Given multivariate data split into several subsamples (classes) the analysis finds linear combinations of variables, called discriminant functions, which discriminate between classes and are uncorrelated. The functions are applied then to assign old or new observations to the classes. Discriminant ...

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What is the correct formula for covariance matrix in quadratic discriminant analysis (QDA)?

I know that in quadratic discriminant analysis (QDA) we use the variance of each class, so is the formula different than that in linear discriminant analysis (LDA)? Is it $$\frac{1}{N-K} \sum (x - ...
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44 views

Testing Logistic Regression Classifier in R

I am testing the logistic regression classifier in R. I created some test data like this: x=runif(10000) y=runif(10000) df=data.frame(x,y,as.factor(x-y>0)) ...
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46 views

How do we generate the ROC curve for Linear Discriminant Analysis method

I know the method to generate the ROC curve for other methods such as naive Bayes where the tuning parameter is the threshold like also in logistic regression. If we want to generate the ROC curve ...
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13 views

Extract features to explain different states of the world

I have a problem that can be seen as the inverse of a classification problem. I don't need to classify points, but to explain the differences (if any) between points in different, pre-specified ...
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72 views

What is the correct formula for between-class scatter matrix in LDA?

At one point in the process of applying linear discriminant analysis (LDA), one has to find the vector $v$ that maximizes the ratio $vBv'/vWv'$, where $B$ is the "between-class scatter" matrix, and ...
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53 views

Log transformation for data?

If the data is between (0,1) because of some kind of vector normalization to get rid of background noise, is it still OK to do log transformation to improve normality? Or we have to do logit ...
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38 views

Cannot perform tests for multivariate normality. Is my data set too large?

I'm examining the performance of quadratic and linear discriminant models at classification. My dataset has 250,000 observations, 2 groups and 30 explanatory variables. I thought it would be worth ...
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77 views

How can MANOVA report a non-significant p-value while LDA results in perfect separation of two groups?

I am new to statistics and currently got a dataset which contains $80$ dependent variables and $1$ independent variable with $2$ groups. MANOVA reports a $p$-value of $> 0.6$ on this dataset. But ...
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16 views

linear discriminant analysis, Bayes approach authors?

I know that in 1936 Fisher proposed the LDA that minimizes the variance within and maximizes between. My question is, the Bayes approach of LDA is attributed to a particular(s) author(s)? and what ...
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16 views

Canonical discriminant analysis - lack of equality of covariance matrices [duplicate]

I have a dataset with 92 observations and two groups that corresponde to two analytical fractions of soil samples (i.e., light fraction or LF, and mineral-associated fraction or MoM). Each group has ...
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35 views

What are F values of the canonical functions in discriminant analysis?

Recently, I read a paper (Pell et al. 2009) in which the authors use Discriminant Analysis, and I quote: The discriminant analysis produced three significant canonical functions (Function 1, ...
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142 views

More recognizable Python implementation of Linear Discriminant Analysis?

I have been using scikit-learn's LDA implementation to do some experiments, and recently wanted to test out some modifications to the LDA derivation. I was looking at the Python implementation that ...
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66 views

What is a “discriminant function” and how to interpret it?

I want to test a model using discriminant function analysis. My question, as the title states, is very basic: What is a discriminant function? That is, how can I interpret the different discriminant ...
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137 views

Does Fisher linear discriminant analysis (LDA) require normal distribution of the data in each class?

Does Fisher linear discriminant analysis really require the data distribution in each category to be normal? I see two versions. The first one states that it requires the normal distribution and ...
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1answer
42 views

Bayes' factor vs. Bayes' Discriminant Rule

When we are comparing two models against some data, will we obtain the same (set of) posterior odds for the models both when we use the Bayes' factor and when we use the discriminant rule? If not, ...
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348 views

Reproduce linear discriminant analysis projection plot

I'm struggling with projection points in linear discriminant analysis (LDA). Many books on multivariate statistical methods illustrate the idea of the LDA with the figure below. The problem ...
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2answers
273 views

Post-hoc tests for MANOVA: univariate ANOVAs or LDA?

I am using a MANOVA test to compare nine different dependent variables (from neuropsychological and neuropsychiatric assessment) between three groups. The output shows a significant influence from ...
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1answer
196 views

Does it make sense to calculate Q2 and R2 values on PLS-DA models?

Since PLS-DA is a computational technique which deals with outcomes expressed as a categorical variable (e.g. "Yellow","Brown","Black","Green") I cannot understand how it is possible to calculate Q2 ...
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167 views

Linear Discriminant Analysis and non-normal distributed data

If I understand correctly, a Linear Discriminant Analysis (LDA) assumes normal distributed data, independent features, and identical covariances for every class for the optimality criterion. Since ...
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750 views

Why Python's scikit-learn LDA results are different from LDA in R or a step-by-step approach

I was using the Linear Discriminant Analysis (LDA) from the scikit-learn machine learning library (Python) for dimensionality reduction and was a little bit curious about the results. I am wondering ...
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135 views

Standardizing before/after/at all when using multi-class LDA for pre-processing step

If a multi-class Linear Discriminant Analysis (or I also read Multiple Discriminant Analysis sometimes) is used for dimensionality reduction (or transformation after dimensionality reduction via PCA), ...
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3answers
175 views

Is linear discriminant analysis (LDA) more likely to overfit than support vector machine (SVM)?

I went to a short talk and the speaker quickly mentioned something like 'LDA (linear discriminant analysis) is more likely to be overfitted than SVM (support vector machine)'. Is this true? And why?
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108 views

Multi-class classification via all pairwise classifications with LDA

I have trained linear discriminant analysis (LDA) classifiers for three classes of the IRIS data and struggling with how to make the classification. Here is the procedure: For the Iris data, I have 3 ...
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46 views

How to check discriminant analysis assumption in R using lda?

I want to use lda in MASS package in R. According to the theory behind that, first need to validate the assumption. Actually I've found some example from the net but they did not bother to validate ...
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319 views

Best practice for dimensionality reduction with PCA and LDA: does it make sense to combine them?

Assume I have a dataset for a supervised statistical classification task, e.g., via a Bayes' classifier. This dataset consists of 20 features and I want to boil it down to 2 features via ...
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61 views

Multiple Discriminant Analysis, Linear Discriminant Analysis, and Multidimensional scaling - how are they related?

Some time ago when I took a Pattern Classification class, the "concept" was introduced as Multiple Discriminant Analysis: You want to project your data onto a subspace (if you are interested in ...
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101 views

A question on discriminant analysis- Linear discriminant function

Above is part of an examination paper. I am not sure how to understand this SAS output. Especially what is there in the last table which looks to me like two discriminant functions. Can someone ...
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70 views

Discriminant analysis

I want to do a discriminant analysis for my study. This study consist of one dependent variable and 8 independent variables. The dependent variable is categorical and has 2 groups. The independent ...
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176 views

LDA - Why differents formulas to calculate covariance and pooled covariance matrix

Reading materials from differents sites some questions have risen about covariance and the pooled covariance matrix calculation to implement LDA: Definitions Ci - covariance matrix of group i (C1 and ...
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89 views

Why do we not look at the covariance matrix when choosing between LDA or QDA

I understand the difference between LDA and QDA (linear and quadratic discriminant analysis), being that with LDA assume that your features have the same covariance matrix in each class. I wonder why ...
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61 views

Modeling: Option to cross-validate and predict afterwards

This is beyond a R question, But why doesn't it make sense to fit a model, say, a linear discriminant (LDA) model, with leave-out-one cross validation, and afterwards to use this model to predict a ...
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1answer
124 views

How to correctly apply LDA following PCA?

I have a high dimensional dataset ($n \times p$: $30 \times 100$) which I want to use as an testing dataset to build a two group classifier (LDA or QDA). I've read that you can do PCA to do an ...
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13 views

Statistical technique to assess nutrition

My goal is to find risk factors for a disease. I think that a malnutrition is a risk factor for this disease. I have 5 variables that indicate the frequencies of ...
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669 views

Logistic regression vs. LDA as two-class classifiers

I am trying to wrap my head around the statistical difference between Linear discriminant analysis and Logistic regression. Is my understanding right that, for a two class classification problem, LDA ...
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19 views

How to discriminate the two different classes using the info from histograms

I have the data from 12 patients and I know the responders and the non responders. I already have calculated some markers from each one and plotting histograms and pdfs it seems that they can be ...
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79 views

Coefficients of Linear Discriminants in R

I've read the answers in What are "coefficients of linear discriminants" in LDA?, but I still don't understand what coefficients of linear discriminants on output of R means. What is it? ...
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1answer
40 views

Similarity Coefficient and Geochemical Correlation

I have a set of around 160 samples from different sediment bodies, or stratigraphic units, which I am attempting to correlate using geochemical analysis of 25 elements for each sample, and a ...
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66 views

Linear Discriminant Analysis matrix dimension

I am trying to implement Linear Discriminant Analysis for face recognition. I have 3 classes and each classes have 10 image each. The dimension of matrix in class A, B and C is 10*500 .So each row ...
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769 views

Compute and graph the LDA decision boundary

I saw an LDA (linear discriminant analysis) plot with decision boundaries from The Elements of Statistical Learning: I understand that data are projected onto a lower-dimensional subspace. However, ...
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364 views

How to interpret the LDA output in R?

Basically, I have following LDA output (below). My question is how do I actually interpret it ? I could not find much resources on the web. Especially, what does "Group Means" really mean here ? I was ...
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52 views

Within scatter matrix linear discriminant analysis

I am trying to implement Linear Discriminant Analysis. I have 10 classes and each class has 3 observations at various instances: ...
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91 views

Standardized LDA loadings

I'm having issue finding code for calculating standardized loadings for LDA, I wrote a code for it, but I'm not sure is this the correct way to standardize the loadings. ...
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68 views

Estimating the covariance matrix in LDA

I was trying to derive the equations from page 109 in "elements of statistical learning" (image below) To be honest, I am not sure how the covariance $\Sigma$ is estimated (the third bullet point in ...
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1answer
463 views

Bayesian and Fisher's approaches to linear discriminant analysis

I know 2 approaches to do LDA, the Bayesian approach and the Fisher's approach. Suppose we have the data $(x,y)$, where $x$ is the $p$-dimensional predictor and $y$ is the dependent variable of $K$ ...
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1k views

What are “coefficients of linear discriminants” in LDA?

In R, I use lda function from library MASS to do classification. As I understand LDA, input ...
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1answer
183 views

How can a standardized canonical coefficient be greater than 1.0 in a discriminant function analysis?

I have a data that I have used discriminant function analysis with. In the results, one variable has a standardized canonical function coefficient that is greater than 1.0. I didn't think these could ...
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1answer
351 views

How to interpret this cross-validated sparse LDA figure using CARET package?

Training data with $p$ =11 predictors and $n$ =165 with 4-class problem was cross-validated (5 times repeated 10-fold CV) using the sparse LDA (aka SDA) using caret ...
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492 views

How is MANOVA related to LDA?

In several places did I see a claim that MANOVA is like ANOVA plus linear discriminant analysis (LDA), but it was always made in a hand-waving sort of way. I would like to know what exactly it is ...
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121 views

Clarification on LDA and the multivariate Gaussian

From my understanding, to calculate the posterior probability of a sample $x$ belonging to a class $k$ using Linear Discriminant Analysis you would first calculate the eigenvector matrix $W$ required ...
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Can the scaling values in a linear discriminant analysis (LDA) be used to plot explanatory variables on the linear discriminants?

Using a biplot of values obtained through principal component analysis, it is possible to explore the explanatory variables that make up each principle component. Is this also possible with Linear ...