Multi-class classification with probabilistic discriminant partial least squares (p-DPLS)

This work describes multi-classification based on binary probabilistic discriminant partial least squares (p-DPLS) models, developed with the strategy one-against-one and the principle of winner-takes-all. The multi-classification problem is split into binary classification problems with p-DPLS models. The results of these models are combined to obtain the final classification result. The classification criterion uses the specific characteristics of an object (position in the multivariate space and prediction uncertainty) to estimate the reliability of the classification, so that the object is assigned to the class with the highest reliability. This new methodology is tested with the well-known Iris data set and a data set of Italian olive oils. When compared with CART and SIMCA, the proposed method has better average performance of classification, besides giving a statistic that evaluates the reliability of classification. For the olive oil set the average percentage of correct classification for the training set was close to 84% with p-DPLS against 75% with CART and 100% with SIMCA, while for the test set the average was close to 94% with p-DPLS as against 50% with CART and 62% with SIMCA.     

Usefulness of chemometrics and mass spectrometry-based electronic nose to classify Australian white wines by their varietal origin

A combination of mass spectrometry-based electronic nose (MS e_nose) and chemometrics was explored to classify two Australian white wines according to their varietal origin namely Riesling and unwooded Chardonnay. The MS e_nose data were analysed using principal components analysis (PCA), discriminant partial least squares (DPLS) and linear discriminant analysis (LDA) applied to principal components scores and validated using full cross validation (leave one out). DPLS gave the highest levels of correct classification for both varieties (>90%). LDA classified correctly 73% of unwooded Chardonnay and 82% of Riesling wines. Even though the conventional analysis provides fundamental information about the volatile compounds present in the wine, the MS e_nose method has a series of advantages over conventional analytical techniques due to simplicity of the sample-preparation and reduced time of analysis and might be considered as a more convenient choice for routine process control in an industrial environment. The work reported here is a feasibility study and requires further development with considerably more commercial samples of different varieties. Further studies are needed in order to improve the calibration specificity, accuracy and robustness, and to extend the discrimination to other wine varieties or blends.     

Classification from microarray data using probabilistic discriminant partial least squares with reject option

Microarrays are used to simultaneously determine the expressions of thousands of genes. An important application of microarrays is in the classification of samples into classes of interest (e.g. either healthy cells or tumour cells). Discriminant partial least squares (DPLS) has often been used for this purpose. In this paper, we describe an improvement to DPLS that uses kernel-based probability density functions and the Bayes rule to classify samples whilst keeping the option of not classifying the sample if this cannot be done with sufficient confidence. With this approach, those samples outside the boundaries of the known classes or from the ambiguity region between classes are rejected and only samples with a high probability of being correctly classified are indeed classified. The optimal model is found by simultaneously minimizing the misclassification and rejection costs. The method (p-DPLS with reject option) was tested with two datasets. For the human cancers dataset the accuracy (obtained by leave-one-out cross-validation) was improved from 97% to 99% when compared to p-DPLS without reject option. For the breast cancer dataset, p-DPLS with reject option was able to reject 100% of the test samples that did not belong to any of the modelled classes. These samples would have been misclassified if the reject option had not been considered.     

蜂蜜真伪的近红外光谱鉴别研究

如何有效鉴别蜂蜜真伪是目前我国蜂产品质量控制的难题之一。提出了一种用傅里叶变换近红外光谱结合判别偏最小二乘法(DPLS)快速鉴别蜂蜜真伪的新方法。首先采集了71个商品蜜样品的近红外光谱数据,其中包括27个纯蜂蜜和44个掺假蜂蜜,然后5次随机划分建模集样本和验证集样本,并对建模样本进行不同光谱预处理,选择并优化不同波段范围和主成分数,用DPLS法建立了5组蜂蜜样本的真伪鉴别模型,外部交叉验证法预测模型。通过对结果进行比较分析,5组校正模型中真蜂蜜和掺假蜂蜜的总体识别准确率分别为91.49%,94.68%,92.98%,93.86%,94.87%;预测样本的识别准确率为86.96%～93.75%,其中模型2,3,4中掺假蜜的识别准确率达100%。研究结果表明,该方法可作为鉴别商品蜜真伪的一种快速筛选技术,在我国蜂蜜质量监控中具有重要意义。     

Multi-class tumor classification by discriminant partial least squares using microarray gene expression data and assessment of classification models

High-throughput DNA microarray provides an effective approach to the monitoring of expression levels of thousands of genes in a sample simultaneously. One promising application of this technology is the molecular diagnostics of cancer, e.g. to distinguish normal tissue from tumor or to classify tumors into different types or subtypes. One problem arising from the use of microarray data is how to analyze the high-dimensional gene expression data, typically with thousands of variables (genes) and much fewer observations (samples). There is a need to develop reliable classification methods to make full use of microarray data and to evaluate accurately the predictive ability and reliability of such derived models. In this paper, discriminant partial least squares was used to classify the different types of human tumors using four microarray datasets and showed good prediction performance. Four different cross-validation procedures (leave-one-out versus leave-half-out; incomplete versus full) were used to evaluate the classification model. Our results indicate that discriminant partial least squares using leave-half-out cross-validation provides a more realistic estimate of the predictive ability of a classification model, which may be overestimated by some of the cross-validation procedures, and the information obtained from different cross-validation procedures can be used to evaluate the reliability of the classification model.     

近红外光谱技术鉴别花椒产地

采集四川、重庆、云南、贵州、陕西五省市8个不同产地205个花椒样品的近红外光谱,使用主成分分析(principal component analysis, PCA)、判别偏最小二乘法(discriminant partial least squares, DPLS)分析了花椒产地的分类鉴别。结果表明：在12 500～3 800 cm-1波数范围内,采用不同的光谱预处理方法可以建立较为稳健的DPLS模式识别模型,对不同产地的花椒有较好的分类鉴别。其校正集交叉验证除了经一阶微分预处理的模型识别率为99.39%外,其他预处理方法识别率均为100%,独立验证集总体识别正确率在85.37%~97.56%之间,其中经标准正态变量变换(standard normal variate, SNV)、多元散射校正(multiplicative scatter correction, MSC)预处理后的DPLS判别模型效果最好,误判数仅分别为1个,表示该方法在花椒产地识别中具有可行性。     

Establishment of multivariate specifications for food commodities with discriminant partial least squares

A novel method for establishing multivariate specifications of food commodities is proposed. The specifications are established for discriminant partial least squares (DPLS) by setting limits on the predictions of the DPLS model together with Hotelling T² and square error of prediction (SPE). These limits can be tuned depending on whether type I error (i.e. a correct sample is declared out-of-specification) or type II error (i.e. an out-of-specification sample is declared within specifications) need to be minimized. The methodology is illustrated with a set of NIR spectra of Italian olive oils, corresponding to five regions and the class Liguria is the class of interest. The results demonstrate the possibility of establishing multivariate specification for olive oils from the Liguria region on the basis of spectral data obtaining type I and type II errors lower than 5%.