Orthogonal discriminant analysis for interactive pattern analysis

Orthogonal discriminant analysis algorithms have recently been proposed. However, these methods don't address the singularity problem in the high dimensional feature space. In this paper, we present a new method called Direct Orthogonal Discriminant Analysis (DODA), which is able to extract all the orthogonal discriminant vectors simultaneously in the high-dimensional feature space and does not suffer the singularity problem. This method is very simple and easy to be implemented. Experimental results show that the proposed method is very competitive in comparison with some existing dimensionality reduction algorithms.

In this study, near-infrared (NIR) spectroscopy and high-performance liquid chromatography (HPLC) combined with chemometrics tools were applied for quick discrimination and quantitative analysis of different varieties and origins of Atractylodis rhizoma samples. Based on NIR data, orthogonal partial least squares discriminant analysis (OPLS-DA) and K-nearest neighbor (KNN) models achieved greater than 90% discriminant accuracy of the three species and two origins of Atractylodis rhizoma. Moreover, the contents of three active ingredients (atractyloxin, atractylone, and β-eudesmol) in Atractylodis rhizoma were simultaneously determined by HPLC. There are significant differences in the content of the three components in the samples of Atractylodis rhizoma from different varieties and origins. Then, partial least squares regression (PLSR) models for the prediction of atractyloxin, atractylone, and β-eudesmol content were successfully established. The complete Atractylodis rhizoma spectra gave rise to good predictions of atractyloxin, atractylone, and β-eudesmol content with R2 values of 0.9642, 0.9588, and 0.9812, respectively. Based on the results of this present research, it can be concluded that NIR is a great nondestructive alternative to be applied as a rapid classification system by the drug industry.

BackgroundPeriapical periodontitis is a common oral inflammatory disease that affects periapical tissues and is caused by bacteria in the root canal system. The relationship among the local metabolome, the inflammatory grade, and the type and abundance of microorganisms associated with periapical periodontitis is discussed in this study.MethodsThe inflammatory grades of periapical samples from 47 patients with chronic periapical periodontitis in permanent anterior teeth were determined based on the immune cell densities in tissues subjected to haematoxylin and eosin staining. The metabolome was evaluated using ultrahigh-performance liquid chromatography-quadrupole time-of-flight mass spectrometry, followed by principal component analysis and orthogonal partial least squares discriminant analysis. The microbiome was accessed using 16 S rRNA high-throughput sequencing. The differences in the metabolomes and microbiomes of the periapical periodontitis samples were assessed using Spearman’s correlation analysis.ResultN-acetyl-D-glucosamine, L-tryptophan, L-phenylalanine, and 15 other metabolites were identified by the comparison between samples with severe inflammation and mild or moderate inflammation. Four amino acid metabolism pathways and one sugar metabolism pathway were associated with the inflammatory grade of periapical periodontitis. The abundance of Actinomycetes was negatively correlated with the abundance of glucosamine (GlcN), while the abundance of Tannerella was positively correlated with the abundance of L-methionine.ConclusionsThe local metabolome of periapical periodontitis is correlated with the inflammatory grade. The abundance of the local metabolites GlcN and L-methionine is correlated with the abundance of the major microorganisms Actinomycetes and Tannerella, respectively.

Heavy ions refer to charged particles with a mass greater than four (i.e., alpha particles). The heavy ion irradiation used in radiotherapy or that astronauts suffer in space flight missions induces toxicity in normal tissue and leads to short-term and long-term damage in both the structure and function of the brain. However, the underlying molecular alterations caused by heavy ion radiation have yet to be completely elucidated. Herein, untargeted and targeted lipidomic profiling of the whole brain tissue and blood plasma 7 days after the administration of the 15 Gy (260 MeV, low linear energy (LET) = 13.9 KeV/μm) plateau irradiation of disposable 12C6+ heavy ions on the whole heads of rats was explored to study the lipid damage induced by heavy ion radiation in the rat brain using ultra performance liquid chromatography-mass spectrometry (UPLC–MS) technology. Combined with multivariate variables and univariate data analysis methods, our results indicated that an orthogonal partial least squares discriminant analysis (OPLS–DA) could clearly distinguish lipid metabolites between the irradiated and control groups. Through the combination of variable weight value (VIP), variation multiple (FC), and differential (p) analyses, the significant differential lipids diacylglycerols (DAGs) were screened out. Further quantitative targeted lipidomic analyses of these DAGs in the rat brain tissue and plasma supported the notion that DAG 47:1 could be used as a potential biomarker to study brain injury induced by heavy ion irradiation.

Linear discriminant analysis (LDA) aims to find a low-dimensional space in which data points in the same class are to be close to each other while keeping data points from different classes apart. To improve the robustness of LDA to non-Gaussian distribution data, most existing discriminant analysis methods extend LDA by approximating the underlying manifold of data. However, these methods suffer from the following problems: 1) local affinity or reconstruction coefficients are learned on the basis of the relationships of all data pairs, which would lead to a sharp increase in the amount of computation and 2) they learn the manifold information in the original space, ignoring the interference of the noise and redundant features. Motivated by these challenges, this article represents a novel discriminant analysis model, called fast and adaptive locality discriminant analysis (FALDA), to improve the efficiency and robustness. First, with the anchor-based strategy, a bipartite graph of each class is constructed to characterize the local structure of data. Since the number of anchor points is far less than that of data points, learning of fuzzy membership relationships between data points and anchor points within each class can save training time. Second, a maximum entropy regularization is introduced to control the uniformity of the weights of graphs and avoid the trivial solution. Third, the above relationships are updated adaptively in the process of dimensionality reduction, which can suppress the interference of the noise and redundant features. Fourth, the whitening constraint is imposed on the projection matrix to remove the relevance between features and restrict the total scatter of data in the subspace. Last but not the least, data with complex distribution can be explicitly divided into sub-blocks according to the learned anchor points (or subclass center points). We test our proposed method on synthetic data, benchmark datasets, and imbalanced datasets. Promising experimental results demonstrate the success of this novel model.

Orthogonal Linear Discriminant Analysis (OLDA) has been widely studied for dimensionality reduction, as the orthogonality constraints on its projection matrix enable more effective elimination of redundant features compared to conventional Linear Discriminant Analysis (LDA). However, most existing methods for solving OLDA rely on iterative optimization to sequentially construct orthogonal components, incurring massive repeated high-cost matrix operations and thus leading to substantial computational inefficiency. To address this limitation, we propose QR decomposition-based Fast OLDA (QR-FOLDA), a method built upon a theoretical result (Theorem 1) established in this work: the optimal solutions of LDA remain valid under any full-rank linear transformation. By leveraging this property, QR-FOLDA applies QR decomposition directly to the optimal LDA solution, thereby enforcing orthogonality while avoiding the repeated high-cost matrix operations typically involved in iterative optimization procedures. Experimental evaluations conducted on nine real-world datasets across various domains show that QR-FOLDA not only achieves substantial improvements in computational efficiency compared to existing OLDA methods but also delivers superior classification performance. These findings position QR-FOLDA as a theoretically sound and practically efficient solution for orthogonal discriminant analysis.

Flavor components detection and discrimination of isomers in Huaguo tea using headspace-gas chromatography-ion mobility spectrometry and multivariate statistical analysis

Feature extraction by learning Lorentzian metric tensor and its extensions

Semi-supervised orthogonal discriminant analysis via label propagation

In this paper, we propose a novel coupled dictionary learning method, namely coupled analysis-synthesis dictionary learning, to improve the performance of person re-identification in the non-overlapping fields of different camera views. Most of the existing coupled dictionary learning methods train a coupled synthesis dictionary directly on the original feature spaces, which limits the representation ability of the dictionary. To handle the diversities of different original spaces, We first employ local Fisher discriminant analysis (LFDA) to learn a common feature space for close relationship of the same people in different views. In order to enhance the representation power of the coupled synthesis dictionary, we then learn a coupled analysis dictionary by transforming the common feature space into the coupled feature space. Experimental results on two publicly available VIPeR and CUHK01 datasets have validated the effectiveness of the proposed method.

Background: In China, rhizome of Curcuma wenyujin (CW) is used to improve blood stasis syndrome-related diseases for many years. Nonsteamed, steamed, and boiled with vinegar rhizomes of CW can be used as three different traditional Chinese medicine s, named as Pian-Jiang-Huang (PJH), Sheng-E-Zhu (SEZ), and Cu-E-Zhu (CEZ), respectively. After processing, the therapeutic effects have changed. Objective: In order to illustrate the effective substance of the three kinds of rhizome of CW, an ultra-performance liquid chromatography-quadrupole time-of-flight mass spectrometry (UPLC-Q/TOF-MS) method coupled with statistical approach was developed. Materials and Methods: Fresh rhizomes of CW were processed into PJH, SEZ, and CEZ according to Chinese pharmacopoeia 2015. UPLC-Q/TOF-MS coupled with chemometric analysis was applied to compare the differences in chemical profiles of the three kinds of rhizome of CW. Results: In this study, 21 compositions in the rhizome of CW were identified. The one-way ANOVA of relative intensities of the 21 compositions was processed by SPSS software version 20.0. The column superposed graph of the relative intensities of 21 components shows that the total relative intensities of the 21 components in SEZ are the topmost and that of PJH is about the same as CEZ, but the proportion of each component is quite differ from each sample. Principal component analysis and orthogonal partial least squares discrimination analysis were processed by Simca-p14.1 software. Finally, five ions including curcumenone, curcumol, curzerenone, furanodiene, and germacrone were discovered to be the Q-Makers of the three kinds of rhizome of CW. Conclusion: This study provides a reliable research basis for the clinical application of the three kinds of rhizome of CW. Abbreviations used: PJH: Pian-Jiang-Huang; SEZ: Sheng-Er-Zhu; CEZ: Cu-Er-Zhu; CW: Curcuma wenyujin; PCA: Principal component analysis; OPLS-DA: Orthogonal partial least squares discrimination analysis; RT: Retention time; TCM: Traditional Chinese medicine; TIC: Total ion chromatogram; QC: Quality control; RSD: Relative standard deviation.

In order to investigate the flavour characteristics of aromatic, glutinous, and nonaromatic rice, gas chromatography-ion mobility spectrometry (GC-IMS) was used to analyse the differences in volatile organic compounds (VOCs) amongst different rice varieties. The results showed that 103 signal peaks were detected in these rice varieties, and 91 volatile flavour substances were identified. Amongst them, 28 aldehydes (28.89~31.17%), 24 alcohols (34.85~40.52%), 14 ketones (12.26~14.74%), 12 esters (2.30~4.15%), 5 acids (7.80~10.85%), 3 furans (0.30~0.68%), 3 terpenes (0.34~0.64%), and 2 species of ethers (0.80~1.78%) were detected. SIMCA14.1 was used to perform principal component analysis (PCA) and orthogonal partial least squares discriminant analysis, and some potential character markers (VIP > 1) were further screened out of the 91 flavour substances identified based on the variable important projections, including ethanol, 1-hexanol, hexanal, heptanal, nonanal, (E)-2-heptenal, octanal, trans-2-octenal, pentanal, acetone, 6-methyl-5-hepten-2-one, ethyl acetate, propyl acetate, acetic acid, and dimethyl sulphide. Based on the established fingerprint information, combined with principal component analysis and orthogonal partial least squares discriminant analysis, different rice varieties were also effectively classified, and the results of this study provide data references for the improvement in aromatic rice varieties.

Phellinus igniarius has antibacterial, antiviral, antioxidative, antitumor, and antimutagenic effects. In this study, an integrative pattern recognition approach using principal component analysis and orthogonal partial least squares discriminant analysis was successfully applied for the rapid analysis of natural compounds in traditional Chinese medicine. An ultra high performance liquid chromatography with synapt high-definition mass spectrometry method and MassLynx software was used. This method employed gradient elution to rapidly analyze and characterize chemical constituents and metabolites after the oral administration of a P. igniarius ethanol extract. There were 24 peaks within 10 min of the analysis time and 20 of these were identified or tentatively characterized on the basis of their fragmentation behaviors. In the S-plot of the orthogonal partial least squares discriminant analysis, 27 ions were extracted to make the serum. Among them, nine absorbed the prototype components and 18 metabolites were identified in vivo. Glucuronidation, oxidation, and methylation were the major metabolic reactions. This study is the first systematic analysis and characterization of the chemical constituents and metabolites in an ethanol extract of P. igniarius. This method can be applied to the rapid analysis and characterization of constituents in rat serum after the oral administration of other compounds used in traditional Chinese medicines.

Chemometrics identification of geographical origin of garlic in Korea using elements concentrations data obtained by ICP-OES and ICP-MS

SAT0199 Nmr-Based Metabolomic Analysis for The Diagnosis of Systemic Sclerosis