There are many distance metrics that are used in various Machine Learning Algorithms. One of them is Euclidean Distance. Euclidean distance is the most used distance metric and it is simply a straight line distance between two points. Euclidean distance between points is given by the formula :

We can use various methods to compute the Euclidean distance between two series. Here are a few methods for the same:**Example 1:**

`import` `pandas as pd` `import` `numpy as np` ` ` ` ` `# create pandas series` `x ` `=` `pd.Series([` `1` `, ` `2` `, ` `3` `, ` `4` `, ` `5` `])` `y ` `=` `pd.Series([` `6` `, ` `7` `, ` `8` `, ` `9` `, ` `10` `])` ` ` `# here we are computing every thing` `# step by step` `p1 ` `=` `np.` `sum` `([(a ` `*` `a) ` `for` `a ` `in` `x])` `p2 ` `=` `np.` `sum` `([(b ` `*` `b) ` `for` `b ` `in` `y])` ` ` `# using zip() function to create an` `# iterator which aggregates elements ` `# from two or more iterables` `p3 ` `=` `-` `1` `*` `np.` `sum` `([(` `2` `*` `a` `*` `b) ` `for` `(a, b) ` `in` `zip` `(x, y)])` `dist ` `=` `np.sqrt(np.` `sum` `(p1 ` `+` `p2 ` `+` `p3))` ` ` `print` `(` `"Series 1:"` `, x)` `print` `(` `"Series 2:"` `, y)` `print` `(` `"Euclidean distance between two series is:"` `, dist)` |

**Output :**

**Example 2:**

`import` `pandas as pd` `import` `numpy as np` ` ` ` ` `x ` `=` `pd.Series([` `1` `, ` `2` `, ` `3` `, ` `4` `, ` `5` `])` `y ` `=` `pd.Series([` `6` `, ` `7` `, ` `8` `, ` `9` `, ` `10` `])` ` ` `# zip() function creates an iterator` `# which aggregates elements from two ` `# or more iterables` `dist ` `=` `np.sqrt(np.` `sum` `([(a` `-` `b)` `*` `(a` `-` `b) ` `for` `a, b ` `in` `zip` `(x, y)])) ` ` ` `print` `(` `"Series 1:"` `)` `print` `(x)` ` ` `print` `(` `"Series 2:"` `)` `print` `(y)` ` ` `print` `(` `"Euclidean distance between two series is:"` `, dist)` |

**Output :**

**Example 3:** In this example we are using **np.linalg.norm()** function which returns one of eight different matrix norms.

`import` `pandas as pd` `import` `numpy as np` ` ` ` ` `x ` `=` `pd.Series([` `1` `, ` `2` `, ` `3` `, ` `4` `, ` `5` `])` `y ` `=` `pd.Series([` `6` `, ` `7` `, ` `8` `, ` `9` `, ` `10` `])` `dist ` `=` `(np.linalg.norm(x` `-` `y))` ` ` `print` `(` `"Series 1:"` `)` `print` `(x)` ` ` `print` `(` `"Series 2:"` `)` `print` `(y)` ` ` `print` `(` `"Euclidean distance between two series is:"` `, dist)` |

**Output :**

**Example 4:** Let’s try on a bigger series now:

`import` `pandas as pd` `import` `numpy as np` ` ` ` ` `x ` `=` `pd.Series([` `1` `, ` `2` `, ` `3` `, ` `4` `, ` `5` `, ` `6` `, ` `7` `, ` `8` `, ` `9` `, ` `10` `])` `y ` `=` `pd.Series([` `12` `, ` `8` `, ` `7` `, ` `5` `, ` `6` `, ` `5` `, ` `3` `, ` `9` `, ` `7` `, ` `1` `])` `dist ` `=` `np.sqrt(np.` `sum` `([(a` `-` `b)` `*` `(a` `-` `b) ` `for` `a, b ` `in` `zip` `(x, y)]))` ` ` `print` `(` `"Series 1:"` `)` `print` `(x)` ` ` `print` `(` `"Series 2:"` `)` `print` `(y)` ` ` `print` `(` `"Euclidean distance between two series is:"` `, dist)` |

**Output :**

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