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Jun 16, 2022 01:21 PM
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Data Science
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Machine Learning
Machine Learning
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Manhattan Distance
- The sum of absolute differences
Application
- Used in the map to calculate the distance between two data points in a grid-like path
Mechanism
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F32a36eb0-82e1-49af-9ec8-af1847899126%2F1_P3cD-9p8JHYm2xn6bUIf_g.png%3Fid%3D54107608-4f2e-4373-8a79-3332b5858244%26table%3Dblock%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1721167200000%26signature%3DejbPBc0AyPC2qTtVLd0wO1Bzk5DhIZLK3DoxQdizOtQ?table=block&id=54107608-4f2e-4373-8a79-3332b5858244&cache=v2)
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F016a17e8-6f46-4a38-95bc-5dcf8934fb85%2FUntitled.png%3Fid%3D4ad8f7b6-c9d3-4af5-92b1-34f1d68352dc%26table%3Dblock%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1721167200000%26signature%3Ddd92L4p6JiH4JozT3nExvnCb9B2eUbIKbAzyOMEjKis?table=block&id=4ad8f7b6-c9d3-4af5-92b1-34f1d68352dc&cache=v2)
Minkowski distance
- A generalization of the Euclidean distance and the Manhattan distance.
- Is applied in machine learning to find out distance similarity.
Application
- To find the distance measured between 2 points in N-dimensional space
- See it as the correlation between 2 points
Mechanism
If C = 1 it is Manhattan Distance.
If C = 2 It is Euclidean distance.
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F69b009d6-3e63-47c0-9202-fbec52f1ac51%2F1_X0pyRCM_uHahr-Um8kd-JQ.png%3Fid%3D40e402be-000d-45d7-8c6e-716731be6d2b%26table%3Dblock%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1721167200000%26signature%3D3vnplNcQ8wQepdUJw0eSzrcjSa6aABSUPEdKHKIUkOs?table=block&id=40e402be-000d-45d7-8c6e-716731be6d2b&cache=v2)
Mahalanobis distance
Mahalanobis distance between two vectors, x and y, where S is the co-variance matrix.
- Co-variance of two feature indicated how values of two features are varying together.
- Measures how values of one feature are varying according to values of another feature.
- Uses inverse of co-variance matrix, that is why we have a T
Application
- Multivariate distance metric that measures the distance between a point (vector) and a distribution.
- Has excellent applications in multivariate anomaly detection, classification on highly imbalanced datasets and one-class classification and more untapped use cases
Mechanism
![notion image](https://www.notion.so/image/https%3A%2F%2Ffile.notion.so%2Ff%2Ff%2Fe1c5ba0e-562a-49b0-8505-ce5e38fc061b%2F11e06ddf-967a-4d39-8534-ff5ea9c518a3%2F1_TuGa5ildAYjE18x65-o3YA.png%3Fid%3D5bbe777a-3095-446b-8e48-259044620858%26table%3Dblock%26spaceId%3De1c5ba0e-562a-49b0-8505-ce5e38fc061b%26expirationTimestamp%3D1721167200000%26signature%3DVRDu2g_jGfYx51wUqvzXxAkjnou1rLNxPkw-7RJvavw?table=block&id=5bbe777a-3095-446b-8e48-259044620858&cache=v2)
Further visit Distance - Understanding the math with examples (python)
Reference
- Author:Jason Siu
- URL:https://jason-siu.com/article%2Fb9b28b73-aa22-4d15-8141-5e4a844e8cb3
- Copyright:All articles in this blog, except for special statements, adopt BY-NC-SA agreement. Please indicate the source!
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