k-NN: This problem derives a performance bound on the 1-NN classifier. Consider the 1-NN binaryclassifier on a two-dimensional space. For an input x and its nearest neighbor xn in the trainingdata, the conditional probabilities of belonging to classes c1 and c2 are as follows:◦ p(c1|x) : probability that x belongs to c1◦ p(c2|x) : probability that x belongs to c2◦ p(c1|xn) : probability that xn belongs to c1◦ p(c2|xn) : probability that xn belongs to c2Knowing that p(c1|x) + p(c2|x) = 1 and p(c1|xn) + p(c2|xn) = 1,(a) Express the conditional probability of misclassification error, e, for x, P (e|x, xn), in terms ofthe probabilities provided above.

In KNN, how is the class of a new data point determined in classification tasks?*1 pointMajority vote of its K nearest neighborsAverage of its K nearest neighbors' valuesWeighted vote of its K nearest neighborsRandom selection from its K nearest neighbors

In K Nearest Neighbours classification, which of the following statements about K and N (the number of training samples) is/are true?Group of answer choicesK impacts both the accuracy and the computational complexity of the KNN algorithm.K and N should be linearly related, i.e. K/N should be a pre-determined constant.The time taken to perform the classification task increases with N.K should be odd to avoid ties.

#<GRADED> def knnclassifier(xTr,yTr,xTe,k): """ function preds=knnclassifier(xTr,yTr,xTe,k); k-nn classifier Input: xTr = nxd input matrix with n row-vectors of dimensionality d xTe = mxd input matrix with m row-vectors of dimensionality d k = number of nearest neighbors to be found Output: preds = 1xd vector of predicted labels, ie preds(i) is the predicted label of xTe(i,:) """ # fix array shapes yTr = yTr.flatten() # Your code goes here raise NotImplementedError('Your code goes here!') return preds #</GRADED> python code with no for loop and return preds

Another training data point, xm, is the 2nd nearest neighbor of x. Show the conditionalprobability of misclassification error considering both xn and xm, P (e|x, xn, xm).

When applying k-Nearest Neighbors (KNN) for classification, what is the role of the "k" parameter?a.It determines the learning rate in the algorithm.b.It sets the number of nearest neighbors to consider for classification.c.It specifies the number of dimensions in the dataset.d.It defines the number of clusters.