It depends only on the direction of the vectors. This indicates that cosine similarity is independent of the magnitude or the size of the vectors. Note that the cosine similarity in case (b) is 1 (similar) though the size of the blue jet ski vector is higher than the orange one. 1 indicates the items are the same whereas -1 represents the compared items are dissimilar. Now to determine if Case(b) and Case(c) are similar to Case(a), we can apply cosine similarity to other two cases,Ĭosine similarity ranges from -1 to 1. So, for case (a) in the figure, cosine similarity is,Ĭosine similarity = cos(blue jet ski, orange jet ski) = cos(30°) = 0.866 Now, to get the cosine similarity between the jet skis in the north-east dimensions, we need to find the cosine of the angle between these two vectors. Image inspired from here: Cosine similarity - Mastering Machine Learning with Spark 2.x The jet ski position is represented by numerical values in both north and east direction and the position of the jet skis can be represented as vectors from the origin. That means, there are two features here (two-dimensional space): North and East. Let’s say that both of the jet skis are riding in the north-east direction. To understand the fundamentals, let us look into the example of two jet skis riding in a lake. We understand that this metric calculates and quantifies the similarity between two items, but how? Let us focus on the most commonly used similarity metric - “Cosine similarity”. There are many similarity metrics used in recommendation systems. The list of items with high similarity values to the ones that the user selected are recommended as “You may also like”. The recommendation system in its core algorithm uses a fundamental mathematical metric called “similarity”, which compares and quantifies the similarity between two items: user selected vs rest of items in the catalog. For example, recommending products in e-commerce sites to recommending movies in movie streaming platforms or recommending a book to borrow from a public library based on your current or previous preferences.Īlgorithms that are used to provide the list of suggestions are called recommendation systems or engines. However, cosine similarity assumes that the two input vectors are not zero-vectors, so it makes sense to me to throw an exception when it happens.Īs 200_success advised, you can omit the entire exception-throwing code and just proceed to division by zero: that will return a special NaN value ("Not a Number").Machine learning algorithms provide customized suggestions in our day-to-day life. Note that sqrt(d_a * d_b) = 0 only when at least one of the input vectors is a zero vector. However, usually a single space is put straight after for: for (int i = 0. Usually people don't put a single space before the semicolon. You can get rid of one call to sqrt double cosine_similarity2(double *A, double *B, unsigned int size) "cosine similarity is not defined whenever one or both " Std::vector::iterator A_iter = A.begin() įor( A_iter != A.end() A_iter++, B_iter++ ) If (A.size() ::iterator B_iter = B.begin() Throw std::logic_error("Vector A and Vector B are not the same size") double cosine_similarity(double *A, double *B, unsigned int size)ĭouble cosine_similarity_vectors(std::vector A, std::vectorB) Use the pointers rather than indexing them. Since the code is already passing pointers The the most efficient way to write the function is to use direct addressing rather than indirect addressing. This is less readable and maintainable than putting the initialization on separate lines: double mul = 0.0 ĭirect Addressing Versus Indirect Addressing Item 1 and 2Ībove belong in the std::logic_error class, item 3 belongs in the Two of the classes are std::runtime_error and std::logic_error. Either d_a or d_b can add up to zero, which can lead to division by zeroĬ++ provides the exception class std:exception that has multiple sub classes.Size variable is the size of the larger vector this can lead to unknown Is the size of the shorter vector this is not a problem, but if the The vectors A and B may not be the same length, if the size variable.The variable size may be zero which will lead to division by zero.There are a number of possible errors in the code:
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