Table of Contents

Enum DistanceMetricType

Namespace
AiDotNet.Enums
Assembly
AiDotNet.dll

Represents different methods for measuring the distance or similarity between data points.

public enum DistanceMetricType

Fields

Cosine = 2

Measures the cosine of the angle between two vectors, focusing on orientation rather than magnitude.

For Beginners: Cosine similarity measures the angle between two vectors, ignoring their magnitude (length).

Think of it as comparing the direction two people are facing, regardless of how far they've walked. Two people facing north are similar (cosine = 1), even if one walked 1 mile and the other 100 miles. People facing opposite directions have maximum dissimilarity (cosine = -1).

Formula: cos(?) = (A·B)/(||A||·||B||)

Best used for:

  • Text documents (comparing document topics regardless of length)
  • Recommendation systems
  • High-dimensional sparse data
  • When the magnitude of vectors doesn't matter, only their direction

Examples:

  • Document similarity in text analysis
  • User preference matching in recommendations
  • Image feature comparison

Note: Cosine similarity ranges from -1 (completely opposite) to 1 (exactly the same), with 0 indicating orthogonality (no correlation). To convert to a distance, use 1 - cosine_similarity.

Euclidean = 0

The straight-line distance between two points in Euclidean space (also known as L2 distance).

Euclidean distance is the most common and intuitive distance measure - it's the straight-line distance between two points "as the crow flies."

Formula: sqrt((x2-x1)² + (y2-y1)² + ...)

Think of it as measuring distance with a ruler in a straight line.

Best used for:

  • Continuous numerical data
  • When features have similar scales
  • When the data space is relatively low-dimensional

Examples:

  • Distance between physical locations
  • Similarity between customer profiles with numerical attributes
  • Image similarity when using pixel values

Note: Euclidean distance is sensitive to the scale of the features, so normalization is often required before using this metric.

Hamming = 4

Counts the number of positions at which corresponding elements differ (used for strings or binary vectors).

For Beginners: Hamming distance counts how many positions have different values when comparing two strings or sequences of equal length.

Think of it as comparing two multiple-choice tests and counting how many answers are different.

For example, comparing "CART" and "PART":

  • Position 1: C vs P (different) ? +1
  • Position 2: A vs A (same) ? +0
  • Position 3: R vs R (same) ? +0
  • Position 4: T vs T (same) ? +0
  • Hamming distance = 1

Best used for:

  • Strings of equal length
  • Binary vectors
  • Error detection in communication
  • Genetic sequence comparison

Examples:

  • DNA sequence comparison
  • Error detection in data transmission
  • Comparing fixed-length binary feature vectors
  • Spell checking for words of the same length

Note: Hamming distance requires sequences of equal length.

Jaccard = 3

Measures dissimilarity between sets by comparing elements they share versus elements they don't.

For Beginners: Jaccard distance measures how different two sets are by comparing what they have in common versus what they don't.

Think of it as comparing two shopping lists:

  • How many items appear on both lists?
  • How many items appear on at least one list?
  • The ratio of these gives you the similarity

Formula: 1 - |AnB|/|A?B| (1 minus the size of intersection divided by size of union)

Best used for:

  • Binary data (presence/absence)
  • Set comparisons
  • Categorical data
  • Sparse binary vectors

Examples:

  • Comparing which movies two users have watched
  • Measuring similarity between text documents based on shared words
  • Comparing species presence/absence in ecological samples
  • Comparing shopping baskets

Jaccard distance ranges from 0 (identical sets) to 1 (completely different sets).

Mahalanobis = 5

Measures distance while accounting for correlations between variables and their relative importance.

For Beginners: Mahalanobis distance is an advanced metric that takes into account how variables are related to each other (their correlations).

Unlike Euclidean distance, which treats all dimensions equally, Mahalanobis distance:

  • Gives less weight to variables that have high variance
  • Accounts for correlations between variables
  • Adjusts for the shape of the data distribution

Think of it as measuring distance while considering the natural "shape" of your data:

  • If you have height and weight data, these are correlated (taller people tend to weigh more)
  • Mahalanobis distance accounts for this correlation when measuring similarity

Formula: sqrt((x-µ)? S?¹ (x-µ)) where S is the covariance matrix

Best used for:

  • Multivariate data with correlated features
  • Outlier detection
  • Classification problems
  • When features have different scales and variances

Examples:

  • Anomaly detection in multivariate systems
  • Face recognition
  • Quality control in manufacturing

Note: Mahalanobis distance requires computing the covariance matrix of your data, which can be computationally expensive for high-dimensional data.

Manhattan = 1

The sum of absolute differences between coordinates (also known as L1 distance or taxicab distance).

Manhattan distance measures the distance between two points by summing the absolute differences of their coordinates.

Formula: |x2-x1| + |y2-y1| + ...

Think of it as the distance a taxi would drive in a city with a grid layout, where you can only travel along the streets (horizontal and vertical movements).

Best used for:

  • Grid-based problems
  • When diagonal movement costs the same as horizontal/vertical
  • Data with discrete or binary features
  • When you want to reduce the influence of outliers

Examples:

  • Navigation in city streets
  • Feature comparison when features are independent
  • Image processing with pixel-wise comparisons

Manhattan distance is less sensitive to outliers than Euclidean distance.

Remarks

For Beginners: Distance metrics are ways to measure how similar or different two data points are.

Think of distance metrics like different ways to measure the distance between two cities:

  • As the crow flies (straight line)
  • By following streets (Manhattan)
  • By considering terrain and obstacles (more complex metrics)

In machine learning, we use these metrics to:

  • Group similar items together (clustering)
  • Find nearest neighbors
  • Measure how well our model is performing

Different distance metrics work better for different types of data and problems. For example, Euclidean distance works well for continuous numerical data, while Jaccard distance is better for comparing sets.

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