what does row oriented and column oriented mean in matrix - linear-algebra

I am reading the paper "Numerics of Gram Schmidt orthogonal", Then I noticed there are some terminologies that I can't understand which are "row-oriented" and "column-oriented" located at P299 in the paper.
the original sentence is "In row-oriented MGS a sequence of matrices, A=A1, A2, ..., An is computed...".
I googled and found that "row/column-oriented" is mainly used in databases. one prone-understandable source is this post.
Then I found that "row/column-major" in matrix theory which I can understand is the store-type in your computer that can be found in this post. based on the context of where it appears in the paper I am pretty sure "row/column-oriented" is not "row/column-major". (If so why does the algorithm still access data by column in the "row_oriented" matrix?)

Related

Checking for similarity of text in two text strings

I have two strings of text (typically two paragraphs). I am looking to check for the "similarity" between them, e.g. check if one paragraph is a plagiarised version of the other. Ideally I need a similarity score, as well as an indication of where the similarities are. I prefer to do this fully in R. Any suggestions please?
The difference of stings can be measured with the levenshtein distance (or concepts that build on top of that). The main idea is to quantify the "editiing distance" of strings: how many letters need to be included/excluded/changed, etc (depending on the algorithm more or less types of editing are allowed). A package in R for this task would be fuzzyjoin.
To look up the similarities you could cut both texts (original and suposed plagiate) in sentences and build the fuzzy joins on this - Then you can filter for best matches. The topic is a bit tricky so I recomend trying out different algorithms (jaccard distance, damerau levenshtein, etc). A start into the topic can be found here: https://cran.r-project.org/web/packages/fuzzyjoin/readme/README.html

Better cluster dendrogram for representation of Cluster in Text Mining in R

I have around 1140 terms in three documents (after removing sparse terms). I want to have the information about the clusters. I have produced clusters as shown in attached image but I am unable to read them. I have also tried k-mean clusters but the same problem persists. I am not so much interested in all the terms but clearly defined few three or four clusters would do the job. I have been using tm package in R for text mining.
Secondly I am also looking for finding association in terms with in a single document; for this how can I split a text file into several text files i.e. if my file has three sentences:
Doc: "My name is ABC. I live in XYZ. I am cousin of TUV."
I would like to split it as:
Doc_1: My name is ABC.
Doc_2:I live in XYZ.
Doc_3: I am cousin of TUV.
So that I have three rows and columns of terms in dtm instead of a single row and column of terms.
and
You ask more than one question. I will address your first one. It seems unrealistic to expect to put 1140 strings in your graph and expect to see anything. You need a way to be able to see a bit of it at a time. You can cut the tree and look a smaller pieces in the lower part of the tree to control how much you are seeing at one time.
Here is an example. Even with 150 points, it is hard to see what is going on.
D = as.dendrogram(hclust(dist(iris[,1:4])))
plot(D)
But if you cut the tree, you can look at individual lower branches and understand that part.
Cuts = cut(D, 4)
plot(Cuts$lower[[2]])
Of course, you will need to experiment around a bit to find good places to cut your tree.

Techniques for finding near duplicate records

I'm attempting to clean up a database that, over the years, had acquired many duplicate records, with slightly different names. For example, in the companies table, there are names like "Some Company Limited" and "SOME COMPANY LTD!".
My plan was to export the offending tables into R, convert names to lower case, replace common synonyms (like "limited" -> "ltd"), strip out non-alphabetic characters and then use agrep to see what looks similar.
My first problem is that agrep only accepts a single pattern to match, and looping over every company name to match against the others is slow. (Some tables to be cleaned will have tens, possibly hundreds of thousands of names to check.)
I've very briefly looked at the tm package (JSS article), and it seems very powerful but geared towards analysing big chunks of text, rather than just names.
I have a few related questions:
Is the tm package appropriate for this sort of task?
Is there a faster alternative to agrep? (Said function uses the
Levenshtein edit distance which is anecdotally slow.)
Are there other suitable tools in R, apart from agrep and tm?
Should I even be doing this in R, or should this sort of thing be
done directly in the database? (It's an Access database, so I'd
rather avoid touching it if possible.)
If you're just doing small batches that are relatively well-formed, then the compare.linkage() or compare.dedup() functions in the RecordLinkage package should be a great starting point. But if you have big batches, then you might have to do some more tinkering.
I use the functions jarowinkler(), levenshteinSim(), and soundex() in RecordLinkage to write my own function that use my own weighting scheme (also, as it is, you can't use soundex() for big data sets with RecordLinkage).
If I have two lists of names that I want to match ("record link"), then I typically convert both to lower case and remove all punctuation. To take care of "Limited" versus "LTD" I typically create another vector of the first word from each list, which allows extra weighting on the first word. If I think that one list may contain acronyms (maybe ATT or IBM) then I'll acronym-ize the other list. For each list I end up with a data frame of strings that I would like to compare that I write as separate tables in a MySQL database.
So that I don't end up with too many candidates, I LEFT OUTER JOIN these two tables on something that has to match between the two lists (maybe that's the first three letters in each list or the first three letters and the first three letters in the acronym). Then I calculate match scores using the above functions.
You still have to do a lot of manual inspection, but you can sort on the score to quickly rule out non-matches.
Maybe google refine could help. It looks maybe more fitted if you have lots of exceptions and you don't know them all yet.
What you're doing is called record linkage, and it's been a huge field of research over many decades already. Luckily for you, there's a whole bunch of tools out there that are ready-made for this sort of thing. Basically, you can point them at your database, set up some cleaning and comparators (like Levenshtein or Jaro-Winkler or ...), and they'll go off and do the job for you.
These tools generally have features in place to solve the performance issues, so that even though Levenshtein is slow they can run fast because most record pairs never get compared at all.
The Wikipedia link above has links to a number of record linkage tools you can use. I've personally written one called Duke in Java, which I've used successfully for exactly this. If you want something big and expensive you can buy a Master Data Management tool.
In your case probably something like edit-distance calculation would work, but if you need to find near duplicates in larger text based documents, you can try
http://www.softcorporation.com/products/neardup/

How can I structure and recode messy categorical data in R?

I'm struggling with how to best structure categorical data that's messy, and comes from a dataset I'll need to clean.
The Coding Scheme
I'm analyzing data from a university science course exam. We're looking at patterns in
student responses, and we developed a coding scheme to represent the kinds of things
students are doing in their answers. A subset of the coding scheme is shown below.
Note that within each major code (1, 2, 3) are nested non-unique sub-codes (a, b, ...).
What the Raw Data Looks Like
I've created an anonymized, raw subset of my actual data which you can view here.
Part of my problem is that those who coded the data noticed that some students displayed
multiple patterns. The coders' solution was to create enough columns (reason1, reason2,
...) to hold students with multiple patterns. That becomes important because the order
(reason1, reason2) is arbitrary--two students (like student 41 and student 42 in my
dataset) who correctly applied "dependency" should both register in an analysis, regardless of
whether 3a appears in the reason column or the reason2 column.
How Can I Best Structure Student Data?
Part of my problem is that in the raw data, not all students display the same
patterns, or the same number of them, in the same order. Some students may do just one
thing, others may do several. So, an abstracted representation of example students might
look like this:
Note in the example above that student002 and student003 both are coded as "1b", although I've deliberately shown the order as different to reflect the reality of my data.
My (Practical) Questions
Should I concatenate reason1, reason2, ... into one column?
How can I (re)code the reasons in R to reflect the multiplicity for some students?
Thanks
I realize this question is as much about good data conceptualization as it is about specific features of R, but I thought it would be appropriate to ask it here. If you feel it's inappropriate for me to ask the question, please let me know in the comments, and stackoverflow will automatically flood my inbox with sadface emoticons. If I haven't been specific enough, please let me know and I'll do my best to be clearer.
Make it "long":
library(reshape)
dnow <- read.csv("~/Downloads/catsample20100504.csv")
dnow <- melt(dnow, id.vars=c("Student", "instructor"))
dnow$variable <- NULL ## since ordering does not matter
subset(dnow, Student%in%c(41,42)) ## see the results
What to do next will depend on the kind of analysis you would like to do. But the long format is the useful for irregular data such as yours.
you should use ddply from plyr and split on all of the columns if you want to take into account the different reasons, if you want to ignore them don't use those columns in the split. You'll need to clean up some of the question marks and extra stuff first though.
x <- ddply(data, c("split_column1", "split_column3" etc),
summarize(result_df, stats you want from result_df))
What's the (bigger picture) question you're attempting to answer? Why is this information interesting to you?
Are you just trying to find patterns such as 'if the student does this, then they also likely do this'?
Something I'd consider if that's the case - split the data set into smaller random samples for your analysis to reduce the risk of false positives.
Interesting problem though!

Fuzzy matching of product names

I need to automatically match product names (cameras, laptops, tv-s etc) that come from different sources to a canonical name in the database.
For example "Canon PowerShot a20IS", "NEW powershot A20 IS from Canon" and "Digital Camera Canon PS A20IS"
should all match "Canon PowerShot A20 IS". I've worked with levenshtein distance with some added heuristics (removing obvious common words, assigning higher cost to number changes etc), which works to some extent, but not well enough unfortunately.
The main problem is that even single-letter changes in relevant keywords can make a huge difference, but it's not easy to detect which are the relevant keywords. Consider for example three product names:
Lenovo T400
Lenovo R400
New Lenovo T-400, Core 2 Duo
The first two are ridiculously similar strings by any standard (ok, soundex might help to disinguish the T and R in this case, but the names might as well be 400T and 400R), the first and the third are quite far from each other as strings, but are the same product.
Obviously, the matching algorithm cannot be a 100% precise, my goal is to automatically match around 80% of the names with a high confidence.
Any ideas or references is much appreciated
I think this will boil down to distinguishing key words such as Lenovo from chaff such as New.
I would run some analysis over the database of names to identify key words. You could use code similar to that used to generate a word cloud.
Then I would hand-edit the list to remove anything obviously chaff, like maybe New is actually common but not key.
Then you will have a list of key words that can be used to help identify similarities. You would associate the "raw" name with its keywords, and use those keywords when comparing two or more raw names for similarities (literally, percentage of shared keywords).
Not a perfect solution by any stretch, but I don't think you are expecting one?
The key understanding here is that you do have a proper distance metric. That is in fact not your problem at all. Your problem is in classification.
Let me give you an example. Say you have 20 entries for the Foo X1 and 20 for the Foo Y1. You can safely assume they are two groups. On the other hand, if you have 39 entries for the Bar X1 and 1 for the Bar Y1, you should treat them as a single group.
Now, the distance X1 <-> Y1 is the same in both examples, so why is there a difference in the classification? That is because Bar Y1 is an outlier, whereas Foo Y1 isn't.
The funny part is that you do not actually need to do a whole lot of work to determine these groups up front. You simply do an recursive classification. You start out with node per group, and then add the a supernode for the two closest nodes. In the supernode, store the best assumption, the size of its subtree and the variation in it. As many of your strings will be identical, you'll soon get large subtrees with identical entries. Recursion ends with the supernode containing at the root of the tree.
Now map the canonical names against this tree. You'll quickly see that each will match an entire subtree. Now, use the distances between these trees to pick the distance cutoff for that entry. If you have both Foo X1 and Foo Y1 products in the database, the cut-off distance will need to be lower to reflect that.
edg's answer is in the right direction, I think - you need to distinguish key words from fluff.
Context matters. To take your example, Core 2 Duo is fluff when looking at two instances of a T400, but not when looking at a a CPU OEM package.
If you can mark in your database which parts of the canonical form of a product name are more important and must appear in one form or another to identify a product, you should do that. Maybe through the use of some sort of semantic markup? Can you afford to have a human mark up the database?
You can try to define equivalency classes for things like "T-400", "T400", "T 400" etc. Maybe a set of rules that say "numbers bind more strongly than letters attached to those numbers."
Breaking down into cases based on manufacturer, model number, etc. might be a good approach. I would recommend that you look at techniques for term spotting to try and accomplish that: http://www.worldcat.org/isbn/9780262100854
Designing everything in a flexible framework that's mostly rule driven, where the rules can be modified based on your needs and emerging bad patterns (read: things that break your algorithm) would be a good idea, as well. This way you'd be able to improve the system's performance based on real world data.
You might be able to make use of a trigram search for this. I must admit I've never seen the algorithm to implement an index, but have seen it working in pharmaceutical applications, where it copes very well indeed with badly misspelt drug names. You might be able to apply the same kind of logic to this problem.
This is a problem of record linkage. The dedupe python library provides a complete implementation, but even if you don't use python, the documentation has a good overview of how to approach this problem.
Briefly, within the standard paradigm, this task is broken into three stages
Compare the fields, in this case just the name. You can use one or more comparator for this, for example an edit distance like the Levenshtein distance or something like the cosine distance that compares the number of common words.
Turn an array fo distance scores into a probability that a pair of records are truly about the same thing
Cluster those pairwise probability scores into groups of records that likely all refer to the same thing.
You might want to create logic that ignores the letter/number combination of model numbers (since they're nigh always extremely similar).
Not having any experience with this type of problem, but I think a very naive implementation would be to tokenize the search term, and search for matches that happen to contain any of the tokens.
"Canon PowerShot A20 IS", for example, tokenizes into:
Canon
Powershot
A20
IS
which would match each of the other items you want to show up in the results. Of course, this strategy will likely produce a whole lot of false matches as well.
Another strategy would be to store "keywords" with each item, such as "camera", "canon", "digital camera", and searching based on items that have matching keywords. In addition, if you stored other attributes such as Maker, Brand, etc., you could search on each of these.
Spell checking algorithms come to mind.
Although I could not find a good sample implementation, I believe you can modify a basic spell checking algorithm to comes up with satisfactory results. i.e. working with words as a unit instead of a character.
The bits and pieces left in my memory:
Strip out all common words (a, an, the, new). What is "common" depends on context.
Take the first letter of each word and its length and make that an word key.
When a suspect word comes up, looks for words with the same or similar word key.
It might not solve your problems directly... but you say you were looking for ideas, right?
:-)
That is exactly the problem I'm working on in my spare time. What I came up with is:
based on keywords narrow down the scope of search:
in this case you could have some hierarchy:
type --> company --> model
so that you'd match
"Digital Camera" for a type
"Canon" for company and there you'd be left with much narrower scope to search.
You could work this down even further by introducing product lines etc.
But the main point is, this probably has to be done iteratively.
We can use the Datadecision service for matching products.
It will allow you to automatically match your product data using statistical algorithms. This operation is done after defining a threshold score of confidence.
All data that cannot be automatically matched will have to be manually reviewed through a dedicated user interface.
The online service uses lookup tables to store synonyms as well as your manual matching history. This allows you to improve the data matching automation next time you import new data.
I worked on the exact same thing in the past. What I have done is using an NLP method; TF-IDF Vectorizer to assign weights to each word. For example in your case:
Canon PowerShot a20IS
Canon --> weight = 0.05 (not a very distinguishing word)
PowerShot --> weight = 0.37 (can be distinguishing)
a20IS --> weight = 0.96 (very distinguishing)
This will tell your model which words to care and which words to not. I had quite good matches thanks to TF-IDF.
But note this: a20IS cannot be recognized as a20 IS, you may consider to use some kind of regex to filter such cases.
After that, you can use a numeric calculation like cosine similarity.

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