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Questions tagged [discriminant-analysis]

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 analysis is both dimensionality reduction and classification technique.

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Gradient equations of gaussian kernel discriminant trained with gradiant descent

I am having a hard time trying to find the gradient equations for the weight $\alpha^t$ and $w_0$ for a gaussian kernel discriminant trained with gradient descent with the following error function $$E(...
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Linear Discriminant - Least Squares Classification Bishop 4.1.3

Pls. refer section 4.1.3 in Pattern Recognition - Bishop: "Least squares for Classification": In a 2 class Linear Discriminat system, we classified vector $\mathbf{x}$ as $\mathcal{C}_1$ if y($\bf{x}...
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Pattern Recognition, Bishop - (Linear) Discriminant Functions 4.1

Please refer "Pattern Recognition and Machine Learning" - Bishop, page 182. I am struggling to visualize the intuition behind equations 4.6 & 4.7. I am presenting my understanding of section 4.1....
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Prove GDA decision boundary is linear

My attempt: (a) I solved that $a=\ln{\frac{P(X|C_0)P(C_0)}{P(X|C_1)P(C_1)}}$ (b) Here is where I'm running into trouble. I'm plugging the distributions into $\ln{\frac{P(X|C_0)P(C_0)}{P(X|C_1)P(C_1)...
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Naive Bayes Classifier - Discriminant Function

To classify my samples, I decided to use Naive Bayes classifier, but I coded it, not used built-in library functions. If I use this equality, I obtain nice classification accuracy: ...
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Performace of Fischer projection as dimension reduction compared to other LDA methods

How is the performance of Fischer projection compared to other LDA methods of dimension reduction? I thought that Fischer projection was a great method of dimension reduction by maximizing class ...
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Convert a pdf into a conditional pdf such that mean increases and std dev falls

Let success metric(for some business use case I am working on) be a continuous random variable S. The mean of pdf defined on S indicates the chance of success. Higher the mean more is the chance of ...
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What is the favored discriminant analysis package in R?

I have been using the LDA package for R, but it is missing quite a few features especially those that can assess the output. Are the any preferred packages that have some of the following? ...
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Gaussian Discriminant Analysis (GDA) package in R

This stack exchange post - https://stats.stackexchange.com/questions/80507/what-is-a-gaussian-discriminant-analysis-gda - discusses GDA, a machine learning method for classification. I would like to ...
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Varying results when calculating scatter matrices for LDA

I'm following a Linear Discriminant Analysis tutorial from here for dimensionality reduction. After working through the tutorial (did the PCA part, too), I shortened the code using sklearn modules ...
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How are Hyperplane Heatmaps created and how should they be interpreted?

For nonlinear data, when we are using Support Vector Machines, we can use kernels such as Gaussian RBF, Polynomial, etc to achieve linearity in a different (potentially unknown to us) feature space ...
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Bayes Optimal Decision Boundaries for Gaussian Data with Equal Covariance

I am drawing samples from two classes in the two-dimensional Cartesian space, each of which has the same covariance matrix $[2, 0; 0, 2]$. One class has a mean of $[1.5, 1]$ and the other has a mean ...