Can we determine the significance of the predictor in KNN?
No
In which case KNN outperforms LDA and Logistic regression?
KNN is a completely non-parametric approach, no assumptions are made about the shape of the decision boundary. So, when the decision boundary is highly non linear, it dominates LDA and Logistic regression.
In case of non-linear data, does KNN always outperforms other classification techniques?
No, even when the data exhibits the complex non-linear relationship, KNN can still give poor result if the level of smoothness is not chosen correctly
How to determine the value of K in KNN?
Cross-validation
However, it is also sometime taken as Sqrt(n)
Disadvantage of KNN?