In this paper, a novel randomized Fisher discriminant analysis (RFDA) based bearing fault diagnosis method is proposed. First, several representative time-domain features are extracted from the raw vibration signals. Second, linear Fisher discriminant analysis (FDA) is extended to nonlinear FDA named RFDA by introducing the random feature map to deal with the non-linearity issue. Specifically, the extracted time-domain features data are mapped onto a high-dimensional space using the random feature map function rather than kernel functions. Third, the time-domain features are fed into the built RFDA model to extract the discriminant features for diagnosis. Moreover, a Bayesian inference is employed to identify the class of the collected vibration signals to diagnose the bearing status. The proposed method uses random Fourier features to approximate the kernel matrix in the kernel Fisher discriminant analysis. Through employing randomized Fisher discriminant analysis, the nonlinearity issue is dealt with, and the computational burden is remarkably reduced compared to the kernel Fisher discriminant analysis (KFDA). To illustrate the superior performance of the proposed RFDA-based bearing fault diagnosis method, comparative experiments are conducted on two widely used datasets, the Case Western Reserve University (CWRU) bearing dataset and the Paderborn University (PU) bearing dataset. For the CWRU dataset, the computation time of RFDA is much shorter than KFDA, while the accuracy rate reaches the same level of KFDA. For the PU dataset, the accuracy rate of RFDA is slightly higher than KFDA, and the computation time is only 44.14% of KFDA.

Prion diseases, including ovine scrapie, bovine spongiform encephalopathy (BSE), human kuru and Creutzfeldt-Jakob disease (CJD), originate from a conformational change of the normal cellular prion protein (PrP(C)) into abnormal protease-resistant prion protein (PrP(Sc)). There is concern regarding these prion diseases because of the possibility of their zoonotic infections across species. Mutations and polymorphisms of prion sequences may influence prion-disease susceptibility through the modified expression and conformation of proteins. Rapid determination of susceptibility based on prion-sequence polymorphism information without complex structural and molecular biological analyses may be possible. Information regarding the effects of mutations and polymorphisms on prion-disease susceptibility was collected based on previous studies to classify the susceptibilities of sequences, whereas the BLOSUM62 scoring matrix and the position-specific scoring matrix were utilised to determine the distance of target sequences. The k-nearest neighbour analysis was validated with cross-validation methods. The results indicated that the number of polymorphisms did not influence prion-disease susceptibility, and three and four k-objects showed the best accuracy in identifying the susceptible group. Although sequences with negative polymorphisms showed relatively high accuracy for determination, polymorphisms may still not be an appropriate factor for estimating variation in susceptibility. Discriminant analysis of prion sequences with scoring matrices was attempted as a possible means of determining susceptibility to prion diseases. Further research is required to improve the utility of this method.

The functional brain networks, extracted from fMRI images using independent component analysis, have been demonstrated informative for distinguishing brain states of cognitive function and brain disorders. Rather than analyzing each network encoded by a spatial independent component separately, we propose a novel algorithm for discriminant analysis of functional brain networks jointly at an individual level. The functional brain networks of each individual are used as bases for a linear subspace, referred to as a functional connectivity pattern, which facilitates a comprehensive characterization of fMRI data. The functional connectivity patterns of different individuals are analyzed on the Grassmann manifold by adopting a principal angle based Riemannian distance. In conjunction with a support vector machine classifier, a forward component selection technique is proposed to select independent components for constructing the most discriminative functional connectivity pattern. The discriminant analysis method has been applied to an fMRI based schizophrenia study with 31 schizophrenia patients and 31 healthy individuals. The experimental results demonstrate that the proposed method not only achieves a promising classification performance for distinguishing schizophrenia patients from healthy controls, but also identifies discriminative functional brain networks that are informative for schizophrenia diagnosis.

Sumoylation is a multifunctional post-translation modification (PTM) in proteins by the small ubiquitin-related modifiers (SUMOs), which have relations to ubiquitin in molecular structure. Sumoylation has been found to be involved in some cellular processes. It is very significant to identify the exact sumoylation sites in proteins for not only basic researches but also drug developments. Comparing with time exhausting experiment methods, it is highly desired to develop computational methods for prediction of sumoylation sites as a complement to experiment in the post-genomic age. In this work, three feature constructions (AAIndex, position-specific amino acid propensity and modification of composition of k-space amino acid pairs) and five different combinations of them were used to construct features. At last, 178 features were selected as the optimal features according to the Mathew's correlation coefficient values in 10-fold cross validation based on linear discriminant analysis. In 10-fold cross-validation on the benchmark dataset, the accuracy and Mathew's correlation coefficient were 86.92% and 0.6845. Comparing with those existing predictors, SUMO_LDA showed its better performance.

Segmentation (tissue classification) of medical images obtained from a magnetic resonance (MR) system is a primary step in most applications of medical image post-processing. This paper describes nonparametric discriminant analysis methods to segment multispectral MR images of the brain. Starting from routinely available spin-lattice relaxation time, spin-spin relaxation time, and proton density weighted images (T1w, T2w, PDw), the proposed family of statistical methods is based on: (i) a transform of the images into components that are statistically independent from each other; (ii) a nonparametric estimate of probability density functions of each tissue starting from a training set; (iii) a classic Bayes 0-1 classification rule. Experiments based on a computer built brain phantom (brainweb) and on eight real patient data sets are shown. A comparison with parametric discriminant analysis is also reported. The capability of nonparametric discriminant analysis in improving brain tissue classification of parametric methods is demonstrated. Finally, an assessment of the role of multispectrality in classifying brain tissues is discussed.

The present study explores if EEG spectral parameters can discriminate between healthy elderly controls (HC), Alzheimer's disease (AD) and vascular dementia (VaD) using. We considered EEG data recorded during normal clinical routine with 114 healthy controls (HC), 114 AD, and 114 VaD patients. The spectral features extracted from the EEG were the absolute delta power, decay from lower to higher frequencies, amplitude, center and dispersion of the alpha power and baseline power of the entire frequency spectrum. For discrimination, we submitted these EEG features to regularized linear discriminant analysis algorithm with a 10-fold cross-validation. To check the consistency of the results obtained by our classifiers, we applied bootstrap statistics. Four binary classifiers were used to discriminate HC from AD, HC from VaD, AD from VaD, and HC from dementia patients (AD or VaD). For each model, we measured the discrimination performance using the area under curve (AUC) and the accuracy of the cross-validation (cv-ACC). We applied this procedure using two different sets of predictors. The first set considered all the features extracted from the 22 channels. For the second set of features, we automatically rejected features poorly correlated with their labels. Fairly good results were obtained when discriminating HC from dementia patients with AD or VaD (AUC = 0.84). We also obtained AUC = 0.74 for discrimination of AD from HC, AUC = 0.77 for discrimination of VaD from HC, and finally AUC = 0.61 for discrimination of AD from VaD. Our models were able to separate HC from dementia patients, and also and to discriminate AD from VaD above chance. Our results suggest that these features may be relevant for the clinical assessment of patients with dementia.

Single-cell RNA-sequencing (scRNA-seq) techniques provide unprecedented opportunities to investigate phenotypic and molecular heterogeneity in complex biological systems. However, profiling massive amounts of cells brings great computational challenges to accurately and efficiently characterize diverse cell populations. Single cell discriminant analysis (scDA) solves this problem by simultaneously identifying cell groups and discriminant metagenes based on the construction of cell-by-cell representation graph, and then using them to annotate unlabeled cells in data. We demonstrate scDA is effective to determine cell types, revealing the overall variabilities between cells from eleven data sets. scDA also outperforms several state-of-the-art methods when inferring the labels of new samples. In particular, we found scDA less sensitive to drop-out events and capable to label a mass of cells within or across datasets after learning even from a small set of data. The scDA approach offers a new way to efficiently analyze scRNA-seq profiles of large size or from different batches. scDA was implemented and freely available at https://github.com/ZCCQQWork/scDA.

The recently proposed L2-norm linear discriminant analysis criterion based on Bhattacharyya error bound estimation (L2BLDA) was an effective improvement over linear discriminant analysis (LDA) and was used to handle vector input samples. When faced with two-dimensional (2D) inputs, such as images, converting two-dimensional data to vectors, regardless of the inherent structure of the image, may result in some loss of useful information. In this paper, we propose a novel two-dimensional Bhattacharyya bound linear discriminant analysis (2DBLDA). 2DBLDA maximizes the matrix-based between-class distance, which is measured by the weighted pairwise distances of class means and minimizes the matrix-based within-class distance. The criterion of 2DBLDA is equivalent to optimizing the upper bound of the Bhattacharyya error. The weighting constant between the between-class and within-class terms is determined by the involved data that make the proposed 2DBLDA adaptive. The construction of 2DBLDA avoids the small sample size (SSS) problem, is robust, and can be solved through a simple standard eigenvalue decomposition problem. The experimental results on image recognition and face image reconstruction demonstrate the effectiveness of 2DBLDA.

In this work, we demonstrate that Linear Discriminant Analysis (LDA) applied to atomic positions in two different states of a biomolecule produces a good reaction coordinate between those two states. Atomic coordinates of a macromolecule are a direct representation of a macromolecular configuration, and yet, they are not used in enhanced sampling studies due to a lack of rotational and translational invariance. We resolve this issue using the technique of our prior work, whereby a molecular configuration is considered a member of an equivalence class in size-and-shape space, which is the set of all configurations that can be translated and rotated to a single point within a reference multivariate Gaussian distribution characterizing a single molecular state. The reaction coordinates produced by LDA applied to positions are shown to be good reaction coordinates both in terms of characterizing the transition between two states of a system within a long molecular dynamics (MD) simulation and also ones that allow us to readily produce free energy estimates along that reaction coordinate using enhanced sampling MD techniques.

The cochlear nucleus (CN) transforms the spike trains of spiral ganglion cells into a set of sensory representations that are essential for auditory discriminations and perception. These transformations require the coordinated activity of different classes of neurons that are embryologically derived from distinct sets of precursors. Decades of investigation have shown that the neurons of the CN are differentiated by their morphology, neurotransmitter receptors, ion channel expression and intrinsic excitability. In the present study we have used linear discriminant analysis (LDA) to perform an unbiased analysis of measures of the responses of CN neurons to current injections to objectively categorize cells on the basis of both morphology and physiology. Recordings were made from cells in brain slices from CBA/CaJ mice and a transgenic mouse line, NF107, crossed against the Ai32 line. For each cell, responses to current injections were analyzed for spike rate, spike shape, input resistance, resting membrane potential, membrane time constant, hyperpolarization-activated sag and time constant. Cells were filled with dye for morphological classification, and visually classified according to published accounts. The different morphological classes of cells were separated with the LDA. Ventral cochlear nucleus (VCN) bushy cells, planar multipolar (T-stellate) cells, and radiate multipolar (D-stellate) cells were in separate clusters and separate from all of the neurons from the dorsal cochlear nucleus (DCN). Within the DCN, the pyramidal cells and tuberculoventral cells were largely separated from a distinct cluster of cartwheel cells. principal axes, whereas VCN cells were in 3 clouds approximately orthogonal to this plane. VCN neurons from the two mouse strains overlapped but were slightly separated, indicating either a strain dependence or differences in slice preparation methods. We conclude that cochlear nucleus neurons can be objectively distinguished based on their intrinsic electrical properties, but such distinctions are still best aided by morphological identification.

The chemical composition and daily mineral intake (DMI) of six macro (calcium, magnesium, sodium, potassium, phosphorous, and chloride) and four microminerals (copper, iron, manganese, and zinc) were determined in four types of Portuguese breads (white wheat, maize, wheat/maize, and maize/rye breads). Samples were processed with microwave assisted digestion and mineral composition was determined with a high-resolution continuum-source atomic absorption spectrometer with flame and graphite furnace. Bread contributes to an equilibrated diet since it is rich in several minerals (0.21 mg/100 g of copper in wheat bread to 537 mg/100 g of sodium in maize/rye bread). Maize/rye bread presented the highest content of all minerals (except phosphorous and chloride), while the lowest levels were mainly found in wheat bread. Median sodium concentrations (422-537 mg/100 g) represented more than 28% of the recommended daily allowance, being in close range of the maximum Portuguese limit (550 mg/100 g). Maize/rye bread exhibited the highest DMI of manganese (181%), sodium (36%), magnesium (32%), copper (32%), zinc (24%), iron (22%), potassium (20%), and calcium (3.0%). A Principal Component Analysis (PCA) model based on the mineral content allowed the differentiation among white wheat, maize, and maize/rye bread. Zinc, magnesium, manganese, iron, phosphorus, potassium, copper, and calcium proved to be good chemical markers to differentiate bread compositions.

Researchers have only recently begun using functional neuroimaging to explore the human response to periods of sustained anxious anticipation, namely potential threat. Here, we investigated brain responses acquired with functional MRI during an instructed threat of shock paradigm used to create sustained periods of aversive anticipation. In this re-analysis of previously published data, we employed quadratic discriminant analysis to classify the multivariate pattern of whole-brain functional connectivity and to identify connectivity changes during periods of potential threat. Our method identifies clusters with altered connectivity on a voxelwise basis, thus eschewing the need to define regions a priori. Classifier generalization was evaluated by testing on data from participants not used during training. Robust classification between threat and safe contexts was possible, and inspection of "diagnostic features" revealed altered functional connectivity involving the intraparietal sulcus, task-negative regions, striatum, and anterior cingulate cortex. We anticipate that the proposed method will prove useful to experimenters wishing to identify large-scale functional networks that distinguish between experimental conditions or groups.

In the gait recognition problem, most studies are devoted to developing gait descriptors rather than introducing new classification methods. This paper proposes hybrid methods that combine regularized discriminant analysis (RDA) and swarm intelligence techniques for gait recognition. The purpose of this study is to develop strategies that will achieve better gait recognition results than those achieved by classical classification methods. In our approach, particle swarm optimization (PSO), grey wolf optimization (GWO), and whale optimization algorithm (WOA) are used. These techniques tune the observation weights and hyperparameters of the RDA method to minimize the objective function. The experiments conducted on the GPJATK dataset proved the validity of the proposed concept.

Although Linear Discriminant Analysis (LDA) is commonly used for classification, it may not be directly applied in genomics studies due to the large p, small n problem in these studies. Different versions of sparse LDA have been proposed to address this significant challenge. One implicit assumption of various LDA-based methods is that the covariance matrices are the same across different classes. However, rewiring of genetic networks (therefore different covariance matrices) across different diseases has been observed in many genomics studies, which suggests that LDA and its variations may be suboptimal for disease classifications. However, it is not clear whether considering differing genetic networks across diseases can improve classification in genomics studies.

Breast cancer tumours among African Americans are usually more aggressive than those found in Caucasian populations. African-American patients with breast cancer also have higher mortality rates than Caucasian women. A better understanding of the disease aetiology of these breast cancers can help to improve and develop new methods for cancer prevention, diagnosis and treatment. The main goal of this project was to identify genes that help differentiate between oestrogen receptor-positive and -negative samples among a small group of African-American patients with breast cancer. Breast cancer microarrays from one of the largest genomic consortiums were analysed using 13 African-American and 201 Caucasian samples with oestrogen receptor status. We used a shrinkage-based classification method to identify genes that were informative in discriminating between oestrogen receptor-positive and -negative samples. Subset analysis and permutation were performed to obtain a set of genes unique to the African-American population. We identified a set of 156 probe sets, which gave a misclassification rate of 0.16 in distinguishing between oestrogen receptor-positive and -negative patients. The biological relevance of our findings was explored through literature-mining techniques and pathway mapping. An independent dataset was used to validate our findings and we found that the top ten genes mapped onto this dataset gave a misclassification rate of 0.15. The described method allows us best to utilise the information available from small sample size microarray data in the context of ethnic minorities.

The objective of this study was to investigate the effectiveness of a machine learning algorithm in diagnosing OSA in children based on clinical features that can be obtained in nonnocturnal and nonmedical environments.

The dramatic progress in sequencing technologies offers unprecedented prospects for deciphering the organization of natural populations in space and time. However, the size of the datasets generated also poses some daunting challenges. In particular, Bayesian clustering algorithms based on pre-defined population genetics models such as the STRUCTURE or BAPS software may not be able to cope with this unprecedented amount of data. Thus, there is a need for less computer-intensive approaches. Multivariate analyses seem particularly appealing as they are specifically devoted to extracting information from large datasets. Unfortunately, currently available multivariate methods still lack some essential features needed to study the genetic structure of natural populations.

We developed a preoperative assessment system to predict surgical workload in hand-assisted laparoscopic donor nephrectomy (HALDNx) using the normal-based linear discriminant rule (NLDR). A total of 128 cases of left HALDNx performed by a single operator were used as training data. Surgical workload was measured by operative time. The optimized model had 9 explanatory variables: age, total protein, total cholesterol, number of renal arteries (numberRA), 4 variables of perinephric fat (PNF), and thickness of subcutaneous fat. This model was validated using cross-validation and the .632 estimator to estimate discrimination rates with future test data. PNF and numberRA were the predominant factors affecting workload followed by the computed tomography value of PNF, body weight, and male sex. The estimated accuracy of the prediction system was 94.6%. The complication rate was 9.38% and did not correlate with surgical workload. We also made our program available online for constructing assessment functions from other cohort data. In conclusion, the surgical workload of HALDNx could be predicted with PNF and numberRA as the dominant risk factors.

Cattle include a large number of breeds that are characterized by marked phenotypic differences and thus constitute a valuable model to study genome evolution in response to processes such as selection and domestication. Detection of "signatures of selection" is a useful approach to study the evolutionary pressures experienced throughout history. In the present study, signatures of selection were investigated in five cattle breeds farmed in Italy using a multivariate approach.

Classification on the basis of gene expression data derived from RNA-seq promises to become an important part of modern medicine. We propose a new classification method based on a model where the data is marginally negative binomial but dependent, thereby incorporating the dependence known to be present between measurements from different genes. The method, called qtQDA, works by first performing a quantile transformation (qt) then applying Gaussian quadratic discriminant analysis (QDA) using regularized covariance matrix estimates. We show that qtQDA has excellent performance when applied to real data sets and has advantages over some existing approaches. An R package implementing the method is also available on https://github.com/goknurginer/qtQDA.