scispace - formally typeset
Search or ask a question
Topic

Linear discriminant analysis

About: Linear discriminant analysis is a research topic. Over the lifetime, 18361 publications have been published within this topic receiving 603195 citations. The topic is also known as: Linear discriminant analysis & LDA.


Papers
More filters
Journal ArticleDOI
TL;DR: In this paper, the authors used ten advanced and soft computing models applied to the Beheshtabad Watershed, Iran to model groundwater potential by qanat locations as indicators.
Abstract: Considering the unstable condition of water resources in Iran and many other countries in arid and semi-arid regions, groundwater studies are very important. Therefore, the aim of this study is to model groundwater potential by qanat locations as indicators and ten advanced and soft computing models applied to the Beheshtabad Watershed, Iran. Qanat is a man-made underground construction which gathers groundwater from higher altitudes and transmits it to low land areas where it can be used for different purposes. For this purpose, at first, the location of the qanats was detected using extensive field surveys. These qanats were classified into two datasets including training (70%) and validation (30%). Then, 14 influence factors depicting the region’s physical, morphological, lithological, and hydrological features were identified to model groundwater potential. Linear discriminant analysis (LDA), quadratic discriminant analysis (QDA), flexible discriminant analysis (FDA), penalized discriminant analysis (PDA), boosted regression tree (BRT), random forest (RF), artificial neural network (ANN), K-nearest neighbor (KNN), multivariate adaptive regression splines (MARS), and support vector machine (SVM) models were applied in R scripts to produce groundwater potential maps. For evaluation of the performance accuracies of the developed models, ROC curve and kappa index were implemented. According to the results, RF had the best performance, followed by SVM and BRT models. Our results showed that qanat locations could be used as a good indicator for groundwater potential. Furthermore, altitude, slope, plan curvature, and profile curvature were found to be the most important influence factors. On the other hand, lithology, land use, and slope aspect were the least significant factors. The methodology in the current study could be used by land use and terrestrial planners and water resource managers to reduce the costs of groundwater resource discovery.

131 citations

Journal ArticleDOI
TL;DR: In this paper, a framework for investigating predictability based on information theory is presented, which connects and unifies a wide variety of statistical methods traditionally used in predictability analysis, including linear regression, canonical correlation analysis, singular value decomposition, discriminant analysis, and data assimilation.
Abstract: [1] This paper summarizes a framework for investigating predictability based on information theory. This framework connects and unifies a wide variety of statistical methods traditionally used in predictability analysis, including linear regression, canonical correlation analysis, singular value decomposition, discriminant analysis, and data assimilation. Central to this framework is a procedure called predictable component analysis (PrCA). PrCA optimally decomposes variables by predictability, just as principal component analysis optimally decomposes variables by variance. For normal distributions the same predictable components are obtained whether one optimizes predictive information, the dispersion part of relative entropy, mutual information, Mahalanobis error, average signal to noise ratio, normalized mean square error, or anomaly correlation. For joint normal distributions, PrCA is equivalent to canonical correlation analysis between forecast and observations. The regression operator that maps observations to forecasts plays an important role in this framework, with the left singular vectors of this operator being the predictable components and the singular values being the canonical correlations. This correspondence between predictable components and singular vectors occurs only if the singular vectors are computed using Mahalanobis norms, a result that sheds light on the role of norms in predictability. In linear stochastic models the forcing that minimizes predictability is the one that renders the “whitened” dynamical operator normal. This condition for minimum predictability is invariant to linear transformation and is equivalent to detailed balance. The framework also inspires some new approaches to accounting for deficiencies of forecast models and estimating distributions from finite samples.

131 citations

Proceedings ArticleDOI
23 Jun 1998
TL;DR: The rationales behind PCA and LDA and the pros and cons of applying them to pattern classification task are illustrated and the improved performance of this combined approach is demonstrated.
Abstract: In face recognition literature, holistic template matching systems and geometrical local feature based systems have been pursued. In the holistic approach, PCA (Principal Component Analysis) and LDA (Linear Discriminant Analysis) are popular ones. More recently, the combination of PCA and LDA has been proposed as a superior alternative over pure PCA and LDA. In this paper, we illustrate the rationales behind these methods and the pros and cons of applying them to pattern classification task. A theoretical performance analysis of LDA suggests applying LDA over the principal components from the original signal space or the subspace. The improved performance of this combined approach is demonstrated through experiments conducted on both simulated data and real data.

131 citations

Journal ArticleDOI
TL;DR: This work compares the performances of many classical criteria to select these models: information criteria as AIC, the Bayesian criterion BIC, classification criteria as NEC and cross-validation, and finds that information criteria and BIC outperform the classification criteria.
Abstract: Using an eigenvalue decomposition of variance matrices, Celeux and Govaert (1993) obtained numerous and powerful models for Gaussian model-based clustering and discriminant analysis. Through Monte Carlo simulations, we compare the performances of many classical criteria to select these models: information criteria as AIC, the Bayesian criterion BIC, classification criteria as NEC and cross-validation. In the clustering context, information criteria and BIC outperform the classification criteria. In the discriminant analysis context, cross-validation shows good performance but information criteria and BIC give satisfactory results as well with, by far, less time-computing.

131 citations

Journal ArticleDOI
TL;DR: The enhanced classification accuracy of the SVM using only two easily obtainable basic gait parameters makes it attractive for identifying CP children as well as for evaluating the effectiveness of various treatment methods and rehabilitation techniques.
Abstract: Accurate identification of cerebral palsy (CP) gait is important for diagnosis as well as for proper evaluation of the treatment outcomes. This paper explores the use of support vector machines (SVM) for automated detection and classification of children with CP using two basic temporal-spatial gait parameters (stride length and cadence) as input features. Application of the SVM method to a children's dataset (68 normal healthy and 88 with spastic diplegia form of CP) and testing on tenfold cross-validation scheme demonstrated that an SVM classifier was able to classify the children groups with an overall accuracy of 83.33% [sensitivity 82.95%, specificity 83.82%, area under the receiver operating curve (AUC-ROC=0.88)]. Classification accuracy improved significantly when the gait parameters were normalized by the individual leg length and age, leading to an overall accuracy of 96.80% (sensitivity 94.32%, specificity 100%, AUC-DROC area=0.9924). This accuracy result was, respectively, 3.21% and 1.93% higher when compared to an linear discriminant analysis and an multilayer-perceptron-based classifier. SVM classifier also attains considerably higher ROC area than the other two classifiers. Among the four SVM kernel functions (linear, polynomial, radial basis, and analysis of variance spline) studied, the polynomial and radial basis kernel performed comparably and outperformed the others. Classifier's performance as functions of regularization and kernel parameters was also investigated. The enhanced classification accuracy of the SVM using only two easily obtainable basic gait parameters makes it attractive for identifying CP children as well as for evaluating the effectiveness of various treatment methods and rehabilitation techniques

131 citations


Network Information
Related Topics (5)
Regression analysis
31K papers, 1.7M citations
85% related
Artificial neural network
207K papers, 4.5M citations
80% related
Feature extraction
111.8K papers, 2.1M citations
80% related
Cluster analysis
146.5K papers, 2.9M citations
79% related
Image segmentation
79.6K papers, 1.8M citations
79% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20251
20242
2023756
20221,711
2021678
2020815