Similarity metric

As explained in Grokking Machine Learning

A numerical measure of the closeness between two data points.

A similarity function assigns a value to a pair of points to indicate how close or different they are. In the RBF example, similarity decreases as distance increases: similarity(p, q) = e^−distance(p,q)². These values can serve as added features, helping an SVM separate data that a straight boundary cannot. section 11.3

Comparing points on a line

For points at −1, 0, and 1, the similarity of the point at −1 to those three points is 1, 0.368, and 0.018. Adding a column of such values for each point creates features that can make the labeled data linearly separable. section 11.3

Figure 11.26 Two points that are close to each other are defined to have high similarity. Two points that are far away are defined to have low similarity.

The diagram contrasts high similarity for nearby points with low similarity for distant points. section 11.3

How Grokking Machine Learning covers it

How deep it goes

Defines closeness through distance, gives an exponential formula, and defers the full theory of kernels and feature maps.

Examples

Uses one- and two-dimensional labeled datasets, distance-based similarity values, and added similarity columns.

What you can do after

Apply similarity values as added features to classify nonlinear data with an SVM.

How it connects

Connects similarity functions to radial basis function kernels, feature maps, and support vector machines.

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Related concepts

• kernel functionincludes · A kernel function is a mathematical function that measures similarity between pairs of inputs, often representing an inner product in an implicit feature space.
• embeddinguses · A numerical vector representation of an item or input that encodes features or relationships useful for computational tasks.
• recommender systemused by · A recommender system is software that predicts, selects, or ranks items, content, or actions for users based on available information about users, items, or context.
• similarity searchused by · Similarity search is a retrieval technique that finds or ranks items by comparing their representations with a query according to a similarity or distance measure.
• inner productmeasured by · An inner product is a scalar-valued operation on two vectors that combines their corresponding components, summing their products and, for complex vectors, using conjugation.
• cosine similarityincludes · Cosine similarity measures the directional alignment of two nonzero vectors as the cosine of the angle between them, equivalently their dot product divided by the product of their magnitudes.

This explainer was generated by Manning's knowledge graph from the text of Grokking Machine Learning. The section links point to the parts of the book it draws on.