Full text document similarity search - php

I have big database of articles and I'd like before adding new items to DB check if already similar items exist and if so - group them together, so that later I can easily display them as a group of similar items.
Currently we use very simple, but shockingly very precise and our needs fully satisfying PHP's similar_text() function. The problem is, that before we add an item to DB, we first need to pull X amount of items from DB to then loop through every single one in order to check whether our new item is at least 75% similar to other items in order to group them together. This uses a lot of resources and time that we don't really have.
We use MySQL and Solr for all our queries. I've tried using MySQL Full-Text Search, Solr More like this. Compared to PHPs implementation, they are super fast and efficient, but I just can't get a robust percentage score which PHP similar_text() provides. It is crucial for our grouping to be accurate.
For example using this MySQL query:
SELECT id, body, ROUND(((MATCH(body) AGAINST ('ARTICLE TEXT')) / scores.max_score) * 100) as relevance
FROM natural_text_test,
(SELECT MAX(MATCH(body) AGAINST('ARTICLE TEXT')) as max_score FROM natural_text_test LIMIT 1) scores
HAVING relevance > 75
ORDER BY relevance DESC
i get that article with 130 words is 85% similar with another article with 4700 words. And in comparison PHP's similar_text() returns only 3% similarity score which is well below our threshold and is correct in our case.
I've also looked into Levenshtein distance algorithm, but it seems that the same problem as with MySQL and Solr arises.
There has to be a better way to handle similarity checks, maybe I'm using the algorithms incorrectly?

Based on some of the Comments, I might propose this...
It seems that 75%-similar documents would have a lot of the same sentences in the same order.
Break the doc into sentences
Take a crude hash of each sentence, map it to a visible ascii character. This gives you a string that is, perhaps, 1/100th the size of the original doc.
Store that with the doc.
When searching, use levenshtein() on this string to find 'similar' documents.
Sure, hashing is imperfect, etc. But this is fast. And you could apply some other technique to double-check the few docs that are close.
For a hash, I might do
$md5 = md5($sentence);
$x = somehow get 6 bits out of that hex string
$hash = chr(ord('0' + $x));

Related

PHP Get peak from dataset with value and timestamp

I need to get the peak from a dataset using PHP. This dataset is made with timestamp and value. I need to get the 3 peak like the image with the 3 relative timestamp
This is a graphic rappresentation of the dataset:
But i don't need to rappresentate graphically, i'd like just a simple return of an array of the three value/timestamp. I need also a sort of threshold for avoid flase positive peak, for example minimum variation like from 0 to 400 (i'll define it in case but i need a threshold)
You can find the example dataset here:
https://wetransfer.com/downloads/d7d20a726285ea29ae2ff682764b045020210401192032/13e788
Many thanks for the help, i'm stuck with this. I have searched on Stackoverflow, i have see some algorithm but i cant apply to my necessity
I think that your sample data size suggests a database as a proper tool for the job. So assuming that data is already stored in table readings with two numeric columns - ts and reading, then this query may help.
select ts, reading
from
(
select ts, reading, lag(reading) over (order by ts) as variation from readings
) as t
where variation < 400 -- or whatever your threshold value may be
order by reading desc
limit 3;
This is Postgresql dialect that I am most comfortable with. You can re-write it in another SQL dialect if necessary and then easily pull the result data in PHP using PDO for example.

Calculating the distance between two articles accurately

I am writing a software to compare articles. I am looking for an efficient and accurate algorithm to calculate the difference (variation) between two articles. The variation should completely depend on words and not letters. I have tried levenshtein() but it has a time complexity of O(n*m) which is very expensive when performed on big texts like an article. I have also tried similar_text() which has a higher time complexity of O(n*m*3). Moreover, levenshtein() and similar_text() calculates the number of operations needed to transform one string to another which is not an accurate way to calculate the difference between two big articles.
What other options do I have?
EDIT:
I am trying to calculate the variation approximately from the point of view of a search engine (Google).
PostgreSQL uses a tsvector for it's full-text search feature. Maybe that's something that could get quite handy for you.
If you can define how to measure text similarity based on words, you are half way through. For example: You may count the occurence of each word for both article and then create a simple difference of the two lists. However, this does not work for similarity by meaning.
If you have a database, use their fulltext features. As mentioned before, PostGres offers such a feature. I work with MSSQL and you could simply call the FREETEXT function which will calculate a 'rank' indicating how similar two texts are.
I highly recommend using a mature product, instead of trying to write your own.
There is no way to compare two articles. levenshtein() and similar_text() designed to compare two words, not articles.
The simplest algorythm is to explode your articles by words, find word-by-word similaryty and do some math, depending on your task, like this:
// not tested!
function similar_articles($articleA, $articleB) {
$wordsA = array_unique(preg_split('#[\W]+#', $articleA));
$wordsB = array_unique(preg_split('#[\W]+#', $articleA));
$resultSimilarity = 0;
foreach($wordsA as $wordA) {
$wordSimilarity = 0;
foreach($wordsB as $wordB) {
similar_text($wordA, $wordB, $percent);
$wordSimilarity = max($wordSimilarity, $percent);
}
$resultSimilarity += $wordSimilarity;
}
return($resultSimilarity / count($wordsA));
}
Note: similar_articles($artileA, $articleB) != similar_articles($artileB, $articleA) because of similar_text($wordA, $wordB) != similar_text($wordB, $wordA).
A simple method for calculate a type of distance is to compare references. Another method is to select some key word in concordance to a dictionary and calculate the distance in order of social relevance.
Also, in order to use Levenshtein distance take a look on stringmetric.
In my case, I needed to calculate the variation between two articles. So, I found that very simple solution working for me very well. It works by simply calculating the similarity as the common words between the two articles divided by max(number of words in article A, number of words in article B). The variation then is calculated by subtracting the similarity from 100 to get the variation percentage. The code below explains it all.
function get_variation($article1,$article2){
$wordsA = array_unique(preg_split('#[\W]+#', $article1));
$wordsB = array_unique(preg_split('#[\W]+#', $article2));
$intersection = array_intersect($wordsA, $wordsB);
$similarity = (count($intersection)/ (max(count($wordsA),count($wordsB))) * 100);
$similarity = number_format($similarity, 2, '.', '');
$variation = 100-$similarity;
return $variation;
}

What is the most efficient way to find the euclidean distance in 3d using mysql?

I have a MySQL table with thousands of data points stored in 3 columns R, G, B. how can I find which data point is closest to a given point (a,b,c) using Euclidean distance?
I'm saving RGB values of colors separately in a table, so the values are limited to 0-255 in each column. What I'm trying to do is find the closest color match by finding the color with the smallest euclidean distance.
I could obviously run through every point in the table to calculate the distance but that wouldn't be efficient enough to scale. Any ideas?
I think the above comments are all true, but they are - in my humble opinion - not answering the original question. (Correct me if I'm wrong). So, let me here add my 50 cents:
You are asking for a select statement, which, given your table is called 'colors', and given your columns are called r, g and b, they are integers ranged 0..255, and you are looking for the value, in your table, closest to a given value, lets say: rr, gg, bb, then I would dare trying the following:
select min(sqrt((rr-r)*(rr-r)+(gg-g)*(gg-g)+(bb-b)*(bb-b))) from colors;
Now, this answer is given with a lot of caveats, as I am not sure I got your question right, so pls confirm if it's right, or correct me so that I can be of assistance.
Since you're looking for the minimum distance and not exact distance you can skip the square root. I think Squared Euclidean Distance applies here.
You've said the values are bounded between 0-255, so you can make an indexed look up table with 255 values.
Here is what I'm thinking in terms of SQL. r0, g0, and b0 represent the target color. The table Vector would hold the square values mentioned above in #2. This solution would visit all the records but the result set can be set to 1 by sorting and selecting only the first row.
select
c.r, c.g, c.b,
mR.dist + mG.dist + mB.dist as squared_dist
from
colors c,
vector mR,
vector mG,
vector mB
where
c.r-r0 = mR.point and
c.g-g0 = mG.point and
c.b-b0 = mB.point
group by
c.r, c.g, c.b
The first level of optimization that I see you can do would be square the distance to which you want to limit the query so that you don't need to perform the square root for each row.
The second level of optimization I would encourage would be some preprocessing to alleviate the need for extraneous squaring for each query (which could possibly create some extra run time for large tables of RGB's). You'd have to do some benchmarking to see, but by substituting in values for a, b, c, and d and then performing the query, you could alleviate some stress from MySQL.
Note that the performance difference between the last two lines may be negligible. You'll have to use test queries on your system to determine which is faster.
I just re-read and noticed that you are ordering by distance. In which case, the d should be removed everything should be moved to one side. You can still plug in the constants to prevent extra processing on MySQL's end.
I believe there are two options.
You have to either as you say iterate across the entire set and compare and check against a maximum that you set initially at an impossibly low number like -1. This runs in linear time, n times (since you're only comparing 1 point to every point in the set, this scales in a linear way).
I'm still thinking of another option... something along the lines of doing a breadth first search away from the input point until a point is found in the set at the searched point, but this requires a bit more thought (I imagine the 3D space would have to be pretty heavily populated for this to be more efficient on average though).
If you run through every point and calculate the distance, don't use the square root function, it isn't necessary. The smallest sum of squares will be enough.
This is the problem you are trying to solve. (Planar case, select all points sorted by a x, y, or z axis. Then use PHP to process them)
MySQL also has a Spatial Database which may have this as a function. I'm not positive though.

MySql speed of executing max(), min(), sum() on relatively large database

I have a relatively large database (130.000+ rows) of weather data, which is accumulating very fast (every 5minutes a new row is added). Now on my website I publish min/max data for day, and for the entire existence of my weatherstation (which is around 1 year).
Now I would like to know, if I would benefit from creating additional tables, where these min/max data would be stored, rather than let the php do a mysql query searching for day min/max data and min/max data for the entire existence of my weather station. Would a query for max(), min() or sum() (need sum() to sum rain accumulation for months) take that much longer time then a simple query to a table, that already holds those min, max and sum values?
That depends on weather your columns are indexed or not. In case of MIN() and MAX() you can read in the MySQL manual the following:
MySQL uses indexes for these
operations:
To find the MIN() or MAX() value for a
specific indexed column key_col. This
is optimized by a preprocessor that
checks whether you are using WHERE
key_part_N = constant on all key parts
that occur before key_col in the
index. In this case, MySQL does a
single key lookup for each MIN() or
MAX() expression and replaces it with
a constant.
In other words in case that your columns are indexed you are unlikely to gain much performance benefits by denormalization. In case they are NOT you will definitely gain performance.
As for SUM() it is likely to be faster on an indexed column but I'm not really confident about the performance gains here.
Please note that you should not be tempted to index your columns after reading this post. If you put indices your update queries will slow down!
Yes, denormalization should help performance a lot in this case.
There is nothing wrong with storing calculations for historical data that will not change in order to gain performance benefits.
While I agree with RedFilter that there is nothing wrong with storing historical data, I don't agree with the performance boost you will get. Your database is not what I would consider a heavy use database.
One of the major advantages of databases is indexes. They used advanced data structures to make data access lightening fast. Just think, every primary key you have is an index. You shouldn't be afraid of them. Of course, it would probably be counter productive to make all your fields indexes, but that should never really be necessary. I would suggest researching indexes more to find the right balance.
As for the work done when a change happens, it is not that bad. An index is a tree like representation of your field data. This is done to reduce a search down to a small number of near binary decisions.
For example, think of finding a number between 1 and 100. Normally you would randomly stab at numbers, or you would just start at 1 and count up. This is slow. Instead, it would be much faster if you set it up so that you could ask if you were over or under when you choose a number. Then you would start at 50 and ask if you are over or under. Under, then choose 75, and so on till you found the number. Instead of possibly going through 100 numbers, you would only have to go through around 6 numbers to find the correct one.
The problem here is when you add 50 numbers and make it out of 1 to 150. If you start at 50 again, your search is less optimized as there are 100 numbers above you. Your binary search is out of balance. So, what you do is rebalance your search by starting at the mid-point again, namely 75.
So the work a database is just an adjustment to rebalance the mid-point of its index. It isn't actually a lot of work. If you are working on a database that is large and requires many changes a second, you would definitely need to have a strong strategy for your indexes. In a small database that gets very few changes like yours, its not a problem.

LSA - Latent Semantic Analysis - How to code it in PHP?

I would like to implement Latent Semantic Analysis (LSA) in PHP in order to find out topics/tags for texts.
Here is what I think I have to do. Is this correct? How can I code it in PHP? How do I determine which words to chose?
I don't want to use any external libraries. I've already an implementation for the Singular Value Decomposition (SVD).
Extract all words from the given text.
Weight the words/phrases, e.g. with tf–idf. If weighting is too complex, just take the number of occurrences.
Build up a matrix: The columns are some documents from the database (the more the better?), the rows are all unique words, the values are the numbers of occurrences or the weight.
Do the Singular Value Decomposition (SVD).
Use the values in the matrix S (SVD) to do the dimension reduction (how?).
I hope you can help me. Thank you very much in advance!
LSA links:
Landauer (co-creator) article on LSA
the R-project lsa user guide
Here is the complete algorithm. If you have SVD, you are most of the way there. The papers above explain it better than I do.
Assumptions:
your SVD function will give the singular values and singular vectors in descending order. If not, you have to do more acrobatics.
M: corpus matrix, w (words) by d (documents) (w rows, d columns). These can be raw counts, or tfidf or whatever. Stopwords may or may not be eliminated, and stemming may happen (Landauer says keep stopwords and don't stem, but yes to tfidf).
U,Sigma,V = singular_value_decomposition(M)
U: w x w
Sigma: min(w,d) length vector, or w * d matrix with diagonal filled in the first min(w,d) spots with the singular values
V: d x d matrix
Thus U * Sigma * V = M
# you might have to do some transposes depending on how your SVD code
# returns U and V. verify this so that you don't go crazy :)
Then the reductionality.... the actual LSA paper suggests a good approximation for the basis is to keep enough vectors such that their singular values are more than 50% of the total of the singular values.
More succintly... (pseudocode)
Let s1 = sum(Sigma).
total = 0
for ii in range(len(Sigma)):
val = Sigma[ii]
total += val
if total > .5 * s1:
return ii
This will return the rank of the new basis, which was min(d,w) before, and we'll now approximate with {ii}.
(here, ' -> prime, not transpose)
We create new matrices: U',Sigma', V', with sizes w x ii, ii x ii, and ii x d.
That's the essence of the LSA algorithm.
This resultant matrix U' * Sigma' * V' can be used for 'improved' cosine similarity searching, or you can pick the top 3 words for each document in it, for example. Whether this yeilds more than a simple tf-idf is a matter of some debate.
To me, LSA performs poorly in real world data sets because of polysemy, and data sets with too many topics. It's mathematical / probabilistic basis is unsound (it assumes normal-ish (Gaussian) distributions, which don't makes sense for word counts).
Your mileage will definitely vary.
Tagging using LSA (one method!)
Construct the U' Sigma' V' dimensionally reduced matrices using SVD and a reduction heuristic
By hand, look over the U' matrix, and come up with terms that describe each "topic". For example, if the the biggest parts of that vector were "Bronx, Yankees, Manhattan," then "New York City" might be a good term for it. Keep these in a associative array, or list. This step should be reasonable since the number of vectors will be finite.
Assuming you have a vector (v1) of words for a document, then v1 * t(U') will give the strongest 'topics' for that document. Select the 3 highest, then give their "topics" as computed in the previous step.
This answer isn't directly to the posters' question, but to the meta question of how to autotag news items. The OP mentions Named Entity Recognition, but I believe they mean something more along the line of autotagging. If they really mean NER, then this response is hogwash :)
Given these constraints (600 items / day, 100-200 characters / item) with divergent sources, here are some tagging options:
By hand. An analyst could easily do 600 of these per day, probably in a couple of hours. Something like Amazon's Mechanical Turk, or making users do it, might also be feasible. Having some number of "hand-tagged", even if it's only 50 or 100, will be a good basis for comparing whatever the autogenerated methods below get you.
Dimentionality reductions, using LSA, Topic-Models (Latent Dirichlet Allocation), and the like.... I've had really poor luck with LSA on real-world data sets and I'm unsatisfied with its statistical basis. LDA I find much better, and has an incredible mailing list that has the best thinking on how to assign topics to texts.
Simple heuristics... if you have actual news items, then exploit the structure of the news item. Focus on the first sentence, toss out all the common words (stop words) and select the best 3 nouns from the first two sentences. Or heck, take all the nouns in the first sentence, and see where that gets you. If the texts are all in english, then do part of speech analysis on the whole shebang, and see what that gets you. With structured items, like news reports, LSA and other order independent methods (tf-idf) throws out a lot of information.
Good luck!
(if you like this answer, maybe retag the question to fit it)
That all looks right, up to the last step. The usual notation for SVD is that it returns three matrices A = USV*. S is a diagonal matrix (meaning all zero off the diagonal) that, in this case, basically gives a measure of how much each dimension captures of the original data. The numbers ("singular values") will go down, and you can look for a drop-off for how many dimensions are useful. Otherwise, you'll want to just choose an arbitrary number N for how many dimensions to take.
Here I get a little fuzzy. The coordinates of the terms (words) in the reduced-dimension space is either in U or V, I think depending on whether they are in the rows or columns of the input matrix. Off hand, I think the coordinates for the words will be the rows of U. i.e. the first row of U corresponds to the first row of the input matrix, i.e. the first word. Then you just take the first N columns of that row as the word's coordinate in the reduced space.
HTH
Update:
This process so far doesn't tell you exactly how to pick out tags. I've never heard of anyone using LSI to choose tags (a machine learning algorithm might be more suited to the task, like, say, decision trees). LSI tells you whether two words are similar. That's a long way from assigning tags.
There are two tasks- a) what are the set of tags to use? b) how to choose the best three tags?. I don't have much of a sense of how LSI is going to help you answer (a). You can choose the set of tags by hand. But, if you're using LSI, the tags probably should be words that occur in the documents. Then for (b), you want to pick out the tags that are closest to words found in the document. You could experiment with a few ways of implementing that. Choose the three tags that are closest to any word in the document, where closeness is measured by the cosine similarity (see Wikipedia) between the tag's coordinate (its row in U) and the word's coordinate (its row in U).
There is an additional SO thread on the perils of doing this all in PHP at link text.
Specifically, there is a link there to this paper on Latent Semantic Mapping, which describes how to get the resultant "topics" for a text.

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