A lower bound on the performance of the quadratic discriminant function

The quadratic discriminant function is often used to separate two classes of points in a multidimensional space. When the two classes are normally distributed, this results in the optimum separation. In some cases however, the assumption of normality is a poor one and the classification error is increased. The current paper derives an upper bound for the classification error due to a quadratic decision surface. The bound is strict when the class means and covariances and the quadratic discriminant surface satisfy certain specified symmetry conditions.     

Higher discriminants of binary forms

We propose a method for constructing systems of polynomial equations that define submanifolds of degenerate binary forms of an arbitrary degeneracy degree. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 2, pp. 147–157, November, 2007.     

奇异类内离差矩阵条件下的Fisher最优判据

特征提取是模式分类与识别的重要环节，Fisher最优判据是特征提取的基本方法之一．本文提出了一种计算奇异类内离差矩阵条件下Fisher最优判据的新方法，并给出了计算步骤．     

A two step algorithm for solving a large scale semi-definite logit model

This paper proposes a two step algorithm for solving a large scale semi-definite logit model, which is appreciated as a powerful model in failure discriminant analysis. This problem has been successfully solved by a cutting plane (outer approximation) algorithm. However, it requires much more computation time than the corresponding linear logit model. A two step algorithm to be proposed in this paper is intended to reduce the amount of computation time by eliminating a certain portion of the data based on the information obtained by solving an associated linear logit model. It will be shown that this algorithm can generate a solution with almost the same quality as the solution obtained by solving the original large scale semi-definite model within a fraction of computation time.     

关于企业经济效益综合评价模型的再讨论——利用费歇判别值进行排序的质疑

本文从理论上讨论了费歇判别与回归模型的等价，指出了利用费歇判别值对企业的综合经济效益进行排序是不合理的，并提出了改进的综合评价方法     

Characterisation of the comonomer composition and distribution of copolymers using chemometric techniques

Chemometric techniques have been applied to FTIR and DSC data to correlate polymer composition. Since structural differences in the polymers with only hydrocarbon structure, often cause subtle changes in spectra, the ability of chemometric techniques is required to discern these differences. FTIR spectra and thermal fractionation using DSC were measured for 28 types of polyethylenes (PE) varying in chain branching type, content and distribution. Unsupervised clustering methods such as principal component analysis (PCA) and supervised discriminant analysis were used to classify the PEs according to their structural class. The DSC data was the more successful in both classifying PEs according to their class. This revised version was published online in July 2006 with corrections to the Cover Date.     

Metabolomic-based investigation of Yinlan alleviating hyperlipidemia by inhibiting blood stasis and phlegm turbidity through the PXR-CYP3A4-ABCB1-FXR pathway

Yinlan lipid regulatory capsule (YL) is a composite traditional Chinese medicine (TCM) new drug to alleviate hyperlipidemia, while its therapeutic mechanism in vivo was not clarified with nontargeted metabolomics investigation. An animal model was established in rats fed a high-fat diet, and their body weights, body mass index (BMI) and blood cholesterol levels were measured. Serum, liver and kidney tissue samples were also extracted for PXR-CYP3A4-ABCB1-FXR signaling pathway research using PCR and UHPLC–MS. The obtained plasma samples were analyzed by UHPLC-Q-TOF-MS metabolomic investigation, which revealed PXR-CYP3A4-related metabolites and changes induced by YL. Finally, the key metabolites were chosen as index components, and their levels in the serum, liver, small intestine and bile were used for simultaneous UHPLC–MS-MS determination. The results indicated that YL was effective in rebalancing blood TG and TC levels (compared to controls). With respect to the PXR-CYP3A4-ABCB1 pathway, as a result of YL’s effect, gene expression or activity of the two targets decreased significantly in both the liver and kidney. The same trend was observed in the serum samples mentioned above. Metabolomics screening and data revealed that 44 metabolites can be regarded as biomarkers related to hyperlipidemia, fatty acids synthesis, and body energy consumption, as well as synthesis, transportation and exertion of cholesterol. YL’s treatment focused on 26 of them, primarily bile acids, indicating that the antihyperlipidemic effect of this drug lies in its inhibitory activity of cholesterol metabolism. Subsequent analysis of those in vivo components revealed that significant increases (compared to the model group) occurred in the blood, liver, small intestine and bile in groups that received medium and high doses of YL (while the low dose was relatively unchanged). Those target components exhibit a close relationship with PXR and/or CYP3A4. The use of YL repressed PXR expression and subsequently decreased CYP3A4 activity. As a result, synthesis of related bile acids increased, while cholesterol levels decreased, consequently leading to the attenuation of hyperlipidemia. This study comprehensively investigated the antihyperlipidemia mechanism of YL based on its repression of PXR-CYP3A4 activity and related metabolite yield, establishing an accurate method for evaluating the therapeutic effect of YL.     

Quality evaluation of fingerprints of herbal medicine with chromatographic data

In this study, local least squares (LLS) and principal component analysis (PCA) were applied to deal with the disturbances in a data set of chromatographic fingerprints after necessary data transformations. It has been demonstrated that PCA with standard normal variate (SNV) transformation of data led to meaningful classification of 33 different Erigeron breviscapus herbal samples. The result was also corroborated by variance squares discriminant method. The quality of herbal objects was further evaluated, and the causes of this fact have been explained from a chemical point of view. At the same time, it implied an idea for qualitative evaluation of the herbal objects with a common class pattern of chromatographic fingerprints.     

Chemometric classification of gunshot residues based on energy dispersive X-ray microanalysis and inductively coupled plasma analysis with mass-spectrometric detection

A gunshot residue sample that was collected from an object or a suspected person is automatically searched for gunshot residue relevant particles. Particle data (such as size, morphology, position on the sample for manual relocation, etc.) as well as the corresponding X-ray spectra and images are stored. According to these data, particles are classified by the analysis-software into different groups: ‘gunshot residue characteristic’, ‘consistent with gunshot residue’ and environmental particles, respectively. Potential gunshot residue particles are manually checked and – if necessary – confirmed by the operating forensic scientist.     

Chemometric interpretation of pesticide occurence in soil samples from an intensive horticulture area in north Portugal

An extensive monitoring programme of pesticides was carried out in soil samples from an intensive horticulture area in north of Portugal, putting into practice the needs for increased control of soil quality as far as organic pollution is concerned. The area under investigation was additionally defined as vulnerable to nitrates due to local soil and aquifer characteristics, which might be extended to pesticides contamination. Five sampling sites were selected and soils analysed at three depths in eight sampling campaigns, for the period of 2 years. A stepwise multivariate statistical approach was selected to uncover most relevant patterns inside a complex environmental data matrix. Cluster analysis was applied both to group pesticides and samples, giving a primary and unsupervised overlook of privileged relationships. Clusters of persistent pesticides and selected herbicides were identified, whereas sample classes were also formed and disposed geographically. Thirty eight percent of analysed soils samples fell into one class characterized by low contamination (class 1 in cluster analysis), which is entirely representative of the sampling site no. 1. Afterwards, linear discriminant analysis was applied to identify those pesticides, which had a higher impact in the definition of classes. Finally, factor analysis using a five component model was implemented in order to bring to light the constitution and data variance explained by each of the five main principal components, as well as, their relation to pest management practices. A factor was identified (PC1 – 22% variance) composed of chlorinated pesticides, which was representative of one of the investigated sites indicating its high contamination status. Qualitative main findings and class average concentration values were obtained through this multivariate statistical approach.