$$ \newcommand{\R}{\mathbb{R}} \newcommand{\E}{\mathbb{E}} \newcommand{\x}{\mathbf{x}} \newcommand{\y}{\mathbf{y}} \newcommand{\wv}{\mathbf{w}} \newcommand{\av}{\mathbf{\alpha}} \newcommand{\bv}{\mathbf{b}} \newcommand{\N}{\mathbb{N}} \newcommand{\id}{\mathbf{I}} \newcommand{\ind}{\mathbf{1}} \newcommand{\0}{\mathbf{0}} \newcommand{\unit}{\mathbf{e}} \newcommand{\one}{\mathbf{1}} \newcommand{\zero}{\mathbf{0}} \newcommand\rfrac[2]{^{#1}\!/_{#2}} \newcommand{\norm}[1]{\left\lVert#1\right\rVert} $$

1. Application Development
2. Libraries
3. Machine Learning
4. Distance Metrics

Distance Metrics

• Description
• Built-in Implementations
• Custom Implementation

Description

Different metrics of distance are convenient for different types of analysis. Flink ML provides built-in implementations for many standard distance metrics. You can create custom distance metrics by implementing the DistanceMetric trait.

Built-in Implementations

Currently, FlinkML supports the following metrics:

Metric	Description
Euclidean Distance	$$d(\x, \y) = \sqrt{\sum_{i=1}^n \left(x_i - y_i \right)^2}$$
Squared Euclidean Distance	$$d(\x, \y) = \sum_{i=1}^n \left(x_i - y_i \right)^2$$
Cosine Similarity	$$d(\x, \y) = 1 - \frac{\x^T \y}{\Vert \x \Vert \Vert \y \Vert}$$
Chebyshev Distance	$$d(\x, \y) = \max_{i}\left(\left \vert x_i - y_i \right\vert \right)$$
Manhattan Distance	$$d(\x, \y) = \sum_{i=1}^n \left\vert x_i - y_i \right\vert$$
Minkowski Distance	$$d(\x, \y) = \left( \sum_{i=1}^{n} \left( x_i - y_i \right)^p \right)^{\rfrac{1}{p}}$$
Tanimoto Distance	$$d(\x, \y) = 1 - \frac{\x^T\y}{\Vert \x \Vert^2 + \Vert \y \Vert^2 - \x^T\y}$$ with $\x$ and $\y$ being bit-vectors

Custom Implementation

You can create your own distance metric by implementing the DistanceMetric trait.

class MyDistance extends DistanceMetric {
  override def distance(a: Vector, b: Vector) = ... // your implementation for distance metric
}

object MyDistance {
  def apply() = new MyDistance()
}

val myMetric = MyDistance()

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