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.

Detecting hidden messages using higher-order statistical models

Abstract: Techniques for information hiding have become increasingly more sophisticated and widespread. With high-resolution digital images as carriers, detecting hidden messages has become considerably more difficult. This paper describes a new approach to detecting hidden messages in images. The approach uses a wavelet-like decomposition to build higher-order statistical models of natural images. A Fisher (1936) linear discriminant analysis is then used to discriminate between untouched and adulterated images.

Statistics for Sensory and Consumer Science

Abstract: Preface. Acknowledgements. 1 Introduction. 1.1 The Distinction between Trained Sensory Panels and Consumer Panels. 1.2 The Need for Statistics in Experimental Planning and Analysis. 1.3 Scales and Data Types. 1.4 Organisation of the Book. 2 Important Data Collection Techniques for Sensory and Consumer Studies. 2.1 Sensory Panel Methodologies. 2.2 Consumer Tests. PART I PROBLEM DRIVEN. 3 Quality Control of Sensory Profile Data. 3.1 General Introduction. 3.2 Visual Inspection of Raw Data. 3.3 Mixed Model ANOVA for Assessing the Importance of the Sensory Attributes. 3.4 Overall Assessment of Assessor Differences Using All Variables Simultaneously. 3.5 Methods for Detecting Differences in Use of the Scale. 3.6 Comparing the Assessors Ability to Detect Differences between the Products. 3.7 Relations between Individual Assessor Ratings and the Panel Average. 3.8 Individual Line Plots for Detailed Inspection of Assessors. 3.9 Miscellaneous Methods.- 4 Correction Methods and Other Remedies for Improving Sensory Profile Data. 4.1 Introduction. 4.2 Correcting for Different Use of the Scale. 4.3 Computing Improved Panel Averages. 4.4 Pre-processing of Data for Three-Way Analysis. 5 Detecting and Studying Sensory Differences and Similarities between Products. 5.1 Introduction. 5.2 Analysing Sensory Profile Data: Univariate Case. 5.3 Analysing Sensory Profile Data: Multivariate Case. 6 Relating Sensory Data to Other Measurements. 6.1 Introduction. 6.2 Estimating Relations between Consensus Profiles and External Data. 6.3 Estimating Relations between Individual Sensory Profiles and External Data. 7 Discrimination and Similarity Testing. 7.1 Introduction. 7.2 Analysis of Data from Basic Sensory Discrimination Tests. 7.3 Examples of Basic Discrimination Testing. 7.4 Power Calculations in Discrimination Tests. 7.5 Thurstonian Modelling: What Is It Really? 7.6 Similarity versus Difference Testing. 7.7 Replications: What to Do? 7.8 Designed Experiments, Extended Analysis and Other Test Protocols. 8 Investigating Important Factors Influencing Food Acceptance and Choice. 8.1 Introduction. 8.2 Preliminary Analysis of Consumer Data Sets (Raw Data Overview). 8.3 Experimental Designs for Rating Based Consumer Studies. 8.4 Analysis of Categorical Effect Variables. 8.5 Incorporating Additional Information about Consumers. 8.6 Modelling of Factors as Continuous Variables. 8.7 Reliability/Validity Testing for Rating Based Methods. 8.8 Rank Based Methodology. 8.9 Choice Based Conjoint Analysis. 8.10 Market Share Simulation. 9 Preference Mapping for Understanding Relations between Sensory Product Attributes and Consumer Acceptance. 9.1 Introduction. 9.2 External and Internal Preference Mapping. 9.3 Examples of Linear Preference Mapping. 9.4 Ideal Point Preference Mapping. 9.5 Selecting Samples for Preference Mapping. 9.6 Incorporating Additional Consumer Attributes. 9.7 Combining Preference Mapping with Additional Information about the Samples. 10 Segmentation of Consumer Data. 10.1 Introduction. 10.2 Segmentation of Rating Data. 10.3 Relating Segments to Consumer Attributes. PART II METHOD ORIENTED. 11 Basic Statistics. 11.1 Basic Concepts and Principles. 11.2 Histogram, Frequency and Probability. 11.3 Some Basic Properties of a Distribution (Mean, Variance and Standard Deviation). 11.4 Hypothesis Testing and Confidence Intervals for the Mean . 11.5 Statistical Process Control. 11.6 Relationships between Two or More Variables. 11.7 Simple Linear Regression. 11.8 Binomial Distribution and Tests. 11.9 Contingency Tables and Homogeneity Testing. 12 Design of Experiments for Sensory and Consumer Data. 12.1 Introduction. 12.2 Important Concepts and Distinctions. 12.3 Full Factorial Designs. 12.4 Fractional Factorial Designs: Screening Designs. 12.5 Randomised Blocks and Incomplete Block Designs. 12.6 Split-Plot and Nested Designs. 12.7 Power of Experiments. 13 ANOVA for Sensory and Consumer Data. 13.1 Introduction. 13.2 One-Way ANOVA. 13.3 Single Replicate Two-Way ANOVA. 13.4 Two-Way ANOVA with Randomised Replications. 13.5 Multi-Way ANOVA. 13.6 ANOVA for Fractional Factorial Designs. 13.7 Fixed and Random Effects in ANOVA: Mixed Models. 13.8 Nested and Split-Plot Models. 13.9 Post Hoc Testing. 14 Principal Component Analysis. 14.1 Interpretation of Complex Data Sets by PCA. 14.2 Data Structures for the PCA. 14.3 PCA: Description of the Method. 14.4 Projections and Linear Combinations. 14.5 The Scores and Loadings Plots. 14.6 Correlation Loadings Plot. 14.7 Standardisation. 14.8 Calculations and Missing Values. 14.9 Validation. 14.10 Outlier Diagnostics. 14.11 Tucker-1. 14.12 The Relation between PCA and Factor Analysis (FA). 15 Multiple Regression, Principal Components Regression and Partial Least Squares Regression. 15.1 Introduction. 15.2 Multivariate Linear Regression. 15.3 The Relation between ANOVA and Regression Analysis. 15.4 Linear Regression Used for Estimating Polynomial Models. 15.5 Combining Continuous and Categorical Variables. 15.6 Variable Selection for Multiple Linear Regression. 15.7 Principal Components Regression (PCR). 15.8 Partial Least Squares (PLS) Regression. 15.9 Model Validation: Prediction Performance. 15.10 Model Diagnostics and Outlier Detection. 15.11 Discriminant Analysis. 15.12 Generalised Linear Models, Logistic Regression and Multinomial Regression. 16 Cluster Analysis: Unsupervised Classification. 16.1 Introduction. 16.2 Hierarchical Clustering. 16.3 Partitioning Methods. 16.4 Cluster Analysis for Matrices. 17 Miscellaneous Methodologies. 17.1 Three-Way Analysis of Sensory Data. 17.2 Relating Three-Way Data to Two-Way Data. 17.3 Path Modelling. 17.4 MDS-Multidimensional Scaling. 17.5 Analysing Rank Data. 17.6 The L-PLS Method. 17.7 Missing Value Estimation. Nomenclature, Symbols and Abbreviations. Index.

Capitalize on dimensionality increasing techniques for improving face recognition grand challenge performance

Abstract: This paper presents a novel pattern recognition framework by capitalizing on dimensionality increasing techniques. In particular, the framework integrates Gabor image representation, a novel multiclass kernel Fisher analysis (KFA) method, and fractional power polynomial models for improving pattern recognition performance. Gabor image representation, which increases dimensionality by incorporating Gabor filters with different scales and orientations, is characterized by spatial frequency, spatial locality, and orientational selectivity for coping with image variabilities such as illumination variations. The KFA method first performs nonlinear mapping from the input space to a high-dimensional feature space, and then implements the multiclass Fisher discriminant analysis in the feature space. The significance of the nonlinear mapping is that it increases the discriminating power of the KFA method, which is linear in the feature space but nonlinear in the input space. The novelty of the KFA method comes from the fact that 1) it extends the two-class kernel Fisher methods by addressing multiclass pattern classification problems and 2) it improves upon the traditional generalized discriminant analysis (GDA) method by deriving a unique solution (compared to the GDA solution, which is not unique). The fractional power polynomial models further improve performance of the proposed pattern recognition framework. Experiments on face recognition using both the FERET database and the FRGC (face recognition grand challenge) databases show the feasibility of the proposed framework. In particular, experimental results using the FERET database show that the KFA method performs better than the GDA method and the fractional power polynomial models help both the KFA method and the GDA method improve their face recognition performance. Experimental results using the FRGC databases show that the proposed pattern recognition framework improves face recognition performance upon the BEE baseline algorithm and the LDA-based baseline algorithm by large margins.

Comparison of discrimination techniques applied to a complex data set of head injured patients

Abstract: Several techniques for discriminant analysis are applied to a set of data from patients with severe head injuries, for the purpose of prognosis. The data are such that multidimensionality, continuous, binary and ordered categorical variables and missing data must be coped with. The various methods are compared using criteria of prognostic success and reliability. In general, performance varies more with choice of the set of predictor variables than with that of the discriminant rule.