Euclidean distance is a measure of the straight-line distance between two points in Euclidean space. It is commonly used in mathematics and various fields such as machine learning, statistics, and physics.
Formula:
For two points ( A(x_1, y_1) ) and ( B(x_2, y_2) ) in 2D space, the Euclidean distance ( d ) is calculated as:
[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
]
In general, for two points in ( n )-dimensional space, ( A(a_1, a_2, ..., a_n) ) and ( B(b_1, b_2, ..., b_n) ):
[
d = \sqrt{\sum_{i=1}^{n} (b_i - a_i)^2}
]
Key Points:
- Straight-Line Distance: It represents the shortest path between two points.
- Applications: Used in clustering, classification, and various algorithms in data analysis.
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