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.
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Book•
01 Jan 2000
TL;DR: In this article, the authors discuss the role of theory and experimental design in multivariate analysis and mathematical modeling, and propose an approach for the use of multiple regression analysis in mathematical models.
Abstract: Introduction. H.E.A. Tinsley and S.D. Brown, Multivariate Statistics and Mathematical Modeling. J. Hetherington, Role of Theory and Experimental Design in Multivariate Analysis and Mathematical Modeling. R.V. Dawis, Scale Construction and Psychometric Considerations. H.E.A. Tinsley and D.J. Weiss, Interrater Reliability and Agreement. M. Hallahan and R. Rosenthal, Interpreting and Reporting Results. A. Venter and S.E. Maxwell, Issues in the Use and Application of Multiple Regression Analysis. C.J. Huberty and M.D. Petoskey, Multivariate Analysis of Variance and Covariance. M.T. Brown and L.R. Wicker, Discriminant Analysis. R.M. Thorndike, Canonical Correlation Analysis. R. Cudeck, Exploratory Factor Analysis. P.A. Gore, Jr., Cluster Analysis. M.L. Davison and S.G. Sireci, Multidimensional Scaling. M.M. Mark, C.S. Reichardt, and L.J. Sanna, Time-Series Designs and Analyses. P.B. Imrey, Poisson Regression, Logistic Regression, and Loglinear Models for Random Counts. L.F. Dilalla, Structural Equation Modeling: Uses and Issues. R.H. Hoyle, Confirmatory Factor Analysis. B.J. Becker, Multivariate Meta-analysis. G.A. Marcoulides, Generalizability Theory. R.K. Hambelton, F. Robin, and D. Xing, Item Response Models for the Analysis of Educational and Psychological Test Data. L. Dumenci, Multitrait-Multimethod Analysis. I.G.G. Kreft, Using Random Coefficient Linear Models for the Analysis of Hierarchically Nested Data. T.J.G. Tracey, Analysis of Circumplex Models. J.B. Willett and M.K. Keiley, Using Covariance Structure Analysis to Model Change over Time. Author Index. Subject Index.
1,010 citations
Book•
01 Jan 2005
TL;DR: A review of basic statistics with SPSS can be found in this paper, where the authors present several measures of reliability, such as repeated measures and mixed ANOVAs, as well as a survey of the literature.
Abstract: Introduction and Review of Basic Statistics With SPSS. Data Coding and Exploratory Analysis (EDA). Several Measures of Reliability. Exploratory Factor Analysis and Principal Components Analysis. Selecting and Interpreting Inferential Statistics. Multiple Regression. Logistic Regression and Discriminant Analysis. Factorial ANOVA and ANCOVA. Repeated Measures and Mixed ANOVAs. Multivariate Analysis of Variance (MANOVA) and Canonical Correlation. Multilevel Linear Modeling/Hierarchical Linear Modeling. Appendices.
986 citations
TL;DR: This paper investigates the predictability of financial movement direction with SVM by forecasting the weekly movement direction of NIKKEI 225 index and proposes a combining model by integrating SVM with the other classification methods.
984 citations
Book•
06 Feb 1998TL;DR: An overview of applied multivariate methods, Matrix results, quadratic forms, eigenvalues and eigenvectors, distances and angles, miscellaneous results work attitudes survey, data file structure, SPSS data entry commands, SAS data entry command study.
Abstract: 1. Applied multivariate methods. An Overview of Multivariate Methods. Two Examples. Types of Variables. Data Matrices and Vectors. The Multivariate Normal Distribution. Statistical Computing. Multivariate Outliers. Multivariate Summary Statistics. Standardized Data and/or z-Scores. Exercises. 2. Sample correlations. Statistical Tests and Confidence Intervals. Summary. Exercises. 3. Multivariate data plots. Three-Dimensional Data Plots. Plots of Higher Dimensional Data. Plotting to Check for Multivariate Normality. Exercises. 4. Eigenvalues and eigenvectors. Trace and Determinant. Eigenvalues. Eigenvectors. Geometrical Descriptions (p=2). Geometrical Descriptions (p=3). Geometrical Descriptions (p>3). Exercises. 5. Principal components analysis. Reasons For Doing a PCA. Objectives of a PCA. PCA on the Variance-Covariance Matrix, Sigma. Estimation of Principal Components. Determining the Number of Principal Components. Caveats. PCA on the Correlation Matrix, P. Testing for Independence of the Original Variables. Structural Relationships. Statistical Computing Packages. Exercises. 6. Factor analysis. Objectives of an FA. Caveats. Some History on Factor Analysis. The Factor Analysis Model. Factor Analysis Equations. Solving the Factor Analysis Equations. Choosing the Appropriate Number of Factors. Computer Solutions of the Factor Analysis Equations. Rotating Factors. Oblique Rotation Methods. Factor Scores. Exercises. 7. Discriminant analysis. Discrimination for Two Multivariate Normal Populations. Cost Functions and Prior Probabilities (Two Populations). A General Discriminant Rule (Two Populations). Discriminant Rules (More Than Two Populations). Variable Selection Procedures. Canonical Discriminant Functions. Nearest Neighbour Discriminant Analysis. Classification Trees. Exercises. 8. Logistic regression methods. The Logit Transformation. Logistic Discriminant Analysis (More than Two Populations.) Exercises. 9. Cluster analysis. Measures of Similarity and/or Dissimilarity. Graphical Aids in Clustering. Clustering Methods. Multidimensional Scaling. Exercises. 10. Mean vectors and variance-covariance matrices. Inference Procedures for Variance-Covariance Matrices. Inference Procedures for a Mean Vector. Two Sample Procedures. Profile Analyses. Additional Two Groups Analyses. Exercises. 11. Multivariate analysis of variance. manova. Dimensionality of the Alternative Hypothesis. Canonical Variates Analysis. Confidence Regions for Canonical Variates. Exercises. 12. Prediction models and multivariate regression. Multiple Regression. Canonical Correlation Analysis. Factor Analysis and Regression. Exercises. Appendices: Matrix results, quadratic forms, eigenvalues and eigenvectors, distances and angles, miscellaneous results work attitudes survey, data file structure, SPSS data entry commands, SAS data entry commands family control study.
982 citations
TL;DR: Although each classifier could yield a very accurate classification, > 90% correct, the classifiers differed in the ability to correctly label individual cases and so may be suitable candidates for an ensemble-based approach to classification.
Abstract: Support vector machines (SVMs) have considerable potential as classifiers of remotely sensed data. A constraint on their application in remote sensing has been their binary nature, requiring multiclass classifications to be based upon a large number of binary analyses. Here, an approach for multiclass classification of airborne sensor data by a single SVM analysis is evaluated against a series of classifiers that are widely used in remote sensing, with particular regard to the effect of training set size on classification accuracy. In addition to the SVM, the same datasets were classified using a discriminant analysis, decision tree, and multilayer perceptron neural network. The accuracy statements of the classifications derived from the different classifiers were compared in a statistically rigorous fashion that accommodated for the related nature of the samples used in the analyses. For each classification technique, accuracy was positively related with the size of the training set. In general, the most accurate classifications were derived from the SVM approach, and with the largest training set the SVM classification was significantly (p 90% correct, the classifiers differed in the ability to correctly label individual cases and so may be suitable candidates for an ensemble-based approach to classification.
962 citations