Sparse Discriminant Analysis Research Articles

High dimensional discriminant analysis under weak sparsity

. In this work, we consider the discriminant analysis under the weak sparsity where many entries of the parameters are nearly zero. We develop a unified LASSO-typed framework to estimate the parameters for sparse discriminant analysis and derive the general non asymptotic error bound under the weak sparsity condition. As applications, we revisit the sparse linear discriminant analysis and sparse quadratic discriminant analysis. We establish the consistency of the estimators and also the misclassification error rate. These results extend the sparse discriminant analysis methods to weak sparsity setting and refine the existing theoretical results.

Conjugated linoleic acid (CLA) modulates bovine peripheral blood mononuclear cells (PBMC) proteome in vitro

Conjugated linoleic acid (CLA) is a group of natural isomers of the n-6 polyunsaturated fatty acid (PUFA) linoleic acid, exerting biological effects on cow physiology. This study assessed the impact of the mixture 50:50 (vol:vol) of CLA isomers (cis-9, trans-11 and trans-10, cis-12) on bovine peripheral blood mononuclear cells (PBMC) proteome, identifying 1608 quantifiable proteins. A supervised multivariate statistical analysis, sparse variant partial least squares – discriminant analysis (sPLS-DA) for paired data identified 407 discriminant proteins (DP), allowing the clustering between the CLA and controls. The ProteINSIDE workflow found that DP with higher abundance in the CLA group included proteins related to innate immune defenses (PLIN2, CD36, C3, C4, and AGP), with antiapoptotic (SERPINF2 and ITIH4) and antioxidant effects (HMOX1). These results demonstrated that CLA modulates the bovine PBMC proteome, supports the antiapoptotic and immunomodulatory effects observed in previous in vitro studies on bovine PBMC, and suggests a cytoprotective role against oxidative stress. SignificanceIn this study, we report for the first time that the mixture 50:50 (vol:vol) of cis-9, trans-11, and trans-10, cis-12-CLA isomers modulates the bovine PBMC proteome. Our results support the immunomodulatory and antiapoptotic effects observed in bovine PBMC in vitro. In addition, the present study proposes a cytoprotective role of CLA mixture against oxidative stress. We suggest a molecular signature of CLA treatment based on combining a multivariate sparse discriminant analysis and a clustering method. This demonstrates the great value of sPLS-DA as an alternative option to identify discriminant proteins with relevant biological significance.

Learning binary codes for fast image retrieval with sparse discriminant analysis and deep autoencoders

Image retrieval with relevant feedback on large and high-dimensional image databases is a challenging task. In this paper, we propose an image retrieval method, called BCFIR (Binary Codes for Fast Image Retrieval). BCFIR utilizes sparse discriminant analysis to select the most important original feature set, and solve the small class problem in the relevance feedback. Besides, to increase the retrieval performance on large-scale image databases, in addition to BCFIR mapping real-valued features to short binary codes, it also applies a bagging learning strategy to improve the ability general capabilities of autoencoders. In addition, our proposed method also takes advantage of both labeled and unlabeled samples to improve the retrieval precision. The experimental results on three databases demonstrate that the proposed method obtains competitive precision compared with other state-of-the-art image retrieval methods.

Integrating data from spontaneous and induced trans-10 shift of ruminal biohydrogenation reveals discriminant bacterial community changes at the OTU level.

Microbial digestion is of key importance for ruminants, and disturbances can affect efficiency and quality of products for human consumers. Ruminal biohydrogenation of dietary unsaturated fatty acids leads to a wide variety of specific fatty acids. Some dietary conditions can affect the pathways of this transformation, leading to trans-10 fatty acids rather than the more usual trans-11 fatty acids, this change resulting in milk fat depression in dairy cows. We combined data from an induced and spontaneous trans-10 shift of ruminal biohydrogenation, providing new insight on bacterial changes at different taxonomic levels. A trans-10 shift was induced using dietary addition of concentrate and/or unsaturated fat, and the spontaneous milk fat depression was observed in a commercial dairy herd. Most changes of microbial community related to bacteria that are not known to be involved in the biohydrogenation process, suggesting that the trans-10 shift may represent the biochemical marker of a wide change of bacterial community. At OTU level, sparse discriminant analysis revealed strong associations between this change of biohydrogenation pathway and some taxa, especially three taxa belonging to [Eubacterium] coprostanoligenes group, Muribaculaceae and Lachnospiraceae NK3A20 group, that could both be microbial markers of this disturbance and candidates for studies relative to their ability to produce trans-10 fatty acids.

1331-P: Associations between Insulin Resistance and Plasma Lipids and Metabolomics in Women with and without Type 1 Diabetes

Insulin resistance (IR) increases risk for cardiovascular disease and mortality in people with type 1 diabetes (T1D) . We previously found associations between plasma lipids, metabolites and IR; whether these associations differ in people with and without T1D is not well understood. We analyzed targeted plasma lipidomics and untargeted plasma metabolomics in 25 premenopausal women aged 18-45 yrs (12 with T1D and 13 without diabetes [non-DM]) who had a hyperinsulinemic euglycemic clamp to measure glucose infusion rate (GIR) . After stratifying by diabetes, women were classified by tertiles of GIR. We used sparse partial least-squares discriminant analysis to predict and moderated t-tests to compare most IR vs. most insulin sensitive (IS) tertile. Among women with T1D, 3 lipids, 4 amino acids, 3 peptides, 3 xenobiotics, 1 carbohydrate, and 1 nucleotide were lower and 1 lipid and 1 fatty acid were higher in the most IS tertile (Table) . Among non-DM women, 4 lipids, 1 cofactor, 1 fatty acid, and 1 phosphatidylethanolamine were lower and 1 nucleotide and 1 lipid were higher in the most IS tertile. None of the top features were the same in the T1D and non-DM groups. Plasma lipids and metabolites were differentially associated with IR in women with and without T1D. Future work should validate these findings in a larger sample of women and men, and explore how these biomarkers relate to IR and metabolism in T1D. Disclosure T.B.Vigers: None. L.Pyle: None. I.E.Schauer: None. B.C.Bergman: Research Support; Eli Lilly and Company. J.K.Snell-bergeon: Stock/Shareholder; GlaxoSmithKline plc. Funding American Diabetes Association (7-13-CD-10) ; National Heart, Lung, and Blood Institute (grant HL61753 and HL113029) , JDRF Diabetes Foundation (grant 17-2013-313) , DERC Clinical Investigation Core (grant P30 DK57516) , NIH-M01-RR00051, NIH P30-DK116073

Fault Diagnosis Method for Rolling Bearing Based on Sparse Principal Subspace Discriminant Analysis

Rolling bearings are omnipresent parts in industrial fields. To comprehensively reflect the status of rolling bearing and improve the classification accuracy, fusion information is widely used in various studies, which may result in high dimensionality, redundancy information of dataset, and time consumption. Thus, it is of crucial significance in extracting optimal features from high-dimensional and redundant feature space for classification. In this study, a fault diagnosis of rolling bearings model based on sparse principal subspace discriminant analysis is proposed. It extracts sparse discrimination information, meanwhile preserving the main energy of original dataset, and the sparse regularization term and sparse error term constrained by l2,1-norm are introduced to improve the performance of feature extraction and the robustness to noise and outliers. The multi-domain feature space involved a time domain, frequency domain, and time-frequency domain is first derived from the original vibration signals. Then, the intrinsic geometric features extracted by sparse principal subspace discriminant analysis are fed into a support vector machine classifier to recognize different operating conditions of bearings. The experimental results demonstrated that the feasibility and effectiveness of the proposed fault diagnosis model based on a sparse principal subspace discriminant analysis algorithm can achieve higher recognition accuracy than fisher discriminant analysis and its extensions, and it is relatively insensitive to the impact of noise and outliers owing to the sparse property.

Benchmarking Eliminative Radiomic Feature Selection for Head and Neck Lymph Node Classification.

Simple SummaryPathologic cervical lymph nodes (LN) in head and neck squamous cell carcinoma (HNSCC) deteriorate prognosis. Current radiologic criteria for LN-classification are primarily shape-based. Radiomics is an emerging data-driven technique that aids in extraction, processing and analyzing features and is potentially capable of LN-classification. Currently available sets of features are too complex for clinical applicability. We identified the combination of sparse discriminant analysis and genetic algorithms as a potentially useful algorithm for eliminative feature selection. In this retrospective, cohort-study, from 252 LNs with over extracted 30,000 features, this algorithm retained a classification accuracy of up to 90% with only 10% of the original number of features. From a clinical perspective, the selected features appeared plausible and potentially capable of correctly classifying LNs. Both the identified algorithm and features need further exploration of their potential as prospective classifiers for LNs in HNSCC.In head and neck squamous cell carcinoma (HNSCC) pathologic cervical lymph nodes (LN) remain important negative predictors. Current criteria for LN-classification in contrast-enhanced computed-tomography scans (contrast-CT) are shape-based; contrast-CT imagery allows extraction of additional quantitative data (“features”). The data-driven technique to extract, process, and analyze features from contrast-CTs is termed “radiomics”. Extracted features from contrast-CTs at various levels are typically redundant and correlated. Current sets of features for LN-classification are too complex for clinical application. Effective eliminative feature selection (EFS) is a crucial preprocessing step to reduce the complexity of sets identified. We aimed at exploring EFS-algorithms for their potential to identify sets of features, which were as small as feasible and yet retained as much accuracy as possible for LN-classification. In this retrospective cohort-study, which adhered to the STROBE guidelines, in total 252 LNs were classified as “non-pathologic” (n = 70), “pathologic” (n = 182) or “pathologic with extracapsular spread” (n = 52) by two experienced head-and-neck radiologists based on established criteria which served as a reference. The combination of sparse discriminant analysis and genetic optimization retained up to 90% of the classification accuracy with only 10% of the original numbers of features. From a clinical perspective, the selected features appeared plausible and potentially capable of correctly classifying LNs. Both the identified EFS-algorithm and the identified features need further exploration to assess their potential to prospectively classify LNs in HNSCC.

Abstract 13312: Comprehensive Sequencing of Small Non-Coding RNA Reveals Plasma Circulating Biomarkers of Hypertrophic Cardiomyopathy and Dysregulated Signaling Pathways

Background: Hypertrophic cardiomyopathy (HCM) is caused by mutations in the genes essential in normal myocardial contraction. However, it remains unclear through which signaling pathways gene mutations mediate the development of HCM. Growing evidence indicates that small non-coding RNAs (snRNAs) play important roles in post-transcriptional regulation of gene expression. Hypothesis: Comprehensive sequencing of snRNAs in plasma reveals circulating HCM biomarkers and differentially regulated signaling pathways. Methods: We conducted a multicenter case-control study of cases with HCM and age-, sex-, and body mass index-matched controls with hypertensive left ventricular hypertrophy. We carried out RNA-seq of 3293 snRNAs in plasma. We performed a sparse partial least squares discriminant analysis to develop snRNA-based discrimination model using samples retrieved during the first two-thirds of the study period (the training set). We prospectively tested the discriminative ability in independent samples that were collected thereafter (the test set). We also identified signaling pathways associated with snRNAs that were significantly dysregulated in HCM with Bonferroni-adjusted P<0.05. Results: The study included 324 patients (165 cases and 159 controls; n=224 in the training set, n=100 in the test set). Using the transcriptomics-based model derived from the training set, the area under the receiver-operating-characteristic curve in the test set was 0.89 (95%CI 0.81-0.96; Figure ). Pathway analysis revealed that the Ras-MAPK pathway was upregulated in HCM (false discovery rate [FDR]=0.000002). Pathways involved in inflammation and fibrosis - e.g., TNF (FDR=0.000003) and TGF-β (FDR=0.002) - were also upregulated. Conclusions: This study serves as the largest-scale investigation to reveal circulating snRNA biomarkers of HCM and exhibits both novel (e.g., Ras-MAPK) and known (e.g., TNF, TGF-β) pathways that are differentially regulated in HCM.

Comprehensive proteomics profiling reveals molecular pathways that are differentially regulated in hypertrophic cardiomyopathy and correlate with clinical markers of disease severity

Abstract Background Hypertrophic cardiomyopathy (HCM) is caused by mutations in the genes coding for proteins essential in normal myocardial contraction. However, it remains unclear through which molecular pathways gene mutations mediate the development and progression of HCM. Purpose To determine protein biomarkers and molecular pathways that are differentially regulated in HCM and correlated with disease severity. Methods We conducted a multicenter case-control study of cases with HCM and controls with hypertensive left ventricular hypertrophy. We carried out plasma proteomics profiling of 1681 proteins using the SOMAscan assay. We performed a sparse partial least squares discriminant analysis to develop a proteomics-based discrimination model with data from 1 institution (i.e., the training set). We tested the discriminative ability in independent samples from the other institutions (i.e., the test set). We executed pathway analysis using significantly dysregulated proteins with Bonferroni-corrected p<0.05. Pathways with false discovery rate (FDR) <0.05 and dysregulation of ≥5 member proteins were declared positive. In HCM, we also identified proteins with significant correlation with clinical markers of disease severity (e.g., New York Heart Association [NYHA] class, left atrial diameter) and performed pathway analysis. Results The study included 266 cases and 167 controls (n=308 in the training set; n=125 in the test set). Using the proteomics-based model derived from the training set, the area under the receiver-operating-characteristic curve was 0.89 (95% confidence interval [CI] 0.83–0.94, p<0.001) in the test set (Figure). The sensitivity was 0.84 (95% CI 0.76–0.92) and the specificity was 0.78 (95% CI 0.66–0.90). A total of 508 proteins were significantly associated with the disease status. As shown in the Table, pathway analysis revealed that the Ras-MAPK pathway, along with its upstream and downstream (e.g., Rap1, PI3K-Akt) pathways, was upregulated in HCM (FDR <0.001). Pathways involved in inflammation and fibrosis – e.g., the TGF-β pathway – were also found to be upregulated in HCM. In patients with HCM, 207 out of the 1681 proteins were significantly correlated with NYHA functional class. This number is more than twice as large as what would be expected by chance (i.e., 84 proteins at α=0.05 level). Pathway analysis of these 207 proteins showed upregulation of the Ras-MAPK and related pathways – e.g., PI3K-Akt, Rap1, and TNF. Similarly, 264 of the 1681 proteins were correlated with left atrial diameter in HCM. Pathway analysis of the 264 proteins revealed upregulation of the MAPK and the PI3K-Akt pathways. Conclusions This multicenter case-control study with independent validation serves as the largest-scale investigation with the most comprehensive proteomics profiling in HCM, exhibiting both novel (e.g., Ras-MAPK) and known (e.g., TGF-β) pathways that are differentially regulated in HCM and correlated with disease severity. Funding Acknowledgement Type of funding sources: Public grant(s) – National budget only. Main funding source(s): National Institute of Health and American Heart Association Figure 1. ROC curveTable 1. Differentially regulated pathways

Prediction of major adverse cardiovascular events in patients with hypertrophic cardiomyopathy using proteomics profiling

Abstract Background Hypertrophic cardiomyopathy (HCM) is one of the most common genetic cardiac diseases, affecting 1 in 200–500 people in the US. HCM often causes major adverse cardiovascular events (MACE) – e.g., arrhythmias (atrial fibrillation, ventricular tachycardia/fibrillation), cerebrovascular accident, heart failure (HF), and sudden cardiac death (SCD). Although these HCM-related morbidities and mortality substantially affect the patients' quality and quantity of life, no systems are available to predict MACE. Furthermore, it remains unclear which signaling pathways mediate MACE. Purpose To prospectively determine protein biomarkers that predict MACE in patients with HCM and to identify signaling pathways differentially regulated in patients with HCM who subsequently develop MACE. Methods In this multi-center prospective cohort study of patients with HCM, we carried out plasma proteomics profiling of 4,979 proteins upon enrollment. We defined MACE as a composite of new-onset arrhythmias, cerebrovascular accident, increase in New York Heart Association class, HF death, SCD, and emergency department visit or non-elective hospitalization for HCM-related morbidities. We performed a sparse partial least squares discriminant analysis to develop a proteomics-based model to predict MACE using data from one institution (i.e., the training set). We tested the predictive ability in independent samples from the other institution (i.e., the test set) and performed time-to-event analysis. Additionally, we executed pathway analysis of the predictive proteins. A pathway was declared positive (i.e., dysregulated) if the false discovery rate (FDR) of the pathway was <0.01 and there were ≥5 proteins that map to the pathway. Results The study included 257 patients with HCM (n=186 in the training set; n=71 in the test set). The median follow-up duration was 2.5 years (interquartile range, 1.4–3.1 years). Each year, 11.7% of patients had MACE. Using the proteomics-based prediction model derived from the training set, the area under the receiver-operating-characteristic curve was 0.84 (95% confidence interval [CI] 0.72–0.96) in the test set (Figure 1). The sensitivity was 0.82 (95% CI, 0.72–0.91) and the specificity was 0.84 (95% CI, 0.79–0.89) in the test set. In the test set, high-risk group determined by the proteomics-based predictive model had significantly higher rate of developing MACE (hazard ratio 20.2; 95% CI 2.4–168; p=0.005; Figure 2). The Ras-MAPK and related pathways were upregulated in patients who subsequently developed MACE (FDR<0.001). Pathways involved in inflammation and fibrosis – e.g., the TGF-β pathway – were also upregulated. Conclusions This multi-center prospective cohort study with validation serves as the first to demonstrate the ability of proteomics profiling to predict MACE in HCM, exhibiting both novel (e.g., Ras-MAPK) and known (e.g., TGF-β) pathways that are differentially regulated in patients who subsequently experience MACE. Funding Acknowledgement Type of funding sources: Public grant(s) – National budget only. Main funding source(s): National Institute of Health, American Heart Association Figure 1Figure 2

Comprehensive characterisation of Culicoides clastrieri and C. festivipennis (Diptera: Ceratopogonidae) according to morphological and morphometric characters using a multivariate approach and DNA barcode

Biting midges are widespread around the world and play an essential role in the epidemiology of over 100 veterinary and medical diseases. For taxonomists, it is difficult to correctly identify species because of affinities among cryptic species and species complexes. In this study, species boundaries were examined for C. clastrieri and C. festivipennis and compared with six other Culicoides species. The classifiers are partial least squares discriminant analysis (PLS-DA) and sparse partial least squares discriminant analysis (sPLS-DA).The performance of the proposed method was evaluated using four models: (i) geometric morphometrics applied to wings; (ii) morphological wing characters, (iii) "Full wing" (landmarks and morphological characters) and (iv) "Full model" (morphological characters—wing, head, abdomen, legs—and wing landmarks). Double cross-validation procedures were used to validate the predictive ability of PLS-DA and sPLS-DA models. The AUC (area under the ROC curve) and the balanced error rate showed that the sPLS-DA model performs better than the PLS-DA model. Our final sPLS-DA analysis on the full wing and full model, with nine and seven components respectively, managed to perfectly classify our specimens. The C. clastrieri and C. festivipennis sequences, containing both COI and 28S genes, revealed our markers’ weak discrimination power, with an intraspecific and interspecific divergence of 0.4% and 0.1% respectively. Moreover, C. clastrieri and C. festivipennis are grouped in the same clade. The morphology and wing patterns of C. clastrieri and C. festivipennis can be used to clearly distinguish them. Our study confirms C. clastrieri and C. festivipennis as two distinct species. Our results show that caution should be applied when relying solely on DNA barcodes for species identification or discovery.

Cigarette Smoking during Pregnancy: Effects on Antioxidant Enzymes, Metallothionein and Trace Elements in Mother-Newborn Pairs.

The effect of maternal smoking as a source of exposure to toxic metals Cd and Pb on superoxide dismutase (SOD) and glutathione peroxidase (GPx) activity, metallothionein (MT), Cd, Pb, Cu, Fe, Mn, Se and Zn concentrations were assessed in maternal and umbilical cord blood and placenta in 74 healthy mother-newborn pairs after term delivery. Sparse discriminant analysis (SDA) was used to identify elements with the strongest impact on the SOD, GPx and MT in the measured compartments, which was then quantified by multiple regression analysis. SOD activity was lower in maternal and cord plasma, and higher in the placenta of smokers compared to non-smokers, whereas GPx activity and MT concentration did not differ between the groups. Although active smoking during pregnancy contributed to higher maternal Cd and Pb concentrations, its contribution to the variability of SOD, GPx or MT after control for other elements identified by SDA was not significant. However, an impaired balance in the antioxidant defence observed in the conditions of relatively low-to-moderate exposure levels to Cd and Pb could contribute to an increased susceptibility of offspring to oxidative stress and risk of disease development later in life. Further study on a larger number of subjects will help to better understand complex interactions between exposure to toxic elements and oxidative stress related to maternal cigarette smoking.

MP 2 SDA

Sparse Discriminant Analysis (SDA) has been widely used to improve the performance of classical Fisher’s Linear Discriminant Analysis in supervised metric learning, feature selection, and classification. With the increasing needs of distributed data collection, storage, and processing, enabling the Sparse Discriminant Learning to embrace the multi-party distributed computing environments becomes an emerging research topic. This article proposes a novel multi-party SDA algorithm, which can learn SDA models effectively without sharing any raw data and basic statistics among machines. The proposed algorithm (1) leverages the direct estimation of SDA to derive a distributed loss function for the discriminant learning, (2) parameterizes the distributed loss function with local/global estimates through bootstrapping, and (3) approximates a global estimation of linear discriminant projection vector by optimizing the “distributed bootstrapping loss function” with gossip-based stochastic gradient descent. Experimental results on both synthetic and real-world benchmark datasets show that our algorithm can compete with the aggregated SDA with similar performance, and significantly outperforms the most recent distributed SDA in terms of accuracy and F1-score.

Review on graph learning for dimensionality reduction of hyperspectral image

ABSTRACTGraph learning is an effective manner to analyze the intrinsic properties of data. It has been widely used in the fields of dimensionality reduction and classification for data. In this paper, we focus on the graph learning-based dimensionality reduction for a hyperspectral image. Firstly, we review the development of graph learning and its application in a hyperspectral image. Then, we mainly discuss several representative graph methods including two manifold learning methods, two sparse graph learning methods, and two hypergraph learning methods. For manifold learning, we analyze neighborhood preserving embedding and locality preserving projections which are two classic manifold learning methods and can be transformed into the form of a graph. For sparse graph, we introduce sparsity preserving graph embedding and sparse graph-based discriminant analysis which can adaptively reveal data structure to construct a graph. For hypergraph learning, we review binary hypergraph and discriminant hyper-Laplacian projection which can represent the high-order relationship of data.

Two-Dimensional Quaternion Sparse Discriminant Analysis.

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 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.

Regularized Group Sparse Discriminant Analysis for P300-Based Brain-Computer Interface.

Event-related potentials (ERPs) especially P300 are popular effective features for brain-computer interface (BCI) systems based on electroencephalography (EEG). Traditional ERP-based BCI systems may perform poorly for small training samples, i.e. the undersampling problem. In this study, the ERP classification problem was investigated, in particular, the ERP classification in the high-dimensional setting with the number of features larger than the number of samples was studied. A flexible group sparse discriminative analysis algorithm based on Moreau-Yosida regularization was proposed for alleviating the undersampling problem. An optimization problem with the group sparse criterion was presented, and the optimal solution was proposed by using the regularized optimal scoring method. During the alternating iteration procedure, the feature selection and classification were performed simultaneously. Two P300-based BCI datasets were used to evaluate our proposed new method and compare it with existing standard methods. The experimental results indicated that the features extracted via our proposed method are efficient and provide an overall better P300 classification accuracy compared with several state-of-the-art methods.

Sparse discriminant analysis based on estimation of posterior probabilities

ABSTRACTFisher's linear discriminant analysis (FLDA) is known as a method to find a discriminative feature space for multi-class classification. As a theory of extending FLDA to an ultimate nonlinear form, optimal nonlinear discriminant analysis (ONDA) has been proposed. ONDA indicates that the best theoretical nonlinear map for maximizing the Fisher's discriminant criterion is formulated by using the Bayesian a posterior probabilities. In addition, the theory proves that FLDA is equivalent to ONDA when the Bayesian a posterior probabilities are approximated by linear regression (LR). Due to some limitations of the linear model, there is room to modify FLDA by using stronger approximation/estimation methods. For the purpose of probability estimation, multi-nominal logistic regression (MLR) is more suitable than LR. Along this line, in this paper, we develop a nonlinear discriminant analysis (NDA) in which the posterior probabilities in ONDA are estimated by MLR. In addition, in this paper, we develop a way to introduce sparseness into discriminant analysis. By applying L1 or L2 regularization to LR or MLR, we can incorporate sparseness in FLDA and our NDA to increase generalization performance. The performance of these methods is evaluated by benchmark experiments using last_exam17 standard datasets and a face classification experiment.

Automatic and Efficient Fault Detection in Rotating Machinery using Sound Signals

Vibration and acoustic emission have received great attention of the research community for condition-based maintenance in rotating machinery. Several signal processing algorithms were either developed or used efficiently to detect and classify faults in bearings and gears. These signals are recorded, using sensors like tachometer or accelerometer, connected directly or mounted very close to the system under observation. This is not a feasible option in case of complex machinery and/or temperature and humidity. Therefore, it is required to sense the signals remotely, in order to reduce installation and maintenance cost. However, its installation far away from the intended device may pollute the required signal with other unwanted signals. In an attempt to address these issues, sound signal-based fault detection and classification in rotating bearings is presented. In this research work, audible sound of machine under test is captured using a single microphone and different statistical, spectral and spectro-temporal features are extracted. The selected features are then analyzed using different machine learning techniques, such as K-nearest neighbor (KNN) classifier, support vector machine (SVM), kernel liner discriminant analysis (KLDA) and sparse discriminant analysis (SDA). Simulation results show successful classification of faults into ball fault, inner and outer race faults. Best results were achieved using the KLDA followed by SDA, KNN and SVM. As far as features are concerned, the average FFT outperformed all the other features, followed by average PSD, RMS values of PSD, PSD and STFT.

A chemometric strategy for forensic analysis of condom residues: Identification and marker profiling of condom brands from direct analysis in real time-high resolution mass spectrometric chemical signatures

The rapid and accurate identification of condom-derived lubricant traces takes on heightened importance in sexual assault cases where the assailant has used a condom in order to avoid leaving behind incriminating DNA evidence. Previous reports have demonstrated that a variety of techniques can be used to confirm that a given residue is condom-derived, based on the detection of spermicides, slip agents and/or other common additives. However, limited success has been achieved in differentiating brands from among a broad range of condom types. In this study, the utility of direct analysis in real time-high resolution mass spectrometry (DART-HRMS) combined with chemometrics, for the rapid and accurate attribution of brands to condom residues of various types, was explored and developed. A database of condom residue spectra comprised of 110 different condom types representing 16 brands was generated, with the spectra serving as representative fingerprints for each brand. The spectral fingerprints were subjected to pre-processing prior to the application of Partial Least Squares-Discriminant Analysis (PLS-DA) which was used to generate a classifier that permitted identification of condom brands with an accuracy of 97.4%. An additional criterion was imposed on the PLS-DA to provide the confidence level and credibility of each prediction. The effect of time since deposition, the presence of contaminants and the influence of residue transfer on the prediction accuracy of the model were also assessed.The results from Sparse Discriminant Analysis (SDA) and PLS-DA were followed by application of the Student's t-test to determine m/z values representative of small-molecule markers that were most important for defining brand classes. The m/z values revealed by the two methods were found to be consistent in indicating which masses were representative of markers. The SDA method also provided low-dimensional views of the discriminative directions for classification of condom residues, thereby enabling easy visualization of the relationship between the indicated m/z values and brand discrimination. The results further revealed a subset of 14 m/z values that were observed in all 110 condoms representing the 16 brands, and some of these may serve as potential universal small-molecule condom markers. Overall, the results show that the DART-HRMS database of condom residue spectra can be used to identify residues based on differences in chemical components peculiar to each brand. The database can be readily expanded to include more condoms.

Direct Analysis in Real Time-Mass Spectrometry and Kohonen Artificial Neural Networks for Species Identification of Larva, Pupa and Adult Life Stages of Carrion Insects.

Species determination of the various life stages of flies (Order: Diptera) is challenging, particularly for the immature forms, because analogous life stages of different species are difficult to differentiate based on morphological features alone. It is demonstrated here that direct analysis in real time-high-resolution mass spectrometry (DART-HRMS) combined with supervised Kohonen Self-Organizing Maps (SOM) enables accomplishment of species-level identification of larva, pupa, and adult life stages of carrion flies. DART-HRMS data for each life stage were acquired from analysis of ethanol suspensions representing Calliphoridae, Phoridae, and Sarcophagidae families, without additional sample preparation. After preprocessing, the data were subjected to a combination of minimum Redundancy Maximal Relevance (mRMR) and Sparse Discriminant Analysis (SDA) methods to select the most significant variables for creating accurate SOM models. The resulting data were divided into training and validation sets and then analyzed by the SOM method to define the proper discrimination models. The 5-fold venetian blind cross-validation misclassification error was below 7% for all life stages, and the validation samples were correctly identified in all cases. The multiclass SOM model also revealed which chemical components were the most significant markers for each species, with several of these being amino acids. The results show that processing of DART-HRMS data using artificial neural networks (ANNs) based on the Kohonen SOM approach enables rapid discrimination and identification of fly species even for the immature life stages. The ANNs can be continuously expanded to include a larger number of species and can be used to screen DART-HRMS data from unknowns to rapidly determine species identity.