Similarity

[!sam] - Data Visualization Techniques - Summary Statistics and Insights - Identifying Patterns and Anomalies - Correlation Analysis

Similarity

Image: Types of Similarity

• Direct | Literally, how far away are the points

• Contextual | Think clusters. Points within a cluster are similar.

• Conceptual | Think philosophy.

Computing | Continuous Data

Distance Metric	Summary	When to use	When NOT to use	LaTeX Formula
Euclidean	As the crow flies	When you want shortest direct distance between points, and all variables are equally important.	High dimensionality, outliers	\(d = \sqrt{\sum_{i=1}^n (a_i - b_i)^2}\)
Manhattan	Adds up distances along each axis, like walking city blocks in a grid.	When movement happens in straight lines or when variables are on different units/scales.		\(d = \sum_{i=1}^n \|a_i - b_i\|\)
Minkowski	Can act like Euclidean, Manhattan, or something in between	When you want a general approach that can adjust to the problem’s needs, especially for varied data.	When simpler methods work too	\(d = \left(\sum_{i=1}^n \|a_i - b_i\|^p\right)^{1/p}\)
Max-Coordinate (Chebyshev)	Looks at biggest difference between points.	When you care about largest / most extreme impact	When overall distance is important.	\(d = \max_i \|a_i - b_i\|\)

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Computing | Mixed Data (Gower)

Gower Distance For each variable type:

1. Select distance metric

2. Scale from 0 to 1 Then, apply linear combo to calculate final distance matrix

Variable types:

• Interval: Manhattan

• Ordinal: Variable is first ranked, then Manhattan distance is used with a special adjustment for ties

• Nominal: Variables of k categories are first converted into k binary columns and then the Dice coefficient is used

Computing | Nominal

Cosine Similarity (for text or high-dimensional data)