Adaptive fast local discriminant analysis with whitening transform.

Background: Linear Discriminant Analysis (LDA) is a powerful and widely used technique for classification with correlated variables. Principal Components (PCs) group these variables into linear combinations and produce independent variables. The LDA on these PC’s may provide better classification accuracy in clinical diagnostics than on usual measurements. Methodology: Two datasets were utilized for demonstration: one from a Sudden Sensorineural Hearing Loss (SSNHL) case-control study and the other from a Gall Bladder (GB) case-control study. Linear Discriminant Analysis (LDA) was conducted on the actual correlated measured variables for group classification, as well as on the derived principal component variables, to compare their classification accuracies. Performance metrics including Sensitivity, Specificity, Positive Predictive Value (PPV), Negative Predictive Value (NPV), Classification Accuracy, and F1 Score were assessed. For validation, a third simulated dataset was employed. Additionally, LDA was performed on each dataset using eigenvectors of the control group applied to the cases and vice versa, revealing a strong agreement in classification as measured by the kappa statistic. Results: When LDA was applied to the actual lipid measurements in the SSNHL dataset, the classification accuracy was 57.2%, and the F1 score was 39.7%. However, when LDA was performed using principal components (PCs), the classification accuracy markedly improved to 99.2%, with an F1 score of 98.5%. Similarly, for the GB cancer dataset, the classification accuracy and F1 score were initially 77.2% and 77.3%, respectively. Upon applying LDA with the PCs, these metrics were significantly enhanced to 98.4% and 98.3%, respectively. For the simulated dataset, both the classification accuracy and F1 score were 99.1%. The study also demonstrated that the classification accuracy and F1 score remained consistent regardless of whether the eigenvectors from the cases or controls were used to classify new subjects (Kappa Statistic = 0.962, P < 0.001). Conclusion: In group separation, utilizing principal components significantly improves classification accuracy and overall performance metrics, outperforming the use of the original correlated predictors.

Hyperspectral imagery generally contains enormous amounts of data due to hundreds of spectral bands. Classification for these high-dimensional data often requires a large set of training samples and enormous processing time. Therefore, dimension reduction methods for hyperspectral data are catching the attention of researchers lately. In this paper, a dimension reduction method based on sparse penalty regularized linear discriminant analysis was experimented on hyperspectral data. Through imposing sparsity regularization penalty on the Fisher's discriminant analysis projection matrix via the optimal scoring technique, sparse linear discriminant vectors can be achieved. Therefore, interpretability of the spectral bands' physical meaning and effective low dimensional data transforming can be achieved simultaneously in the same model. Experimental analysis on the sparsity and efficacy of low dimensional outputs showed that, sparse linear discriminant analysis can yield good classification results and interpretability in spectral domain.

Dimension reduction of multimodal data by auto-weighted local discriminant analysis

Linear discriminant analysis (LDA) is a classical method for discriminative dimensionality reduction. The original LDA may degrade in its performance for non-Gaussian data, and may be unable to extract sufficient features to satisfactorily explain the data when the number of classes is small. Two prominent extensions to address these problems are subclass discriminant analysis (SDA) and mixture subclass discriminant analysis (MSDA). They divide every class into subclasses and re-define the within-class and between-class scatter matrices on the basis of subclass. In this paper we study the issue of how to obtain subclasses more effectively in order to achieve higher class separation. We observe that there is significant overlap between models of the subclasses, which we hypothesise is undesirable. In order to reduce their overlap we propose an extension of LDA, separability oriented subclass discriminant analysis (SSDA), which employs hierarchical clustering to divide a class into subclasses using a separability oriented criterion, before applying LDA optimisation using re-defined scatter matrices. Extensive experiments have shown that SSDA has better performance than LDA, SDA and MSDA in most cases. Additional experiments have further shown that SSDA can project data into LDA space that has higher class separation than LDA, SDA and MSDA in most cases.

Sufficient dimension-reduction methods provide effective ways to visualize discriminant analysis problems. For example, Cook and Yin showed that the dimension-reduction method of sliced average variance estimation (SAVE) identifies variates that are equivalent to a quadratic discriminant analysis (QDA) solution. This article makes this connection explicit to motivate the use of SAVE variates in exploratory graphics for discriminant analysis. Classification can then be based on the SAVE variates using a suitable distance measure. If the chosen measure is Mahalanobis distance, then classification is identical to QDA using the original variables. Just as canonical variates provide a useful way to visualize linear discriminant analysis (LDA), so do SAVE variates help visualize QDA. This would appear to be particularly useful given the lack of graphical tools for QDA in current software. Furthermore, whereas LDA and QDA can be sensitive to nonnormality, SAVE is more robust.

The problems of adulteration and mislabeling are very common in the food industry. Laser-induced breakdown spectroscopy (LIBS) coupled with chemometric methods has many intrinsic advantages on adulteration analysis of various materials. In this work, several chemometric algorithms, i.e., principal component analysis (PCA), decision tree (DT), random forest (RF), partial least squares discriminant analysis (PLS-DA), linear discriminant analysis (LDA), and support vector machine (SVM), were carried out assisted by LIBS technology to study the classification performances on rice geographic origins. A series of samples, including 20 kinds of rice samples from different geographic origins, was detected using LIBS with no pretreatment processes. For data analysis, PCA was employed to reduce the input variables, and to reduce the collinearity of LIBS spectral results as well. The results showed the classification accuracies of the mentioned chemometric algorithms of DT, RF, PLS-DA, LDA, and SVM with 89 input variables of 86.80%, 96.30%, 96.80%, 98.60%, and 99.20%, respectively. At the same time, the operation times of these algorithms were 3.81 s, 54.64 s, 3.63 s, 2.09 s, and 531.01 s, respectively. On the other hand, 30 principal components of input variables were also tested under the same conditions. The classification accuracies for the above algorithms were 81.60%, 98.00%, 95.70%, 98.40%, and 99.20%, respectively. The operation times were 2.01 s, 4.88 s, 3.67 s, 0.36 s, and 308.55 s, respectively. In addition, the five-fold cross-validation classification accuracies with 30 input variables for DT, RF, PLS-DA, LDA, and SVM were 83.75%, 97.95%, 94.75%, 98.35%, and 99.25%, respectively. As a result, LDA was demonstrated to be the best and most efficient tool for rice geographic origin classification assisted by LIBS with high accuracy and analytical speed, which has great potential for rapid identification of adulterated products in agriculture without use of any chemical reagent.

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.

In the current manuscript, we present the results of comparative analysis of seven species of Meromyza flies in the “variegata” cluster and of the evolutionary close species M. inornata, based the following criteria: 1) 14 external key features; 2) shape and area of the anterior processes of postgonites; 3) mtDNA CO1 region and 4) host plant diversity data. We could demonstrate the primary role of host plants in species formation inside genus Meromyza and calculated the timing of the divergence of M. inornata and the species of “variegata” cluster. Based on our estimates of evolution rate for mtDNA CO1 gene, we could conclude that that divergence of herbs happened before the speciation of grass flies Meromyza. Meromyza species, close to the ancestral species of the cluster, are adapted to the wide range of host plants. We revealed the most informative variables h1, S and Plant analysing data with the following statistical methods: linear discriminant analysis - LDA, regularised discriminant analysis - RDA, flexible discriminant analysis – FDA and probabilistic neural network - PNN. The highest classification accuracy was achieved using PNN (99%) and the lowest when using LDA (95.8%). When the Plant trait was excluded, the classification accuracy decreased by 14%. We revealed the significant trends in size change of the anterior process of the postgonite amongst studies species. This morphological structure is an element of male reproductive apparatus critical for the restriction of interspecies mating. We determined three branches of speciation in the “variegata” cluster and five trends in the evolution of this cluster, based on the external morphological features. We showed that M. variegata and especially M. mosquensis, the species closest to the ancestral haplotype, have the largest number of features typical of those of M. inornata. Based on the external features and the area of the anterior process of the postgonite, we reconstructed the phylogenetic position of M. elbergi in the cluster. In accordance with the obtained outcomes, we could conclude that the distribution, species diversity and the adaptation of the grass flies to narrow oligophagy were directly connected to host plant diversity. The adaptation to different host plants could be the main factor in divergence of grass flies and their evolution started later than the diversification in the Pooideae subfamily of grasses.

In the current manuscript, we present the results of comparative analysis of seven species of Meromyza flies in the “variegata” cluster and of the evolutionary close species M. inornata, based the following criteria: 1) 14 external key features; 2) shape and area of the anterior processes of postgonites; 3) mtDNA CO1 region and 4) host plant diversity data. We could demonstrate the primary role of host plants in species formation inside genus Meromyza and calculated the timing of the divergence of M. inornata and the species of “variegata” cluster. Based on our estimates of evolution rate for mtDNA CO1 gene, we could conclude that that divergence of herbs happened before the speciation of grass flies Meromyza. Meromyza species, close to the ancestral species of the cluster, are adapted to the wide range of host plants. We revealed the most informative variables h1, S and Plant analysing data with the following statistical methods: linear discriminant analysis - LDA, regularised discriminant analysis - RDA, flexible discriminant analysis – FDA and probabilistic neural network - PNN. The highest classification accuracy was achieved using PNN (99%) and the lowest when using LDA (95.8%). When the Plant trait was excluded, the classification accuracy decreased by 14%. We revealed the significant trends in size change of the anterior process of the postgonite amongst studies species. This morphological structure is an element of male reproductive apparatus critical for the restriction of interspecies mating. We determined three branches of speciation in the “variegata” cluster and five trends in the evolution of this cluster, based on the external morphological features. We showed that M. variegata and especially M. mosquensis, the species closest to the ancestral haplotype, have the largest number of features typical of those of M. inornata. Based on the external features and the area of the anterior process of the postgonite, we reconstructed the phylogenetic position of M. elbergi in the cluster. In accordance with the obtained outcomes, we could conclude that the distribution, species diversity and the adaptation of the grass flies to narrow oligophagy were directly connected to host plant diversity. The adaptation to different host plants could be the main factor in divergence of grass flies and their evolution started later than the diversification in the Pooideae subfamily of grasses.

In the current manuscript, we present the results of comparative analysis of seven species of Meromyza flies in the “variegata” cluster and of the evolutionary close species M. inornata, based the following criteria: 1) 14 external key features; 2) shape and area of the anterior processes of postgonites; 3) mtDNA CO1 region and 4) host plant diversity data. We could demonstrate the primary role of host plants in species formation inside genus Meromyza and calculated the timing of the divergence of M. inornata and the species of “variegata” cluster. Based on our estimates of evolution rate for mtDNA CO1 gene, we could conclude that that divergence of herbs happened before the speciation of grass flies Meromyza. Meromyza species, close to the ancestral species of the cluster, are adapted to the wide range of host plants. We revealed the most informative variables h1, S and Plant analysing data with the following statistical methods: linear discriminant analysis - LDA, regularised discriminant analysis - RDA, flexible discriminant analysis – FDA and probabilistic neural network - PNN. The highest classification accuracy was achieved using PNN (99%) and the lowest when using LDA (95.8%). When the Plant trait was excluded, the classification accuracy decreased by 14%. We revealed the significant trends in size change of the anterior process of the postgonite amongst studies species. This morphological structure is an element of male reproductive apparatus critical for the restriction of interspecies mating. We determined three branches of speciation in the “variegata” cluster and five trends in the evolution of this cluster, based on the external morphological features. We showed that M. variegata and especially M. mosquensis, the species closest to the ancestral haplotype, have the largest number of features typical of those of M. inornata. Based on the external features and the area of the anterior process of the postgonite, we reconstructed the phylogenetic position of M. elbergi in the cluster. In accordance with the obtained outcomes, we could conclude that the distribution, species diversity and the adaptation of the grass flies to narrow oligophagy were directly connected to host plant diversity. The adaptation to different host plants could be the main factor in divergence of grass flies and their evolution started later than the diversification in the Pooideae subfamily of grasses.

The steady-state visual evoked potential (SSVEP) has been widely applied in brain-computer interfaces (BCIs), such as letter or icon selection and device control. Most of these BCIs used different flickering frequencies to evoke SSVEP with different frequency components that were used as control commands. In this paper, a novel method combining the time phase and EEG frequency components is presented and validated with nine healthy subjects. In this method, four different frequency components of EEG were classified out from four time phases. When the SSVEP is evoked and what is the frequency of the SSVEP is determined by the linear discriminant analysis (LDA) classifier in the same time to locate the target image. The results from offline analysis show that this method yields good performance both in classification accuracy and information transfer rate (ITR).KeywordsBrain-computer interfaces (BCIs)Electroencephalogram (EEG)Steady-state visual evoked potential (SSVEP)Time phase

Non-destructive impact test for assessment of tomato maturity

Improved PCA + LDA Applies to Gastric Cancer Image Classification Process

Research was conducted to investigate the use of optical, air-born acoustic and plasma charge signals for detecting defects in laser welds. Full penetration, partial penetration and gapped-full penetration butt-joint welds were made in 1.4mm cold-rolled steel sheet. A 3 kW CO2 laser was used to produce these three classes of welds while laser power, travel speed and joint fitup were varied to produce the various conditions. Visible light, audible sound and electrical charge near the plume were measured simultaneously in real-time using a silicon photodiode, a condensor microphone and a plasma charge sensing gas nozzle, respectively. The spectra of the sensor signals were analyzed by a statistical technique known as Linear Discriminant Analysis (LDA). Stepwise LDA was used to identify the most important frequency bands and canonical discriminant analysis was employed to develop discriminant functions. Reliability analysis of the training samples revealed that this LDA method classified laser welds with reliability ranging from 85% to 96%, depending on the welds selected for inclusion in the training set. When the linear discriminant function was validated using new (untrained) samples, it distinguished the three different classes of laser welds with approximately 87% accuracy. Among the three signals, sound produced better separation between the classes of welds, although a discriminator based on all three signals combined and one that used only plasma charge and acoustic signals were of almost equal reliability.Research was conducted to investigate the use of optical, air-born acoustic and plasma charge signals for detecting defects in laser welds. Full penetration, partial penetration and gapped-full penetration butt-joint welds were made in 1.4mm cold-rolled steel sheet. A 3 kW CO2 laser was used to produce these three classes of welds while laser power, travel speed and joint fitup were varied to produce the various conditions. Visible light, audible sound and electrical charge near the plume were measured simultaneously in real-time using a silicon photodiode, a condensor microphone and a plasma charge sensing gas nozzle, respectively. The spectra of the sensor signals were analyzed by a statistical technique known as Linear Discriminant Analysis (LDA). Stepwise LDA was used to identify the most important frequency bands and canonical discriminant analysis was employed to develop discriminant functions. Reliability analysis of the training samples revealed that this LDA method classified laser welds with rel...

Analytical capabilities of chemiresistive microsensor arrays in a simulated Martian atmosphere