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# Topic: Linear discriminant analysis

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 Linear discriminant analysis - Wikipedia, the free encyclopedia Discriminant analysis is also different from factor analysis in that it is not an interdependence technique : a distinction between independent variables and dependent variables (also called criterion variables) must be made. The terms Fisher's linear discriminant and LDA are often used interchangeably, although Fisher's original article The Use of Multiple Measures in Taxonomic Problems (1936) actually describes a slightly different discriminant, which does not make some of the assumptions of LDA such as normally distributed classes or equal class covariances. LDA and Fisher's discriminant can be extended for use in non-linear classification via the kernel trick. en.wikipedia.org /wiki/Linear_discriminant_analysis   (1716 words)

 Linear discriminant analysis - MLpedia   (Site not responding. Last check: 2007-10-12) Linear discriminant analysis (LDA) and the related Fisher's linear discriminant are to find the linear combination of features which best separate two or more classes of object or event. LDA can be generalized to multiple discriminant analysis, where c becomes a categorical variable with N possible states, instead of only two. The linear combinations obtained using Fisher's linear discriminant are referred to as Fisher faces, while those obtained using the related principal component analysis are called eigenfaces. www.mlpedia.org /index.php?title=Linear_discriminant_analysis   (829 words)

 Discriminant Function Analysis Therefore, variable height allows us to discriminate between males and females with a better than chance probability: if a person is tall, then he is likely to be a male, if a person is short, then she is likely to be a female. In the two-group case, discriminant function analysis can also be thought of as (and is analogous to) multiple regression (see Multiple Regression; the two-group discriminant analysis is also called Fisher linear discriminant analysis after Fisher, 1936; computationally all of these approaches are analogous). In general Discriminant Analysis is a very useful tool (1) for detecting the variables that allow the researcher to discriminate between different (naturally occurring) groups, and (2) for classifying cases into different groups with a better than chance accuracy. www.statsoft.com /textbook/stdiscan.html   (3751 words)

 Discriminant Analysis (DISCRAN) The task of discriminant analysis is to find the best linear discriminant function(s) of a set of variables which reproduce(s), as far as it is possible, an a priori grouping of the cases considered. Discriminant analysis on all cases together; cases are identified by the V1; 5 steps of analysis are requested; a priori groups are defined by the variable V111 which includes categories 1-6. Repeat analysis described in the Example 1 using the subset of respondents having the value 1 on V5 as the basic sample and test the results on the respondents having the value 2 on V5. www.unesco.org /webworld/idams/Doc/ManualHtml/E1discra.htm   (1213 words)

 Linear Discriminant Analysis Discriminant analysis can be used only for classification (i.e., with a categorical target variable), not for regression. Linear discriminant analysis finds a linear transformation ("discriminant function") of the two predictors, X and Y, that yields a new set of transformed values that provides a more accurate discrimination than either predictor alone: The fl line shows the optimal axis found by linear discriminant analysis that maximizes the separation between the groups when they are projected on the line. www.dtreg.com /lda.htm   (619 words)

 Classification Trees In linear discriminant analysis the number of linear discriminant functions that can be extracted is the lesser of the number of predictor variables or the number of classes on the dependent variable minus one. In the linear discriminant analysis, the raw canonical discriminant function coefficients for Longitude and Latitude on the (single) discriminant function are.122073 and -.633124, respectively, and hurricanes with higher longitude and lower latitude coordinates are classified as Trop. The second basic step in classification tree analysis is to select the splits on the predictor variables which are used to predict membership in the classes of the dependent variables for the cases or objects in the analysis. www3.baylor.edu /~Jack_Tubbs/StatSoft/stclatre.html   (8036 words)

 The MathWorks - Demos - Classification Of the 150 specimens, 20% or 30 specimens are misclassified by the linear discriminant function. Both linear and quadratic discriminant analysis are designed for situations where the measurements from each group have a multivariate normal distribution. This demonstration is not meant to be an ideal analysis of the Fisher iris data. www.mathworks.com /products/demos/statistics/classdemo.html   (1174 words)

 Linear Discriminant Analysis LDA tests whether object attributes measured in an experiment predict categorization of the objects. LDA, not commonly used in HCI experiments, proved an innovative experimental design tactic and its use shows creativity on the part of the research team. LDA and QDA are interchangeable, and which to use is a matter of preference and/or availability of software to support the analysis. www-users.cs.umn.edu /~ludford/Stat_Guide/Linear_Discriminant_Analysis.htm   (487 words)

 Research Statement Discriminant analysis has been studied in both pattern recognition and statistics for many years. For example, the performance of LDA classifier was analysized using matrix perturbation theory [5]. Factor Analysis is generally referred to the statistical method to recover the underlying factors used to model the observations (Independent Component Analysis is the newest addition to this branch). www.cfar.umd.edu /~wyzhao/RS/Research_Statement.html   (2004 words)

 discrim1 Discriminant Analysis of the Fisher Iris Data 1 Sepal Sepal Petal Petal Length Width Length Width Log Log in in in in Sepal Petal OBS mm. Discriminant Analysis of the Fisher Iris Data 2 Sepal Sepal Petal Petal Length Width Length Width Log Log in in in in Sepal Petal OBS mm. Discriminant Analysis of the Fisher Iris Data 3 Sepal Sepal Petal Petal Length Width Length Width Log Log in in in in Sepal Petal OBS mm. www.stat.lsu.edu /faculty/moser/exst7037/discrim.html   (864 words)

 dChip: Sample classification by Linear Discriminant Analysis Linear discriminant analysis (LDA) is a classical statistical approach for classifying samples of unknown classes, based on training samples with known classes. predict.lda function to perform the LDA training on the known classes and predict the class labels for the unknown samples. LD1 and LD2 are the first two linear discrimiants that map the samples with known class from the n-dimensional (n is the number of genes) space to the plane, in such a way that the ratio of the between-group variance and the within-group variance is maximized. biosun1.harvard.edu /complab/dchip/lda.htm   (781 words)

 Fishers LDA That is, can we develop a rule, or discriminant function, from the observed features of the sampled items that will allow us to assign some new item to the correct population by examining its features only. The objective of discriminant analysis is to find a weight vector l that maximizes the ratio of these sum of squares components. You may think of the discriminant function as defining a hypersurface that bisects the points in p dimensional points in such a way that when you view the observations from a direction perpendicular to this surface you can optimally discriminate between the groups. condor.depaul.edu /~jmorgan1/csc334.lda.html   (573 words)

 Statistical Modeling using Linear Discriminant Analysis Each of the functions described in the previous section was a linear combination of the components of xt and used a specific set of weights in a parameter vector w. This analysis also shows that the model had the easiest time with Method 2, likely because of the predictability in the subjects' behavior. For the purposes of this project, we used the Discriminant Analysis Toolbox for Matlab authored by Michael Kiefte from the University of Alberta. web.mit.edu /9.29/www/brett/ca_model.html   (1853 words)

 Subspace Linear Discriminant Analysis for Face Recognition - Zhao, Chellappa, Phillips (ResearchIndex) The method consists of two steps: first we project the face image from the original vector space to a face subspace via Principal Component Analysis where the subspace dimension is carefully chosen, and then we use LDA to obtain a linear classifier in the subspace. Linear Discriminant Analysis of MPF for Face Recognition - Zhao, Nandhakumar (1998) Discriminant Analysis of Principal Components for Face Recognition - Chellappa (1998) citeseer.ist.psu.edu /zhao99subspace.html   (817 words)

 SSRN-Robust Linear Discriminant Analysis for Multiple Groups: Influence and Classification Efficiencies by Christophe ... Linear discriminant analysis for multiple groups is typically carried out using Fisher’s method. Since sample averages and covariance matrices are not robust, it is proposed to use robust estimators of location and covariance instead, yielding a robust version of Fisher’s method. In this paper expressions are derived for the influence that an observation in the training set has on the error rate of the Fisher method for multiple linear discriminant analysis. papers.ssrn.com /sol3/papers.cfm?abstract_id=876896   (408 words)

 Discriminant Analysis by Locally Linear Transformations   (Site not responding. Last check: 2007-10-12) We present a novel learning method for the discriminant analysis which classifies a non-linear structure. Several local linear transformations are considered to yield that the locally transformed classes have maximized covariance of between-class and minimized covariance of within-class. The method is much more benefited in computational efficiency compared to the previous non-linear discriminant analysis based on kernel approach. www.bmva.ac.uk /bmvc/2003/papers/paper-23-31.html   (167 words)

 Generalized Linear Discriminant Analysis   (Site not responding. Last check: 2007-10-12) The conventional linear discriminant analysis (LDA) requires that the within-class scatter matrix Sw be nonsingular. To solve the problem, we propose the generalized linear discriminant analysis (GLDA) that is a general, direct, and complete solution to optimize the modified Fisher's criterion. Different from the conventional LDA, GLDA does not assume the nonsingularity of Sw, and thus solves the small sample size problem. www.cs.ucr.edu /~hli/glda/index.html   (245 words)

 DTREG -- Predictive Modeling Software DTREG is a powerful statistical analysis program that generates classification and regression trees and Support Vector Machine models that can be used to predict values. Since the company has a limited advertising budget, they want to determine how to use the demographic data to predict which people are the most likely buyers of their product so they can focus their advertising on that group. And, a decision tree or SVM model can be used to “score” a set of individuals and rank them by the probability that they will respond positively to a marketing effort. www.dtreg.com   (1611 words)

 Linear Discriminant Analysis (LDA) Tutorial The purpose of Discriminant Analysis is to classify objects (people, customers, things, etc.) into one of two or more groups based on a set of features that describe the objects (e.g. Thus, in discriminant analysis, the dependent variable (Y) is the group and the independent variables (X) are the object features that might describe the group. Linearly separable suggests that the groups can be separated by a linear combination of features that describe the objects. people.revoledu.com /kardi/tutorial/LDA/LDA.html   (681 words)

 R: Linear Discriminant Analysis That is, the response is the grouping factor and the right hand side specifies the (non-factor) discriminators. Unlike in most statistical packages, it will also affect the rotation of the linear discriminants within their space, as a weighted between-groups covariance matrix is used. Thus the first few linear discriminants emphasize the differences between groups with the weights given by the prior, which may differ from their prevalence in the dataset. rweb.stat.umn.edu /R/library/MASS/html/lda.html   (478 words)

 Face Recognition: A Statistical Approach The first statistical approach, principal components analysis (PCA) [1] was proposed in 1991. In the past decade, several modified methods, such as, Fisher’s Linear Discriminant (FLD) [2], Linear Discriminant Analysis (LDA) [3] and Discriminant Analysis of Principal Components (LDA+PCA) [4] were proposed. Due to the ill condition of scatter matrix, the eigenvectors obtained in LDA are not necessarily accurate. www.ee.umd.edu /~gmsu/ENEE739J/pj3/face_recognition.html   (1662 words)

 RR-1793 : Shrinkage parameter for modified linear discriminant analysis   (Site not responding. Last check: 2007-10-12) Abstract : Linear discriminant analysis is considered in the small-sample, high-dimension- al setting. First, we show that the variance of the modified linear discriminant functions is less than those of the classical linear discriminant function. Our procedures are based-one on the cross-validated misclassification risk and one on the cross-validated generalized discriminant function as defined in Rayens and Greene (1991). www.inria.fr /rrrt/rr-1793.html   (310 words)

 Discriminant Analysis (DISCRAN) for analysis with more than 2 original groups, the values of the first two discriminant factors The case ID variable and variables to be transferred can be alphabetic. Create an IDAMS dataset containing transferred variables, case assignment variables, sample type and values of the discriminant factors, if any. www.unesco.org /webworld/portal/idams/html/english/E1discra.htm   (1450 words)

 Keith Price Bibliography Discriminant Analysis Discriminant analysis determines which variables discriminate between two or more groups. Bobrowski, L. Niemiro, W. A method of synthesis of linear discriminant function in the case of nonseparability, 0407Extend LDA by using pseudoinverse with matricies are singular. iris.usc.edu /Vision-Notes/bibliography/pattern602.html   (877 words)

 Keith Price Bibliography Invariants -- Linear Discriminant Analysis Nonlinear discriminant mapping using the Laplacian of a graph, Multi-class object recognition using boosted linear discriminant analysis combined with masking covariance matrix method, Keysers, D. Ney, H. Linear discriminant analysis and discriminative log-linear modeling, iris.usc.edu /Vision-Notes/bibliography/match580.html   (270 words)

 Linear Discriminant Analysis of Mortgag2 Data The LDF (Linear Discriminant Function) is the difference between the two classification functions: Here is an analysis with more realistic prior probabilities. Classification Functions  for Group 0  for Group 1 www.uic.edu /classes/idsc/ids531/mcleod7e/ntsch16c.htm   (71 words)

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