Consider a k$-$nearest$-$neighbors $(k-NN)$ classifier. My goal is to use a training set $(x,y)$ to classify new inputs $x^{\text{'}}.$

$($a$)$ Suppose every input x is represented as a $10,000-$dimensional feature vector. What might be some problems using k$-$NN with Euclidean distance as the classifier in this case?

$($b$)$ Very briefly explain what PCA is and how PCA could help with the problem in $($a$).$