# Questions tagged [discriminant-analysis]

Linear Discriminant Analysis (LDA) is a dimensionality reduction and classification method. It finds low-dimensional subspace with the strongest class separation and uses it to perform classification. Use this tag for quadratic DA (QDA) too.

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### Meaning of within-class Covariance in Linear Discriminant Analysis Dimensionality Reduction

In section 4.3.3 of Elements of Statistical Learning by Hastie, Tibshirani, and Friedman the authors listed a procedure to reduce the dimensions of an input matrix $\mathbf{X}$, first using Linear ...
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### Is it valid to exhaustively test all possible combinations of features to find the best combination?

I have about 1000 labelled observations from about 50 subjects responding physiologically under different situations and am trying to classify the situation (usually into three classes of roughly ...
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### Creating a discriminant function from one known group and one mixed group

I have a dataset composed of captures of individuals (ringed birds), all from the same species. Because the captures took place during spring, summer and autumn, we have trapped breeding and migrating ...
1 vote
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### Can AdaBoost discriminate the data?

Assume that you have an image $X$ and you want to search a specific small object inside the image $X$. It's only one object. So you training an AdaBoost model with only one valid train sample and the ...
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### Two-class LDA with multiple variables: can we separate classes and know the weight of variables?

So far I have performed an LDA having two classes, but I'm really struggling with certain aspectos of the analysis. I am working with biomedical data in which I would like to classify in k=2 groups: ...
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### Is my understanding of dimension reduction in Linear Discriminant Analysis correct?

Here is my understanding of how dimension reduction in LDA works: We have $n$ samples each with $p$ features assigned to $k$ classes. We use the sample mean $\mu_j$ of each class and the pooled ...
1 vote
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### How to balance PCA and LDA in subspace learning?

PCA is a generative model, by which input images or data can be reconstructed. LDA (Linear Discriminant Analysis) is a discriminative model, which extracts better features for classification. How to ...
1 vote
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### Linear Discriminant Analysis with unlabeled data

In section 4.4.5 "Logistic regression or LDA?" of Elements of Statistical Learning by Friedman, Tibshirani and Hastie, it is claimed the following: From the mixture formulation [that is, ...
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### A lot of variables in a Quadratic Discriminant Analysis

I'm trying to make a Quadratic Discriminant Analysis in R, but appears the follow mistake: "some group is too small for 'qda'". I was reading about it and I concluded that I have more ...
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### Does the ID class vector change in Kernel Linear Discriminant Analysis?

Assume that I have a matrix $X$ that has the size $m * n$ and a class ID vector with the length $n$. If I want to apply Kernel Linear Discriminant Analysis (KLDA) onto the matrix $X$ and vector $y$, ...
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### How do I associate or assign a large amount of continuous variables with zero-heavy distributions to different groups?

I have a dataset with about 70 continuous numeric variables. I have about 80 samples which divide more or less equally into two groups. I want to figure out which of these variables is most strongly ...
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1 vote
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### Is Fisher's discriminant analysis equivalent to the Bayes optimal LDA when the no. of classes is greater than two and covariances are all equal?

P.S. While I gave a brief background to make the question complete, informed readers can move to the questions 1 and 2 towards the end of this post, right after 'what are not clear to me are:'. Fisher'...
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### Importance of linear discriminants to classification at a given point

Many outstanding answers here detail the fundamentals of linear discriminant analysis. These include descriptions of its use in dimensionality reduction, an explanation of classification using Bayes' ...
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### LDA: sample mean of two distributions are proportional

I came up with a discussion around what does it mean that the sample mean of two distributions are proportional. This discussion started when talking about linear discriminant analysis and how this ...
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### So how can I project the data with the eigenvectors from LDA?

I have data that look like this. And my goal is to reduce this 3D dimension into 2D dimension so it might looks like this. Turning the angle so the distance between all classes becomes maximum. So ...
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### Best subset of variables to perform discriminant analysis

I have around 33 variables, and 300 observations, although of some variables there are some missing data. I would like to obtain the best subset of variables which can separate the best 3 categories ...
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### Why is the Scaling Matrix in LDA unnormalized?

I was carrying out LDA (linear Discriminant Analysis) and noticed that the Scaling matrix produced by R is not normalized. Here is an example: ...
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1 vote
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### Could I use LDA (Linear discriminant analysis) for outlier detection?

Could I use LDA method to separate outlier from major points? I want to find outlier from certain data with LDA, but I couldn't find use of LDA for outlier detection. Basically I want do the work like ...
1 vote
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### Reduced Rank Linear Discriminant Analysis vs Fisher Discriminant as mentioned in Element of Statistical learning section 4.3.3

In ESL section 4.3.3 , Author gives three steps for finding optimal subspaces using LDA as below compute the K × p matrix of class centroids M and the common covariance matrix W (for within-class ...
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### Is this description of linear discriminant analysis (LDA) correct?

Hang Nguyen writes the following in "Machine learning basics (part 14): Linear Discriminant Analysis": If there are two classes then the LDA draws one hyperplane and projects the data onto ...
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1 vote
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### Shipley's d separation test in piecewise structural equation model

I have created a piecewise structural equation model for when the temperature exceeds 0 degrees Celsius, and how that relates to the green up day across Northern Europe. I have standardised all data <...
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1 vote
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### Is linear discriminant analysis a supervised classifier or dimensionality reduction?

On page 147 of ISLR 2nd Edition, the author is talking about LDA and comparing it to a Bayes Classifier. This leads me to believe LDA is a machine learning algorithm for supervised classification. ...
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### For a generative model, how is modelling p(X,Y) equivalent to modelling P(X|Y=y)?

On the Wikipedia page for generative models it gives the following definitions of a generative model: (X is an observable variable, Y is the target variable) 1) A generative model is a model of the ...
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