Machine Learning For Key Generation
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Candidate generation is the first stage of recommendation. Given a query, thesystem generates a set of relevant candidates. The following table shows twocommon candidate generation approaches:
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Type | Definition | Example |
---|---|---|
content-based filtering | Uses similarity between items to recommend items similar to what the user likes. | If user A watches two cute cat videos, then the system can recommend cute animal videos to that user. |
collaborative filtering | Uses similarities between queries and items simultaneously to provide recommendations. | If user A is similar to user B, and user B likes video 1, then the system can recommend video 1 to user A (even if user A hasn’t seen any videos similar to video 1). |
Machine Learning For Key Generation Kids
Embedding Space
Both content-based and collaborative filtering map each item and each query(or context) to an embedding vector in a common embedding space(E = mathbb R^d). Typically, the embedding space is low-dimensional(that is, (d) is much smaller than the size of the corpus), and capturessome latent structure of the item or query set. Similar items, such as YouTubevideos that are usually watched by the same user, end up close together in theembedding space. The notion of 'closeness' is defined by a similarity measure.
Extra Resource:projector.tensorflow.org isan interactive tool to visualize embeddings.Similarity Measures
A similarity measure is a function (s : E times E to mathbb R) thattakes a pair of embeddings and returns a scalar measuring their similarity.The embeddings can be used for candidate generation as follows: given aquery embedding (q in E), the system looks for item embeddings(x in E) that are close to (q), that is, embeddings with highsimilarity (s(q, x)).
To determine the degree of similarity, most recommendation systems relyon one or more of the following:
- cosine
- dot product
- Euclidean distance
Cosine
This is simply the cosine of the angle between the twovectors, (s(q, x) = cos(q, x))
Dot Product
The dot product of two vectors is(s(q, x) = langle q, x rangle = sum_{i = 1}^d q_i x_i).It is also given by (s(q, x) = x q cos(q, x)) (the cosine of theangle multiplied by the product of norms). Thus, if the embeddings arenormalized, then dot-product and cosine coincide.
Euclidean distance

This is the usual distance in Euclideanspace, (s(q, x) = q - x = left[ sum_{i = 1}^d (q_i - x_i)^2right]^{frac{1}{2}}).A smaller distance means higher similarity. Note that when the embeddingsare normalized, the squared Euclidean distance coincides with dot-product(and cosine) up to a constant, since in thatcase (frac{1}{2} q - x ^2 = 1 - langle q, x rangle).
Comparing Similarity Measures

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Consider the example in the figure to the right. The black vector illustrates thequery embedding. The other three embedding vectors (Item A, Item B, Item C)represent candidate items. Depending on the similarity measure used, theranking of the items can be different.
Using the image, try to determine the item ranking using all three of thesimilarity measures: cosine, dot product, and Euclidean distance.
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How did you do?
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Item A has the largest norm, and is ranked higher according to the dot-product. Item C has the smallest angle with the query, and is thus ranked first according to the cosine similarity. Item B is physically closest to the query so Euclidean distance favors it.
Which Similarity Measure to Choose?
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Compared to the cosine, the dot product similarity is sensitive tothe norm of the embedding. That is, the larger the norm of anembedding, the higher the similarity (for items with an acute angle)and the more likely the item is to be recommended. This can affectrecommendations as follows:
Items that appear very frequently in the training set (for example,popular YouTube videos) tend to have embeddings with large norms.If capturing popularity information is desirable, then you shouldprefer dot product. However, if you're not careful, the popularitems may end up dominating the recommendations. In practice, youcan use other variants of similarity measures that put less emphasison the norm of the item. For example, define(s(q, x) = q ^alpha x ^alpha cos(q, x)) forsome (alpha in (0, 1)).
Items that appear very rarely may not be updated frequently duringtraining. Consequently, if they are initialized with a large norm, thesystem may recommend rare items over more relevant items. To avoid thisproblem, be careful about embedding initialization, and use appropriateregularization. We will detail this problem in the first exercise.