSLDA are analyzed. Extensive experiments show that RSLDA and KRSLDA outperforms other comparison methods on toy datasets and multiple public datasets. [ABSTRACT FROM AUTHOR]

Brain computer interface translates electroencephalogram (EEG) signals into control commands so that paralyzed people can control assistive devices. This human thought translation is a very challenging process as EEG signals contain noise. For noise removal, a bandpass filter or a filter bank is used. However, these techniques also remove useful information from the signal. Furthermore, after feature extraction, there are such features which do not play any significant role in effective classification. Thus, soft computing-based EEG classification followed by extraction and then selection of optimal features can produce better results. In this paper, subband common spatial patterns using sequential backward floating selection is being proposed in order to classify motor-imagery-based EEG signals. The signal is decomposed into subband using a filter bank having overlapped frequency cutoffs. Linear discriminant analysis followed by common spatial pattern is applied to the output of each filter for features extraction. Then, sequential backward floating selection is applied for selection of optimal features to train radial basis function neural networks. Two different datasets have been used for evaluation of results, i.e., Open BCI dataset and EEG signals acquired by Emotiv Epoc. The proposed system shows an overall accuracy of 93.05% and 85.00% for both datasets, respectively. The results show that the proposed optimal feature selection and neural network-based classification approach with overlapped frequency bands is an effective method for EEG classification as compared to previous techniques. [ABSTRACT FROM AUTHOR]

The electroencephalogram (EEG) signals tend to have poor time-frequency localization when analysis techniques involve a fixed set of basis functions such as in short-time Fourier transform and wavelet transform. These signals also exhibit highly non-stationary characteristics and suffer from low signal-to-noise ratio (SNR). As a result, there is often poor task detection accuracy and high error rates in designed brain-computer interfacing (BCI) systems. In this paper, a novel preprocessing method is proposed to automatically reconstruct the EEG signal by selecting the intrinsic mode functions (IMFs) based on a median frequency measure. Multivariate empirical mode decomposition is used to decompose the EEG signals into a set of IMFs. The reconstructed EEG signal has high SNR and contains only information correlated to a specific motor imagery task. The common spatial pattern is used to extract features from the reconstructed EEG signals. The linear discriminant analysis and support vector machine have been utilized in order to classify the features into left hand motor imagery and right hand motor imagery tasks. Our experimental results on the BCI competition IV dataset 2A show that the proposed method with fifteen channels outperforms bandpass filtering with 22 channels (>1%) and by >9 % $(p = 0.0078)$ with raw EEG signals, >13% $(p = 0.0039)$ with empirical mode decomposition-based filtering and >17 % $(p = 0.0039)$ with discrete wavelet transform-based filtering. [ABSTRACT FROM AUTHOR]

The tree Acacia mearnsii is native to south-eastern Australia but has become an aggressive invader in many countries. In South Africa, it is a significant threat to the conservation of biomes. Detecting and mapping its early invasion is critical. The current ground-based methods to map A. mearnsii are accurate but are neither economical nor practical. Remote sensing (RS) provides accurate and repeatable spatial information on tree species. The potential of RS technology to map A. mearnsii distributions remains poorly understood, mainly due to a lack of knowledge on the spectral properties of A. mearnsii relative to co-occurring native plants. We investigated the spectral uniqueness of A. mearnsii compared to co-occurring native plant species within the South African landscape. We explored full-range (400–2500 nm), leaf and canopy hyperspectral reflectance of the species. The spectral reflectance was collected biweekly from December 23, 2016 and May 31, 2017. We conducted a time series analysis, to assess the effect of seasonality on species discrimination. For comparison, two classification models were employed: parametric interval extended canonical variate discriminant (iECVA-DA) and nonparametric random forest discriminant classifiers (RF-DA). The results of this paper suggest that phenology plays a crucial role in discriminating between A. mearnsii and sampled species. The RF classifier discriminated A. mearnsii with slightly higher accuracies (from 92% to 100%) when compared with the iECVA-DA (from 85% to 93%). The study showed the potential of RS to discriminate between A. mearnsii and co-occurring plant species. [ABSTRACT FROM AUTHOR]

Myoelectric-based decoding strategies offer significant advantages in the areas of human-machine interactions because they are intuitive and require less cognitive effort from the users. However, a general drawback in using machine learning techniques for classification is that the decoder is limited to predicting only one movement at any instant and hence restricted to performing the motion in a sequential manner, whereas human motor control strategy involves simultaneous actuation of multiple degrees of freedom (DOFs) and is considered to be a natural and efficient way of performing tasks. Simultaneous decoding in the context of myoelectric-based movement control is a challenge that is being addressed recently and is increasingly popular. In this paper, we propose a novel classification strategy capable of decoding both the individual and combined movements, by collecting data from only the individual motions. Additionally, we exploit low-dimensional representation of the myoelectric signals using a supervised decomposition algorithm called linear discriminant analysis, to simplify the complexity of control and reduce computational cost. The performance of the decoding algorithm is tested in an online context for the two DOFs task comprising the hand and wrist movements. Results indicate an overall classification accuracy of 88.02% for both the individual and combined motions. [ABSTRACT FROM AUTHOR]

Discriminative methods commonly produce models with relatively good generalization abilities. However, this advantage is challenged in real-world applications (e.g., medical image analysis problems), in which there often exist outlier data points (sample-outliers) and noises in the predictor values (feature-noises). Methods robust to both types of these deviations are somewhat overlooked in the literature. We further argue that denoising can be more effective, if we learn the model using all the available labeled and unlabeled samples, as the intrinsic geometry of the sample manifold can be better constructed using more data points. In this paper, we propose a semi-supervised robust discriminative classification method based on the least-squares formulation of linear discriminant analysis to detect sample-outliers and feature-noises simultaneously, using both labeled training and unlabeled testing data. We conduct several experiments on a synthetic, some benchmark semi-supervised learning, and two brain neurodegenerative disease diagnosis datasets (for Parkinson’s and Alzheimer’s diseases). Specifically for the application of neurodegenerative diseases diagnosis, incorporating robust machine learning methods can be of great benefit, due to the noisy nature of neuroimaging data. Our results show that our method outperforms the baseline and several state-of-the-art methods, in terms of both accuracy and the area under the ROC curve. [ABSTRACT FROM AUTHOR]

The research on new materials, fabrication processes, and characterization methods aims at obtaining sensors with low cost, high sensibility, and possibility of integration with electronic circuits. Recently, several works have focused on the development of gas sensors based on nanomaterials deposited on insulating platforms due to the remarkable sensing properties of such materials and simple device fabrication methods. However, the interference of such insulating platforms in the sensing properties of a miniaturized sensor becomes non-negligible depending on the dimensions, the type and amount of material, and the gas species analyzed. Thus, this paper proposes the use of interdigital aluminum microelectrodes patterned on a glass substrate to evaluate the influence of adsorption and desorption mechanisms of humidity and volatile organic compounds on this insulating surface. By analyzing the electrical conduction changes when the device is exposed to the mentioned vapors, we demonstrate that this influence is quite significant, as the electrical resistance of the glass insulating platform presented pronounced and fast resistance variation with repeatability and low drift. In addition, the selectivity among the experimented gas species was achieved by applying principal component analysis and supervised linear discriminant analysis classification methodologies, obtaining a success rate of 94% by using a cross-validation technique. The results show that the sensing properties of insulating platforms must be considered in some situations because they can affect the response of sensors based on nanomaterials deposited on insulating substrates. [ABSTRACT FROM AUTHOR]

Shoulder movements are not considered for electromyography-based pattern classification control, due to the difficulty to manufacture three-degrees-of-freedom shoulder prostheses. This paper aims at exploring the feasibility of classifying up to nine shoulder movements by processing surface electromyography signals from eight trunk muscles. Experimenting with different pattern recognition methods, two classifiers were developed, considering six different combinations of window sizes and increments, and three feature sets for each channel. Applying linear discriminant analysis the best performance was obtained on a window length of 500 ms associated to temporal increments of 62 ms. This setting yielded a 100% accuracy for recognizing four movements, and progressively degraded to 92% for nine movements. Using neural networks, higher accuracy was obtained in particular in the 9-class problem. Finally, the signals from the eight channels were analyzed in order to check the possibility to reduce the number of acquisition channels. [ABSTRACT FROM PUBLISHER]

The trace ratio optimization (TRO) problem consists of finding an orthonormal basis for the discriminative subspace that maximizes the ratio of two trace operators on two covariance matrices corresponding to two distinctive classes or signal components. The TRO problem is encountered in various signal processing problems such as dimensionality reduction, signal enhancement, and discriminative analysis. In this paper, we propose a distributed and adaptive algorithm for solving the TRO problem in the context of wireless sensor networks (WSNs), where the two matrices involved in the trace ratio operators correspond to the (unknown) spatial correlation of the sensor signals across the nodes in the network. We first focus on fully-connected networks where every node can communicate with each other, but only compressed signals observations can be shared to reduce the communication cost. After showing convergence, we modify the algorithm to operate in WSNs with more general topologies. Simulation results are provided to validate and complement the theoretical results. [ABSTRACT FROM AUTHOR]

Bearings are critical components in induction motors and brushless direct current motors. Bearing failure is the most common failure mode in these motors. By implementing health monitoring and fault diagnosis of bearings, unscheduled maintenance and economic losses caused by bearing failures can be avoided. This paper introduces trace ratio linear discriminant analysis (TR-LDA) to deal with high-dimensional non-Gaussian fault data for dimension reduction and fault classification. Motor bearing data with single-point faults and generalized-roughness faults are used to validate the effectiveness of the proposed method for fault diagnosis. Comparisons with other conventional methods, such as principal component analysis, local preserving projection, canonical correction analysis, maximum margin criterion, LDA, and marginal Fisher analysis, show the superiority of TR-LDA in fault diagnosis. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a novel discriminative dimension reduction (DR) method, maximin separation probability analysis (MSPA), which maximizes the minimum separation probability of all classes in the reduced low-dimensional subspace. Separation probability is a novel class separability measure, which gives a lower bound of the generalization accuracy for a learned linear classifier in a binary classification problem. The proposed MSPA duly considers the separation of all class pairs in multiclass linear discriminant analysis (LDA) and thus improves the subsequent classification performance. DR via MSPA leads to a nonconvex optimization problem. We develop an algorithm to solve the problem and the global optimal solution can be found by converting the original problem into a series of second-order cone programming problems. A low-computational cost extension and a non-LDA with kernel mapping of MSPA are also provided in this paper. The experimental results on 14 real-world datasets show our methods are superior to other state-of-the-art algorithms in discriminative DR tasks. [ABSTRACT FROM AUTHOR]

Recent works have proposed two L1-norm distance measure-based linear discriminant analysis (LDA) methods, L1-LD and LDA-L1, which aim to promote the robustness of the conventional LDA against outliers. In LDA-L1, a gradient ascending iterative algorithm is applied, which, however, suffers from the choice of stepwise. In L1-LDA, an alternating optimization strategy is proposed to overcome this problem. In this paper, however, we show that due to the use of this strategy, L1-LDA is accompanied with some serious problems that hinder the derivation of the optimal discrimination for data. Then, we propose an effective iterative framework to solve a general L1-norm minimization–maximization (minmax) problem. Based on the framework, we further develop a effective L1-norm distance-based LDA (called L1-ELDA) method. Theoretical insights into the convergence and effectiveness of our algorithm are provided and further verified by extensive experimental results on image databases. [ABSTRACT FROM PUBLISHER]

This paper investigates the effect of utterance duration to the calibration of a modern i-vector speaker recognition system with probabilistic linear discriminant analysis (PLDA) modeling. A calibration approach to deal with these effects using quality measure functions (QMFs) is proposed to include duration in the calibration transformation. Extensive experiments are performed in order to evaluate the robustness of the proposed calibration approach for unseen conditions in the training of calibration parameters. Using the latest NIST corpora for evaluation, results highlight the importance of considering the quality metrics like duration in calibrating the scores for automatic speaker recognition systems. [ABSTRACT FROM PUBLISHER]

Linear discriminant analysis (LDA) is one of commonly used supervised subspace learning methods. However, LDA will be powerless faced with the no-label situation. In this paper, the unsupervised LDA (Un-LDA) is proposed and first formulated as a seamlessly unified objective optimization which guarantees convergence during the iteratively alternative solving process. The objective optimization is in both the ratio trace and the trace ratio forms, forming a complete framework of a new approach to jointly clustering and unsupervised subspace learning. The extension of LDA into Un-LDA enables to not only complete unsupervised subspace learning via the explicitly presented subspace projection matrix but also simultaneously finish clustering and even clustering out-of-sample data via the explicitly presented transformation matrix. To overcome the difficulty in solving the non-convex objective optimization, we mathematically prove that the Un-LDA optimization in both forms can be transformed into the simple K-means clustering optimization when the subspace is determined. The Un-LDA optimization is eventually completed by alternatively optimizing the clusters using K-means and the subspace using the supervised LDA methods and iterating this whole process until convergence or stopping criterion. The experiments demonstrate that our proposed Un-LDA algorithms are comparable or even much superior to the counterparts. [ABSTRACT FROM AUTHOR]

This paper proposes a novel method called Jointly Sparse Locality Regression (JSLR) for feature extraction and selection. JSLR utilizes joint $L_{2,1}$ -norm minimization on regularization term, and also introduces the locality to characterize the local geometric structure of the data. There are three main contributions in JSLR for face recognition. Firstly, it eliminates the drawback in ridge regression and Linear Discriminant Analysis (LDA) that when the number of the classes is too small, not enough projections can be obtained for feature extraction. Secondly, by using the local geometric structure as the regularization term, JSLR is able to preserve local information and find an embedding subspace which can detect the most essential data manifold structure. Moreover, since the $L_{2,1}$ -norm based loss function is robust to outliers in data points, JSLR provides the joint sparsity for robust feature selection. The theoretical connections of the proposed method and the previous regression methods are explored and the convergence of the proposed algorithm is also proved. Experimental evaluation on several well-known data sets shows the merits of the proposed method on feature selection and classification. [ABSTRACT FROM AUTHOR]

Linear discriminant analysis has been incorporated with various representations and measurements for dimension reduction and feature extraction. In this paper, we propose two-dimensional quaternion sparse discriminant analysis (2D-QSDA) that meets the requirements of representing RGB and RGB-D images. 2D-QSDA advances in three aspects: 1) including sparse regularization, 2D-QSDA relies only on the important variables, and thus shows good generalization ability to the out-of-sample data which are unseen during the training phase; 2) benefited from quaternion representation, 2D-QSDA well preserves the high order correlation among different image channels and provides a unified approach to extract features from RGB and RGB-D images; 3) the spatial structure of the input images is also retained via the matrix-based processing. We tackle the constrained trace ratio problem of 2D-QSDA by solving a corresponding constrained trace difference problem, which is then transformed into a quaternion sparse regression (QSR) model. Afterward, we reformulate the QSR model to an equivalent complex form to avoid the processing of the complicated structure of quaternions. A nested iterative algorithm is designed to learn the solution of 2D-QSDA in the complex space and then we convert this solution back to the quaternion domain. To improve the separability of 2D-QSDA, we further propose 2D-QSDAw using the weighted pairwise between-class distances. Extensive experiments on RGB and RGB-D databases demonstrate the effectiveness of 2D-QSDA and 2D-QSDAw compared with peer competitors. [ABSTRACT FROM AUTHOR]

Non-negative Matrix Factorization (NMF) has been one of the most popular clustering techniques in machine leaning, and involves various real-world applications. Most existing works perform matrix factorization on high-dimensional data directly. However, the intrinsic data structure is always hidden within the low-dimensional subspace. And, the redundant features within the input space may affect the final result adversely. In this paper, a new unsupervised matrix factorization method, Discrimination-aware Projected Matrix Factorization (DPMF), is proposed for data clustering. The main contributions are threefold: (1) The linear discriminant analysis is jointly incorporated into the unsupervised matrix factorization framework, so the clustering can be accomplished in the discriminant subspace. (2) The manifold regularization is introduced to perceive the geometric information, and the ${\ell _{2,1}}$ ℓ 2 , 1 -norm is utilized to improve the robustness. (3) An efficient optimization algorithm is designed to solve the proposed problem with proved convergence. Experimental results on one toy dataset and eight real-world benchmarks show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Dimension reduction is frequently adopted as a data preprocessing technique to facilitate data visualization, interpretation, and classification. Traditional dimension reduction methods such as linear discriminant analysis focus on maximizing the overall discrimination between all classes, which may be easily affected by outliers. To overcome this disadvantage, this paper proposes a novel method for multiclass dimension reduction, named dimension reduction by minimum error minimax probability machine (DR-MEMPM). It elaborately ensures that each pair of classes is well separated in the projected subspace by utilizing the separation probability between different pairwise classes. Therefore, it can put more emphasis on those less distinguishable classes, and the learned projection will not be dominated by some “outlier” classes which lie far away from other classes. We evaluate the proposed DR-MEMPM on a number of synthetic and real-world data sets, and show that it outperforms other state-of-the-art dimension reduction methods in terms of visual intuition and classification accuracy, especially when the distances between classes are unevenly distributed. [ABSTRACT FROM AUTHOR]

Big data applications, such as medical imaging and genetics, typically generate datasets that consist of few observations \boldsymbol n on many more variables \boldsymbol p, a scenario that we denote as \boldsymbol p\gg\boldsymbol n. Traditional data processing methods are often insufficient for extracting information out of big data. This calls for the development of new algorithms that can deal with the size, complexity, and the special structure of such datasets. In this paper, we consider the problem of classifying \boldsymbol p\gg\boldsymbol n data and propose a classification method based on linear discriminant analysis (LDA). Traditional LDA depends on the covariance estimate of the data, but when \boldsymbol p\gg\boldsymbol n, the sample covariance estimate is singular. The proposed method estimates the covariance by using a sparse version of noisy principal component analysis (nPCA). The use of sparsity in this setting aims at automatically selecting variables that are relevant for classification. In experiments, the new method is compared to state-of-the art methods for big data problems using both simulated datasets and imaging genetics datasets. [ABSTRACT FROM PUBLISHER]

Classical linear discriminant analysis (LDA) has the limitation that it requires the within-class scatter matrix to be nonsingular so that it can perform eigen-decomposition to obtain optimal solutions. To break through this limitation, many methods based on LDA have been proposed. However, these methods are either sensitive to outliers or lack joint sparsity for effective feature extraction. To release these problems, this paper proposes a locally joint sparse marginal embedding (LJSME) method. LJSME reconstructs the scatter matrices and utilizes the locality graph to weigh each pair of data, such that it is robust to outliers and able to preserve the neighborhood relationship of the data. Moreover, LJSME can easily avoid the small sample-size problem by a maximum margin criterion and obtain joint sparsity for effective feature extraction by using joint sparse regularization. The comprehensive analysis between the proposed LJSME and the related methods is presented, which indicates the advantages of the proposed method. A series of experiments was conducted to evaluate the performance of LJSME when compared with the state-of-the-art methods. The MATLAB code of LJSME can be downloaded from https://github.com/TungmeeMo/LJSME.git. [ABSTRACT FROM AUTHOR]

Dimensionality reduction is a critical technology in the domain of pattern recognition, and linear discriminant analysis (LDA) is one of the most popular supervised dimensionality reduction methods. However, whenever its distance criterion of objective function uses $L_2$ -norm, it is sensitive to outliers. In this paper, we propose a new formulation of linear discriminant analysis via joint $L_{2,1}$ -norm minimization on objective function to induce robustness, so as to efficiently alleviate the influence of outliers and improve the robustness of proposed method. An efficient iterative algorithm is proposed to solve the optimization problem and proved to be convergent. Extensive experiments are performed on an artificial data set, on UCI data sets, and on four face data sets, which sufficiently demonstrates the efficiency of comparing to other methods and robustness to outliers of our approach. [ABSTRACT FROM AUTHOR]

Practical motor imagery-based brain computer interface (MI-BCI) applications are limited by the difficult to decode brain signals in a reliable way. In this paper, we propose a processing framework to address non-stationarity, as well as handle spectral, temporal, and spatial characteristics associated with execution of motor tasks. Stacked generalization is used to exploit the power of classifier ensembles for combining information coming from multiple sources and reducing the existing uncertainty in EEG signals. The outputs of several regularized linear discriminant analysis (RLDA) models are combined to account for temporal, spatial, and spectral information. The resultant algorithm is called stacked RLDA (SRLDA). Additionally, an adaptive processing stage is introduced before classification to reduce the harmful effect of intersession non-stationarity. The benefits of the proposed method are evaluated on the BCI Competition IV dataset 2a. We demonstrate its effectiveness in binary and multiclass settings with four different motor imagery tasks: left-hand, right-hand, both feet, and tongue movements. The results show that adaptive SRLDA outperforms the winner of the competition and other approaches tested on this multiclass dataset. [ABSTRACT FROM PUBLISHER]

Fisher’s linear discriminant analysis (FLDA) is an important dimension reduction method in statistical pattern recognition. It has been shown that FLDA is asymptotically Bayes optimal under the homoscedastic Gaussian assumption. However, this classical result has the following two major limitations: 1) it holds only for a fixed dimensionality $D$ , and thus does not apply when $D$ and the training sample size $N$ are proportionally large; 2) it does not provide a quantitative description on how the generalization ability of FLDA is affected by $D$ and $N$ . In this paper, we present an asymptotic generalization analysis of FLDA based on random matrix theory, in a setting where both $D$ and $N$ increase and $D/N\;\longrightarrow\; \gamma \in [0,1)$ . The obtained lower bound of the generalization discrimination power overcomes both limitations of the classical result, i.e., it is applicable when $D$ and $N$ are proportionally large and provides a quantitative description of the generalization ability of FLDA in terms of the ratio $\gamma =D/N$ and the population discrimination power. Besides, the discrimination power bound also leads to an upper bound on the generalization error of binary-classification with FLDA. [ABSTRACT FROM AUTHOR]

Linear discriminant analysis (LDA) is a very popular supervised feature extraction method and has been extended to different variants. However, classical LDA has the following problems: 1) The obtained discriminant projection does not have good interpretability for features; 2) LDA is sensitive to noise; and 3) LDA is sensitive to the selection of number of projection directions. In this paper, a novel feature extraction method called robust sparse linear discriminant analysis (RSLDA) is proposed to solve the above problems. Specifically, RSLDA adaptively selects the most discriminative features for discriminant analysis by introducing the $l_{2,1}$ norm. An orthogonal matrix and a sparse matrix are also simultaneously introduced to guarantee that the extracted features can hold the main energy of the original data and enhance the robustness to noise, and thus RSLDA has the potential to perform better than other discriminant methods. Extensive experiments on six databases demonstrate that the proposed method achieves the competitive performance compared with other state-of-the-art feature extraction methods. Moreover, the proposed method is robust to the noisy data. [ABSTRACT FROM AUTHOR]

Bimanual movements are an integral part of everyday activities and are often included in rehabilitation therapies. Yet, electroencephalography (EEG)-based assistive and rehabilitative brain–computer interface (BCI) systems typically rely on motor imagination (MI) of one limb at the time. In this paper, we present a classifier which discriminates between uni-and bi-manual MI. Ten able-bodied participants took part in cue-based motor execution (ME) and MI tasks of the left (L), right (R) and both (B) hands. A 32-channel EEG was recorded. Three linear discriminant analysis classifiers, based on MI of L–B, B–R, and B–L hands were created, with features based on wide band common spatial patterns (CSP) 8–30 Hz, and band specifics common spatial patterns (CSPb). Event-related desynchronization (ERD) was significantly stronger during bimanual compared to unimanual ME on both hemispheres. Bimanual MI resulted in bilateral parietally shifted ERD of similar intensity to unimanual MI. The average classification accuracy for CSP and CSPb was comparable for the L–R task (73% ± 9% and 75% ± 10%, respectively) and for the L–B task (73% ± 11% and 70% ± 9%, respectively). However, for the R–B task (67% ± 3% and 72% ± 6%, respectively), it was significantly higher for CSPb ($p = 0.0351$). Six participants whose L–R classification accuracy exceeded 70% were included in an online task a week later, using the unmodified offline CSPb classifier, achieving 69% ± 3% and 66% ± 3% accuracy for L–R and R–B tasks, respectively. Combined uni- and bi-manual BCI could be used for restoration of motor function of highly disabled patents and for motor rehabilitation of patients with motor deficits. [ABSTRACT FROM AUTHOR]

Spectral regression discriminant analysis (SRDA) has recently been proposed as an efficient solution to large-scale subspace learning problems. There is a tunable regularization parameter in SRDA, which is critical to algorithm performance. However, how to automatically set this parameter has not been well solved until now. So this regularization parameter was only set to be a constant in SRDA, which is obviously suboptimal. This paper proposes to automatically estimate the optimal regularization parameter of SRDA based on the perturbation linear discriminant analysis (PLDA). In addition, two parameter estimation methods for the kernel version of SRDA are also developed. One is derived from the method of optimal regularization parameter estimation for SRDA. The other is to utilize the kernel version of PLDA. Experiments on a number of publicly available databases demonstrate the effectiveness of the proposed methods for face recognition, spoken letter recognition, handwritten digit recognition, and text categorization. [ABSTRACT FROM PUBLISHER]

In this paper, we study canonical correlation analysis (CCA), which is a powerful tool in multivariate data analysis for finding the correlation between two sets of multidimensional variables. The main contributions of the paper are: 1) to reveal the equivalent relationship between a recursive formula and a trace formula for the multiple CCA problem, 2) to obtain the explicit characterization for all solutions of the multiple CCA problem even when the corresponding covariance matrices are singular, 3) to develop a new sparse CCA algorithm, and 4) to establish the equivalent relationship between the uncorrelated linear discriminant analysis and the CCA problem. We test several simulated and real-world datasets in gene classification and cross-language document retrieval to demonstrate the effectiveness of the proposed algorithm. The performance of the proposed method is competitive with the state-of-the-art sparse CCA algorithms. [ABSTRACT FROM PUBLISHER]

Ordinal regression has wide applications in many domains where the human evaluation plays a major role. Most current ordinal regression methods are based on Support Vector Machines (SVM) and suffer from the problems of ignoring the global information of the data and the high computational complexity. Linear Discriminant Analysis (LDA) and its kernel version, Kernel Discriminant Analysis (KDA), take into consideration the global information of the data together with the distribution of the classes for classification, but they have not been utilized for ordinal regression yet. In this paper, we propose a novel regression method by extending the Kernel Discriminant Learning using a rank constraint. The proposed algorithm is very efficient since the computational complexity is significantly lower than other ordinal regression methods. We demonstrate experimentally that the proposed method is capable of preserving the rank of data classes in a projected data space. In comparison to other benchmark ordinal regression methods, the proposed method is competitive in accuracy. [ABSTRACT FROM AUTHOR]

The success of linear discriminant analysis (LDA) is due in part to the simplicity of its formulation, which reduces to a simultaneous diagonalization of two symmetric matrices A and B. However, a fundamental drawback of this approach is that it cannot be efficiently applied wherever the matrix A is singular or when some of the smallest variances in A are due to noise. In this paper, we present a factorization of A-1B and a correlation-based criterion that can be readily employed to solve these problems. We provide detailed derivations for the linear and nonlinear classification problems. The usefulness of the proposed approach is demonstrated thoroughly using a large variety of databases. [ABSTRACT FROM AUTHOR]

Multivariate time series (MTS) is a kind of matrix data, typically consisting of multiple variables measured at multiple time points. Due to the high dimensionality of MTS data, many methods for MTS classification have been proposed within the literature to reduce the redundancy in time or variable mode, but there is relatively little work on exploring the redundancy in both modes concurrently. In this paper we propose a new method for MTS classification based on bidirectional linear discriminant analysis (BLDA). The advantage is that BLDA can utilize label information in reducing the redundancy in time and variable modes simultaneously. Moreover, the existing procedures for BLDA suffer from two problems: (i) BLDA cannot be performed when one of the within-class matrices is singular; (ii) the computational burden could be very heavy when one of the data dimensionality is high. A new procedure for BLDA based on pseudo-inverse (PBLDA) and an efficient algorithm for PBLDA are proposed in this paper to overcome the two problems. The performance of our proposed method is illustrated through the experiments on a number of real MTS datasets.

This paper presents a constructive method for deriving an updated discriminant eigenspace for classification when bursts of data that contains new classes is being added to an initial discriminant eigenspace in the form of random chunks. Basically, we propose an incremental linear discriminant analysis (ILDA) in its two forms: a sequential ILDA and a Chunk ILDA. In experiments, we have tested ILDA using datasets with a small number of classes and small-dimensional features, as well as datasets with a large number of classes and large-dimensional features. We have compared the proposed ILDA against the traditional batch LDA in terms of discriminability, execution time and memory usage with the increasing volume of data addition. The results show that the proposed ILDA can effectively evolve a discriminant eigenspace over a fast and large data stream, and extract features with superior discriminability in classification, when compared with other methods. [ABSTRACT FROM AUTHOR]

Linear Discriminant Analysis (LDA) is a well-known method for feature extraction and dimension reduction. It has been used widely in many applications involving high-dimensional data, such as image and text classification. An intrinsic limitation of classical LDA is the so-called singularity problems; that is, it fails when all scatter matrices are singular. Many LDA extensions were proposed in the past to overcome the singularity problems. Among these extensions, PCA+LDA, a two-stage method, received relatively more attention. In PCA+LDA, the LDA stage is preceded by an intermediate dimension reduction stage using Principal Component Analysis (PCA). Most previous LDA extensions are computationally expensive, and not scalable, due to the use of Singular Value Decomposition or Generalized Singular Value Decomposition. In this paper, we propose a two-stage LDA method, namely LDA/QR, which aims to overcome the singularity problems of classical LDA, while achieving efficiency and scalability simultaneously. The key difference between LDA/QR and PCA+LDA lies in the first stage, where LDA/QR applies QR decomposition to a small matrix involving the class centroids, while PCA+LDA applies PCA to the total scatter matrix involving all training data points. We further justify the proposed algorithm by showing the relationship among LDA/QR and previous LDA methods. Extensive experiments on face images and text documents are presented to show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]