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Results tagged with discriminant-analysis
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user 28666
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.
11
votes
Accepted
Bayesian and Fisher's approaches to linear discriminant analysis
I will provide only a short informal answer and refer you to the section 4.3 of The Elements of Statistical Learning for the details.
Update: "The Elements" happen to cover in great detail exactly th …
- 107k
5
votes
Multi-class classification via all pairwise classifications with LDA
This question is not restricted to LDA, but can be asked about any binary classifier that is used in a multi-class setting by making all pairwise comparisons. The question is how to combine all pairwi …
- 107k
5
votes
Accepted
How can MANOVA report a non-significant p-value while LDA results in perfect separation of t...
This is an excellent question because it touches on so many important concepts. The short answer is: Yes, this is possible, and can happen if your sample size is low.
Let us make the apparent contr …
- 107k
3
votes
Accepted
Comparing four formulations of class scatter matrices
Let's go over your four definitions one by one.
Duda et al. 2012. These are the standard definitions of scatter matrices: within-class, between-class, and the total scatter matrix. They obey a nice …
- 107k
12
votes
Accepted
Linear Discriminant Analysis and non-normally distributed data
Here is what Hastie et al. have to say about it (in context of two-class LDA) in The Elements of Statistical Learning, section 4.3:
Since this derivation of the LDA direction via least squares doe …
- 107k
8
votes
Accepted
What is the correct formula for between-class scatter matrix in LDA?
Within- and between-class scatter matrices in LDA are direct multivariate generalizations of the within- and between-class sums of squares in ANOVA. So let us consider those. The idea is to decompose …
- 107k
8
votes
Accepted
Difference in scaling of Linear Discriminant Analysis coefficients between manual calculatio...
You have correctly computed $$\mathbf {b} = \mathbf{S}_W^{-1}(\boldsymbol\mu_1-\boldsymbol\mu_2),$$ where $\boldsymbol\mu_i$ are class means and $\mathbf{S}_W$ is the within-class pooled covariance ma …
- 107k
27
votes
Accepted
How is MANOVA related to LDA?
In a nutshell
Both one-way MANOVA and LDA start with decomposing the total scatter matrix $\mathbf T$ into the within-class scatter matrix $\mathbf W$ and between-class scatter matrix $\mathbf B$, su …
- 107k
28
votes
Accepted
Compute and graph the LDA decision boundary
This particular figure in Hastie et al. was produced without computing equations of class boundaries. Instead, algorithm outlined by @ttnphns in the comments was used, see footnote 2 in section 4.3, p …
- 107k
4
votes
Accepted
Dimensionality reduction technique similar to LDA when class labels are probabilistic
I liked @ttnphns's suggestion (that he made in the comments above) so much, that could not resist from trying it out.
As @ttnphns said, LDA is equivalent to canonical correlation analysis (CCA) betwee …
- 107k
6
votes
Accepted
Interpretation of the cluster criterion $\operatorname{tr}(S_W^{-1}S_B)$
$S_W^{-1}S_B$ can be interpreted as multivariate signal-to-noise ratio.
The between-class scatter matrix $S_B$ tells us how far from each other class means are located. The within-class scatter matri …
- 107k
12
votes
Proportion of explained variance in PCA and LDA
I will first provide a verbal explanation, and then a more technical one. My answer consists of four observations:
As @ttnphns explained in the comments above, in PCA each principal component has ce …
- 107k
6
votes
Accepted
Reproduce linear discriminant analysis projection plot
The discriminant axis (the onto which the points are projected on your Figure 1) is given by the first eigenvector of $\mathbf{W}^{-1}\mathbf{B}$. In case of only two classes this eigenvector is propo …
- 107k
9
votes
What is the relationship between regression and linear discriminant analysis (LDA)?
The purpose of this answer is to explain the exact mathematical relationship between linear discriminant analysis (LDA) and multivariate linear regression (MLR). It will turn out that the correct fram …
- 107k
7
votes
Accepted
Variable selection using cross-validated PLS model when permutation test shows lack of signi...
For the benefit of other readers I will briefly explain what the permutation test is in this context.
In this specific example there is a binary dependent variable $y$, a large number of independent …
- 107k