R ecently I was working on a project where I have to cluster all the words which have a similar name. For a novice it looks a pretty simple job of using some Fuzzy string matching tools and get this done. However in reality this was a challenge because of multiple reasons starting from pre-processing of the data to clustering the similar words.
Now you see the challenge of matching these similar text. After a research for couple of days and comparing results of our POC using all sorts of tools and algorithms out there we found that cosine similarity is the best way to match the text. What is Cosine Similarity? C osine Similarity tends to determine how similar two words or sentence are, It can be used for Sentiment Analysis, Text Comparison and being used by lot of popular packages out there like word2vec.
Here we are not worried by the magnitude of the vectors for each sentence rather we stress on the angle between both the vectors. So if two vectors are parallel to each other then we may say that each of these documents are similar to each other and if they are Orthogonal An orthogonal matrix is a square matrix whose columns and rows are orthogonal unit vectors then we call that the documents are independent of each other.
Dot Product: This is also called as Scalar product since the dot product of two vectors gives a scalar result. For example. Their dot product vector A. So the Geometric definition of dot product of two vectors is the dot product of two vectors is equal to the product of their lengths, multiplied by the cosine of the angle between them. The most simple and intuitive is BOW which counts the unique words in documents and frequency of each of the words. Example :. Here you can see the Bag of Words vectors tokenize all the words and puts the frequency in front of the word in Document.
Shortcoming of BOW:. The major issue with Bag of Words Model is that the words with higher frequency dominates in the document, which may not be much relevant to the other words in the document. So another approach tf-idf is much better because it rescales the frequency of the word with the numer of times it appears in all the documents and the words like the, that which are frequent have lesser score and being penalized. Here you can see the tf-idf numerical vectors contains the score of each of the words in the document.
Next we would see how to perform cosine similarity with an example:. We will use Scikit learn Cosine Similarity function to compare the first document i.This is a Part 3 of Demystifying Text Analytics series.
In the last two posts, we imported text documents from companies in California. We have transformed and prepared the text data and giving the scores to each term by calculating the TF-IDF. Now, remember the following questions we originally asked in Part 1? But what is Cosine Similarity? It measures the cosine of the angle between two vectors. In this case, each document can be presented as a vector whose direction is determined on a set of the TF-IDF values in the space. If we visualize these values in two-dimensional space it would look something like the below.
If the two vectors are pointing in a similar direction the angle between the two vectors is very narrow. And this means that these two documents represented by the vectors are similar.
So in order to measure the similarity we want to calculate the cosine of the angle between the two vectors. Of course, we have hundreds of terms than just the two for these documents we are working with. But the concept is still the same. Instead, we want to use the cosine similarity algorithm to measure the similarity in such a high-dimensional space.
Curse of dimensionality. Open the data frame we have used in the previous post in Exploratory Desktop. In the previous exercise, we have filtered the data to top 10 for each document. But we want to apply the cosine similarity algorithm on top of the full data, not the filtered data. Remove the last two steps of Group By and Top N. We should have the data like this.
In the dialog, select a grouping column e. Company Name you want to calculate the cosine similarity for, then select a dimension e. This will return the cosine similarity value for every single combination of the documents.
The higher the similarity values are the more similar the two documents are in this case. We can zoom into an area where we can see a high red color concentration by dragging the mouse pointer for the area.
We can filter the data to keep only the document pairs that have greater than 0. Just by looking at these document names company names we can tell that some of these companies are actually related each other e.
As you have seen, calculating the cosine similarity based on TF-IDF helps to find the similarity between two documents. Now, what if we want to understand the overall relationship among the documents rather than the relationship between each pair of the documents?
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Recommending Songs Using Cosine Similarity in R
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Start learning Data Science without Programming!Recommendation engines have a huge impact on our online lives. The content we watch on Netflix, the products we purchase on Amazon, and even the homes we buy are all served up using these algorithms.
There are a few different flavors of recommendation engines. One type is collaborative filteringwhich relies on the behavior of users to understand and predict the similarity between items. There are two subtypes of collaborative filtering: user-user and item-item. In a nutshell, user-user engines will look for similar users to you, and suggest things that these users have liked users like you also bought X. Converting an engine from user-user to item-item can reduce the computational cost of generating recommendations.
Another type of recommendation engine is content-based. Rather than using the behavior of other users or the similarity between ratings, content-based systems employ information about the items themselves e.
Cosine similarity is helpful for building both types of recommender systems, as it provides a way of measuring how similar users, items, or content is. Cosine similarity is built on the geometric definition of the dot product of two vectors:.
From the above expression, we can arrive at cosine similarity:. What does it all mean? This blog post has a great image demonstrating cosine similarity for a few examples.
Image from a blog post by Christian S. A value of 1 will indicate perfect similarity, and 0 will indicate the two vectors are unrelated. In other applications, there may be data which is positive and negative. We use a subset of the data from the Million Song Dataset. The data only has 10K songs, but that should be enough for this exercise. Here are the first few rows of the data. The important variable is playswhich measures how many times a certain user has listened to a song.
There are 76, users in this data set, so combining the number of users with songs makes the data a little too unwieldy for this toy example. This results in having play data for 70, users and songs. From start to finish, this only took about 20 lines of code, indicating how easy it can be to spin up a recommendation engine. We can use the function above to calculate similarities and generate recommendations for a few songs. Each song we recommended is a hip-hop song, which is a good start!
Even on this reduced dataset, the engine is making decent recommendations. Alright, 2 for 2. The other four recommendations seem pretty solid, I guess. Cosine similarity is simple to calculate and is fairly intuitive once some basic geometric concepts are understood. I think that recommendation systems will continue to play a large role in our online lives. It can be helpful to understand the components underneath these systems, so that we treat them less as blackbox oracles and more as the imperfect prediction systems based on data they are.
Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It only takes a minute to sign up. I'm trying to implement item based filtering, with a large feature space representing consumers who bought 1 or did not buy 0 a particular product.
I have a long tail distribution, so the matrix is quite sparse. R is not handling it well. What can I do to streamline the measurement of cosine similarity? R often does not scale well to large data. You may need to move on to more efficient implementations. There are plenty of choices around. But of course, there probably are also various R packages that could help you a bit further. Also, it pays off to stop thinking in matrixes. What you are working with is a graph. An easy way to accelerate computing the similarities here is to cleverly exploit the similarity.
This btw. When you realize that cosine similarity consists of three components: product of A and B, length of A and length of B, you will notice that two parts are independent of the other vector, and the third part has the squared sparsity, this will drastically reduce the computations needed for a cosine similarity "matrix" again, stop seeing it as a matrix. And definitely think about how to store and organize your data in memory.
Don't let R do it automatically, because that probably means it is doing it wrong Here's a simple example of how you would calculate cosine similarity for a netflix-sized matrix in R. Also, note that the cosine similarity matrix is pretty sparse, because many movies do not share any users in common. You can convert to cosine distance using 1-simbut that might take a while I haven't timed it. It utilises sparse representations, and it can be parallelised over different CPUs with threads and different machines with jobswith easy re-integration of the computed parts.
Disclaimer - it was written by me. I am using gensimwhich works pretty well especially with text data which is usually high dimensional and sparse. Sign up to join this community.
Build a Simple Cosine Similarity Search Engine in R
The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Cosine similarity on sparse matrix Ask Question. Asked 6 years, 10 months ago. Active 3 years, 4 months ago.
It only takes a minute to sign up. I'm wondering if there is any relationship among these 3 measures. I can't seem to make a connection among them by referring to the definitions possibly because I am new to these definitions and am having a bit of a rough time grasping them. I know the range of the cosine similarity can be from 0 - 1, and that the pearson correlation can range from -1 to 1, and I'm not sure on the range of the z-score.
I don't know, however, how a certain value of cosine similarity could tell you anything about the pearson correlation or the z-score, and vice versa? TL;DR Cosine similarity is a dot product of unit vectors. Pearson correlation is cosine similarity between centered vectors. Sign up to join this community.
The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Is there any relationship among cosine similarity, pearson correlation, and z-score? Ask Question. Asked 3 years, 7 months ago.
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Viewed 12k times. Jaken Herman Jaken Herman 1 1 gold badge 2 2 silver badges 11 11 bronze badges. For example, if you internally standardize your original variables then the Pearson correlation between x and y is the expected product of their z-scores. Or you might be talking about z-scores of Pearson correlations Pearson correlations minus their expectation under some condition all divided by the standard error of the Pearson correlationwhich would certainly be related to the Pearson correlation.
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The cosine similarity is advantageous because even if the two similar documents are far apart by the Euclidean distance due to the size of the documentchances are they may still be oriented closer together. The smaller the angle, higher the cosine similarity. A commonly used approach to match similar documents is based on counting the maximum number of common words between the documents.
But this approach has an inherent flaw. That is, as the size of the document increases, the number of common words tend to increase even if the documents talk about different topics. Cosine similarity is a metric used to determine how similar the documents are irrespective of their size.
In this context, the two vectors I am talking about are arrays containing the word counts of two documents. When plotted on a multi-dimensional space, where each dimension corresponds to a word in the document, the cosine similarity captures the orientation the angle of the documents and not the magnitude.
If you want the magnitude, compute the Euclidean distance instead. Smaller the angle, higher the similarity.
However, if we go by the number of common words, the two larger documents will have the most common words and therefore will be judged as most similar, which is exactly what we want to avoid.
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The results would be more congruent when we use the cosine similarity score to assess the similarity. When plotted on this space, the 3 documents would appear something like this. It turns out, the closer the documents are by angle, the higher is the Cosine Similarity Cos theta. But you can directly compute the cosine similarity using this math formula. Enough with the theory. Doc Trump A : Mr. Trump became president after winning the political election. Though he lost the support of some republican friends, Trump is friends with President Putin.
He says it was a witchhunt by political parties. He claimed President Putin is a friend who had nothing to do with the election. President Putin had served as the Prime Minister earlier in his political career.
Data Science Stack Exchange is a question and answer site for Data science professionals, Machine Learning specialists, and those interested in learning more about the field. It only takes a minute to sign up. Most discussions of KNN mention Euclidean,Manhattan and Hamming distances, but they dont mention cosine similarity metric.
Is there a reason for this? Short answer: Cosine distance is not the overall best performing distance metric out there. Although similarity measures are often expressed using a distance metricit is in fact a more flexible measure as it is not required to be symmetric or fulfill the triangle inequality. Nevertheless, it is very common to use a proper distance metric like the Euclidian or Manhattan distance when applying nearest neighbour methods due to their proven performance on real world datasets.
They will therefore be often mentioned in discussions of KNN. You might find this review from informative, it attempts to answer the question "which distance measures to be used for the KNN classifier among a large number of distance and similarity measures? In short, they conclude that no surprise no optimal distance metric can be used for all types of datasets, as the results show that each dataset favors a specific distance metric, and this result complies with the no-free-lunch theorem.
It is clear that, among the metrics tested, the cosine distance isn't the overall best performing metric and even performs among the worst lowest precision in most noise levels.
So can I use cosine similarity as a distance metric in a KNN algorithm? Yesand for some datasets, like Irisit should even yield better performance p. If there does exist a reason it probably has to do with the fact the Cosine distance is not a proper distance metric. Nevertheless, it's still a useful little thing. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered.
Asked 2 years, 3 months ago.