Non-Euclidean Distance
Non-Euclidean distance is a distance metric that does not satisfy the triangle inequality, which is a fundamental property of Euclidean distance. In other words, the distance between two points may not be the shortest path between them. Non-Euclidean distance is commonly used in machine learning algorithms, such as k-nearest neighbors and clustering, to measure the similarity between data points. One example of non-Euclidean distance is the Manhattan distance, which measures the distance between two points as the sum of the absolute differences of their coordinates. Another example is the Mahalanobis distance, which takes into account the covariance between variables. Non-Euclidean distance is particularly useful when dealing with high-dimensional data, where the curse of dimensionality makes Euclidean distance less effective.
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