Assume we have a decision tree to classify binary vectors of length 100(that is, each input is of size 100).Can we specify a 1-NN that would result inexactly the same classification as our decision tree? If so, explain why. Ifnot, either explain why or provide a counter example.

Ans:

Yes, it’s possible to specify a 1-nearest neighbor (1-NN) classifier that would result in exactly the same classification as a decision tree for binary vectors of length 100.

Here’s why:

1. Decision Tree: A decision tree classifies data points by splitting the feature space into regions based on the feature values. At each node, a decision is made based on the value of a particular feature. This process continues recursively until a leaf node is reached, which corresponds to a class label.
2. 1-NN Classifier: The 1-nearest neighbor classifier classifies data points based on the class label of the nearest neighbor in the training set. In the case of binary vectors, the “nearest” neighbor is determined by calculating the Hamming distance, which is the number of positions at which the corresponding bits are different between two vectors.

Given a binary vector of length 100, the 1-NN classifier would find the most similar vector in the training set based on the Hamming distance. If the decision tree accurately captures the decision boundaries in the feature space, then the nearest neighbor to any point classified by the decision tree would also be classified the same way by the 1-NN classifier.

If the decision tree accurately represents the underlying structure of the data and can correctly classify binary vectors of length 100, then a 1-NN classifier using Hamming distance would produce exactly the same classification results.