# Distance Metrics in Data Science: Overview and Usage

## Distance Metrics in Data Science

### Euclidean Distance

**Description**: Measures the straight-line distance between two points in Euclidean space.**Formula**: (\sqrt{\sum_{i=1}^{n} (x_i - y_i)^2})**Usage**: Commonly used in tasks requiring measurement of similarity between data points such as clustering and classification.

### Manhattan Distance

**Description**: Measures distance between two points along axes at right angles. Also known as L1 norm or taxicab distance.**Formula**: (\sum_{i=1}^{n} |x_i - y_i|)**Usage**: Useful in grid-based pathfinding algorithms and when differences in individual dimensions need equal treatment.

### Minkowski Distance

**Description**: Generalization of both Euclidean and Manhattan distance.**Formula**: ( \left(\sum_{i=1}^{n} |x_i - y_i|^p\right)^{1/p} )**Parameter**: ( p )- ( p = 1 ): Manhattan distance
- ( p = 2 ): Euclidean distance

**Usage**: Offers flexibility with ( p ) parameter, useful when specific dimensional contributions need to be balanced.

### Cosine Similarity

**Description**: Measures the cosine of the angle between two non-zero vectors. Values range from -1 to 1.**Formula**: ( \cos(\theta) = \frac{A \cdot B}{|A| |B|} )**Usage**: Useful for text analysis, comparing document similarity, and situations where magnitude differs.

### Hamming Distance

**Description**: Counts the number of positions at which corresponding elements differ. Primarily used for binary strings.**Formula**: ( Hamming(A, B) )**Usage**: Error detection and correction in data transmission, binary string comparison.

### Jaccard Similarity

**Description**: Measures similarity between finite sets by comparing the ratio of intersecting elements to the union of elements.**Formula**: ( J(A, B) = \frac{|A \cap B|}{|A \cup B|} )**Usage**: Used in clustering and information retrieval, especially in comparing sets or binary attributes.

### Levenshtein Distance

**Description**: Measures the minimum number of single-character edits required to change one word into another.**Formula**: ( Levenshtein(A, B) )**Usage**: Commonly used in text processing, spell checking, and plagiarism detection.

### Haversine Distance

**Description**: Measures the distance between points on the surface of a sphere. Essential for calculating great-circle distances.**Formula**: Involves spherical trigonometry.**Usage**: Ideal for geographic information systems (GIS) and applications involving global positioning.

### Sørensen–Dice Distance

**Description**: Measures the similarity between two samples. Similar to Jaccard Similarity but doubles the weight of intersection.**Formula**: ( \frac{2 |A \cap B|}{|A| + |B|} )**Usage**: Effective in ecology, biology, and other fields requiring robust similarity measurement between sets.

**Reference:**

medium.com

Exploring Common Distance Measures for Machine Learning and ...

www.linkedin.com

9 Distance Measures in Data Science - LinkedIn

www.analyticsvidhya.com

Understanding Distance Metrics Used in Machine Learning