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Which one of the following statements is true regarding K Nearest Neighbors?1 pointFor high dimensional data, the best distance measure to use for KNN is the Euclidean distance.The Manhattan distance between two data points is the square root of the sum of the squares of the differences between the individual feature values of the data points.The distance between two data points is independent of the scale of their features.K Nearest Neighbors (KNN) assumes that points which are close together are similar.

Question

Which one of the following statements is true regarding K Nearest Neighbors?1 pointFor high dimensional data, the best distance measure to use for KNN is the Euclidean distance.The Manhattan distance between two data points is the square root of the sum of the squares of the differences between the individual feature values of the data points.The distance between two data points is independent of the scale of their features.K Nearest Neighbors (KNN) assumes that points which are close together are similar.

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Solution

The true statement regarding K Nearest Neighbors (KNN) is: "K Nearest Neighbors (KNN) assumes that points which are close together are similar."

Explanation:

  1. For high dimensional data, the best distance measure to use for KNN is not necessarily the Euclidean distance. The choice of distance measure depends on the nature of the data. In high dimensional data, Euclidean distance can be affected by the curse of dimensionality, where distances between points become less meaningful.

  2. The Manhattan distance between two data points is not the square root of the sum of the squares of the differences between the individual feature values of the data points. That's the definition of Euclidean distance. Manhattan distance is the sum of the absolute differences of their coordinates.

  3. The distance between two data points is not independent of the scale of their features. If the scale of features is different, it can greatly affect the distance. That's why feature scaling is important in KNN.

  4. K Nearest Neighbors (KNN) does assume that points which are close together are similar. This is the basic premise of KNN, where the class of an unknown point is determined by the classes of its nearest neighbors.

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