I have a function which takes two strings and gives out the cosine similarity value which shows the relationship between both texts.
If I want to compare 75 texts with each other, I need to make 5,625 single comparisons to have all texts compared with each other.
Is there a way to reduce this number of comparisons? For example sparse matrices or k-means?
I don't want to talk about my function or about ways to compare texts. Just about reducing the number of comparisons.
What Ben says it's true, to get better help you need to tell us what's the goal.
For example, one possible optimization if you want to find similar strings is storing the string vectors in a spatial data structure such as a quadtree, where you can outright discard the vectors that are too far away from each other, avoiding many comparisons.
If your algorithm is pair-wise, then you probably can't reduce the number of comparisons, by definition.
You'll need to use a different algorithm, or at the very least pre-process your input if you want to reduce the number of comparisons.
Without the details of your function, it's difficult to give any concrete help.
Related
These two distance measurements seem to be the most common in NLP from what I've read. I'm currently using cosine similarity (as does the gensim.fasttext distance measurement). Is there any case to be made for the use of Jaccard instead? Does it even work with only single words as input (with the use of ngrams I suppose)?
ft = fasttext.load_model('cc.en.300.bin')
distance = scipy.spatial.distance.cosine(ft['word1'], ft['word2'])
I suppose I could imagine Jaccard similarity over bags-of-ngrams being useful for something. You could try some experiments to see if it correlates with good performance on some particular word-to-word task.
Maybe: typo correction? Or perhaps, when using a plain, non-Fasttext set-of-word-vectors, you might try synthesizing vectors for OOV words, by some weighted average of the most ngram-Jaccard-similar existing words? (In both cases: other simple comparisons, like edit-distance or shared-substring counting, might do better.)
But, I've not noticed projects using Jaccard-over-ngrams in lieu of whole-word-vector to whole-word-vector comparisons, nor libraries offering it as part of their interfaces/examples.
You've also only described its potential use very vaguely, "with the use of ngrams I suppose", with no code either demonstrating such calculation, or the results of such calculation being put to any use.
So potential usefulness seems like a research conjecture that you'd need to probe with your own experiments.
I'm using a pre-trained word2vec model (word2vec-google-news-300) to get the embeddings for a given list of words. Please note that this is NOT a list of words that we get after tokenizing a sentence, it is just a list of words that describe a given image.
Now I'd like to get a single vector representation for the entire list. Does adding all the individual word embeddings make sense? Or should I consider averaging?
Also, I would like the vector to be of a constant size so concatenating the embeddings is not an option.
It would be really helpful if someone can explain the intuition behind considering either one of the above approaches.
Averaging is most typical, when someone is looking for a super-simple way to turn a bag-of-words into a single fixed-length vector.
You could try a simple sum, as well.
But note that the key difference between the sum and average is that the average divides by the number of input vectors. Thus they both result in a vector that's pointing in the exact same 'direction', just of different magnitude. And, the most-often-used way of comparing such vectors, cosine-similarity, is oblivious to magnitudes. So for a lot of cosine-similarity-based ways of later comparing the vectors, sum-vs-average will give identical results.
On the other hand, if you're comparing the vectors in other ways, like via euclidean-distances, or feeding them into other classifiers, sum-vs-average could make a difference.
Similarly, some might try unit-length-normalizing all vectors before use in any comparisons. After such a pre-use normalization, then:
euclidean-distance (smallest to largest) & cosine-similarity (largest-to-smallest) will generate identical lists of nearest-neighbors
average-vs-sum will result in different ending directions - as the unit-normalization will have upped some vectors' magnitudes, and lowered others, changing their relative contributions to the average.
What should you do? There's no universally right answer - depending on your dataset & goals, & the ways your downstream steps use the vectors, different choices might offer slight advantages in whatever final quality/desirability evaluation you perform. So it's common to try a few different permutations, along with varying other parameters.
Separately:
The GoogleNews vectors were trained on news articles back around 2013; their word senses thus may not be optimal for an image-labeling task. If you have enough of your own data, or can collect it, training your own word-vectors might result in better results. (Both the use of domain-specific data, & the ability to tune training parameters based on your own evaluations, could offer benefits - especially when your domain is unique, or the tokens aren't typical natural-language sentences.)
There are other ways to create a single summary vector for a run-of-tokens, not just arithmatical-combo-of-word-vectors. One that's a small variation on the word2vec algorithm often goes by the name Doc2Vec (or 'Paragraph Vector') - it may also be worth exploring.
There are also ways to compare bags-of-tokens, leveraging word-vectors, that don't collapse the bag-of-tokens to a single fixed-length vector 1st - and while they're more expensive to calculate, sometimes offer better pairwise similarity/distance results than simple cosine-similarity. One such alternate comparison is called "Word Mover's Distance" - at some point,, you may want to try that as well.
I am trying solve the Longest Common subsequence problem, which is the problem of finding the longest subsequence common to all sequences in a set of sequences (often just two sequences).
I am trying to do this to calculate the overlap between 2 strings.
This is well know Dynamic programming problem. However, In my case the strings are is too huge. When I tried to use the 2D matrix to memoize, I ran into memory out of bound problem.
One solution could be using sparse matrix instead but I am little concerned about the performance overhead with that.
Also I want to perform this algorithm across multiple strings. And it will be okay to provide approximate answer since I am only trying to measure the overlap between 2 strings.
EDIT: After some investigation I found the following alternatives
Hirschberg Algorithm https://en.wikipedia.org/wiki/Hirschberg%27s_algorithm
Original paper http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.348.4360&rep=rep1&type=pdf
Approximate algorithm : http://cs.haifa.ac.il/~ilan/online-papers/cpm09.pdf
Deposition and Extension Approach to Find Longest Common
Subsequence for Multiple Sequences https://arxiv.org/pdf/0903.2015.pdf
LCS on DNA sequence http://www.sersc.org/journals/IJAST/vol47/2.pdf
Efficient Algorithm http://www.sciencedirect.com/science/article/pii/S0885064X12000635
To reduce memory complexity, you don't need to store the entire 2D table. You can only store the row above and current row and thus you can reduce the memory consumption by O(N) if you store the maximum in another data-structure. This results in O(N) memory usage, but time complexity remains O(N^2).
This is probably a fairly basic NLP question but I have the following task at hand: I have a collection of text documents that I need to score against an (English) lexicon of terms that could be 1-, 2-, 3- etc N-word long. N is bounded by some "reasonable" number but the distribution of various terms in the dictionary for various values of n = 1, ..., N might be fairly uniform. This lexicon can, for example, contain a list of devices of certain type and I want to see if a given document is likely about any of these devices. So I would want to score a document high(er) if it has one or more occurrences of any of the lexicon entries.
What is a standard NLP technique to do the scoring while accounting for various forms of the words that may appear in the lexicon? What sort of preprocessing would be required for both the input documents and the lexicon to be able to perform the scoring? What sort of open-source tools exist for both the preprocessing and the scoring?
I studied LSI and topic modeling almost a year ago, so what I say should be taken as merely a pointer to give you a general idea of where to look.
There are many different ways to do this with varying degrees of success. This is a hard problem in the realm of information retrieval. You can search for topic modeling to learn about different options and state of the art.
You definitely need some preprocessing and normalization if the words could appear in different forms. How about NLTK and one of its stemmers:
>>> from nltk.stem.lancaster import LancasterStemmer
>>> st = LancasterStemmer()
>>> st.stem('applied')
'apply'
>>> st.stem('applies')
'apply'
You have a lexicon of terms that I am going to call terms and also a bunch of documents. I am going to explore a very basic technique to rank documents with regards to the terms. There are a gazillion more sophisticated ways you can read about, but I think this might be enough if you are not looking for something too sophisticated and rigorous.
This is called a vector space IR model. Terms and documents are both converted to vectors in a k-dimensional space. For that we have to construct a term-by-document matrix. This is a sample matrix in which the numbers represent frequencies of the terms in documents:
So far we have a 3x4 matrix using which each document can be expressed by a 3-dimensional array (each column). But as the number of terms increase, these arrays become too large and increasingly sparse. Also, there are many words such as I or and that occur in most of the documents without adding much semantic content. So you might want to disregard these types of words. For the problem of largeness and sparseness, you can use a mathematical technique called SVD that scales down the matrix while preserving most of the information it contains.
Also, the numbers we used on the above chart were raw counts. Another technique would be to use Boolean values: 1 for presence and 0 zero for lack of a term in a document. But these assume that words have equal semantic weights. In reality, rarer words have more weight than common ones. So, a good way to edit the initial matrix would be to use ranking functions like tf-id to assign relative weights to each term. If by now we have applied SVD to our weighted term-by-document matrix, we can construct the k-dimensional query vectors, which are simply an array of the term weights. If our query contained multiple instances of the same term, the product of the frequency and the term weight would have been used.
What we need to do from there is somewhat straightforward. We compare the query vectors with document vectors by analyzing their cosine similarities and that would be the basis for the ranking of the documents relative to the queries.
I'm trying to find similar articles in database via correlation.
So i split text in array of words, then delete frequently used words (articles,pronouns and so on), then compare two text with pearson coefficient function. For some text it's works but for other it's not so good(texts with large text have higher coefficient).
Can somebody advice a good method to find related texts?
Some of the problems you mention boild down to normalizing over document length and overall word frequency. Try tf-idf.
First and foremost, you need to specify what you precisely mean by similarity and when two documents are (more/less) similar.
If the similarity you are looking for is literal, then I would vectorise the documents using term frequencies, and use the cosine similarity to liken them to each other given that texts are inherently directional data. tf-idf and log-entropy weighting schemes may be tested depending on your use-case. The edit distance is inefficient with long texts.
If you care more about the semantics, word embeddings are your ally.