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What is the meaning of "LDA dataset is linear separable"?

"the classes are non-linearly separated"

"the features have nonlinear relationships"

As I know in maths for linear equation and non-linear equation.

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If the classes are linearly separable, there exists a hyperplane (on the same feature space) to separate them. When there is not, the classes are either non-separable or separated by other types of hyper-surfaces, e.g. if instead of a line, a parabola in 2D feature space can separate the classes, it's said non-linearly separable. Features having non-linear relationships is like having features $x,y$ where $y=x^2$. When you add new features using the old ones, to be able to separate your samples in a higher dimensional space linearly (so non-linearly in the original feature space), you add new features that are nonlinearly related to the original ones.

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    $\begingroup$ original features. $\endgroup$ – gunes May 23 at 12:10
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    $\begingroup$ Still, you could do the LDA in the new feature space. $\endgroup$ – gunes May 23 at 13:57
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    $\begingroup$ LDA is not handling features, it handles the classes. Features can surely have nonlinear relationships. For example, we can add a new feature $x^2$ that makes the classes more separable, which means LDA will do a good job. $\endgroup$ – gunes May 26 at 16:47
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    $\begingroup$ I'd say 'classes which have non-linear decision boundaries' $\endgroup$ – gunes May 26 at 20:36
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    $\begingroup$ generally makes sense, and better to stay in your own words. I'd soften the statements a bit, e.g. LDA is less capable ... because ... requires the class separators to be hyperplanes. $\endgroup$ – gunes May 26 at 20:50

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