I am dealing with datasets with missing data and need to be able to fill forward, backward, and gaps. So, for example, if I have data from Jan 1, 2000 to Dec 31, 2010, and some days are missing, when a user requests a timespan that begins before, ends after, or encompasses the missing data points, I need to "fill in" these missing values.
Is there a proper term to refer to this concept of filling in data? Imputation is one term, don't know if it is "the" term for it though.
I presume there are multiple algorithms & methodologies for filling in missing data (use last measured, using median/average/moving average, etc between 2 known numbers, etc.
Anyone know the proper term for this problem, any online resources on this topic, or ideally links to open source implementations of some algorithms (C# preferably, but any language would be useful)
The term you're looking for is interpolation. (obligatory wiki link)
You're asking for a C# solution with datasets but you should also consider doing this at the database level like this.
An simple, brute-force approach in C# could be to build an array of consecutive dates with your beginning and ending values as the min/max values. Then use that array to merge "interpolated" date values into your data set by inserting rows where there is no matching date for your date array in the dataset.
Here is an SO post that gets close to what you need: interpolating missing dates with C#. There is no accepted solution but reading the question and attempts at answers may give you an idea of what you need to do next. E.g. Use the DateTime data in terms of Ticks (long value type) and then use an interpolation scheme on that data. The convert the interpolated long values to DateTime values.
The algorithm you use will depend a lot on the data itself, the size of the gaps compared to the available data, and its predictability based on existing data. It could also incorporate other information you might know about what's missing, as is common in statistics, when your actual data may not reflect the same distribution as the universe across certain categories.
Linear and cubic interpolation are typical algortihms that are not difficult to implement, try googling those.
Here's a good primer with some code:
http://paulbourke.net/miscellaneous/interpolation/
The context of the discussion in that link is graphics but the concepts are universally applicable.
For the purpose of feeding statistical tests, a good search term is imputation - e.g. http://en.wikipedia.org/wiki/Imputation_%28statistics%29
Related
I'm looking for a simple function in C# to interpolate my 3D data.
Given is already a list with around 100-150 data sets and 3 double values.
-25.000000 -0.770568 2.444945
-20.000000 -0.726583 2.467809
-15.000000 -0.723274 2.484167
-10.000000 -0.723114 2.506445
and so on...
The chart created by these values looks usually like this, I'm not sure if this counts as scattered or rather still gridded data ...
In the end I want to hand over two double values and get the third then from the interpolation function. It shouldn't flatten the surface, it should still go through all the given data points.
Since I'm not given the time to look into all possible algorithms and lack the mathematical background I'm a bit overwhelmed by all the possibilities that I get thrown at: Kriging, Delauney triangulation, NURBs and many more ...
In addition to that most solutions I found in the net were either for a different language, outdated or are charged by the time (e.g ilnumerics, still not sure if they have the solution)
In matlab there exists a griddata function that does exactly this (and is based on a kriging algorithm as far as I know) but in this case C# is mandatory for me.
Thank you for your help and criticism and suggestions are welcome.
I've been messing around with the aforge time series genetic algorithm sample and I've got my own version working, atm it's just 'predicting' Fibonacci numbers.
The problem is when I ask it to predict new values beyond the array I've given it (which contains the first 21 numbers of the sequence, using a window size of 5) it won't do it, it throws an exception that says "Data size should be enough for window and prediction".
As far as I can tell I'm supposed to decipher the bizarre formula contained in "population.BestChromosome" and use that to extrapolate future values, is that right? Is there an easier way? Am I overlooking something massively obvious?
I'd ask on the aforge forum but the developer is not supporting it anymore.
As far as I can tell I'm supposed to decipher the bizarre formula
contained in "population.BestChromosome" and use that to extrapolate
future values, is that right?
What you call a "bizarre formula" is called a model in data analysis. You learn such a model from past data and you can feed it new data to get a predicted outcome. Whether that new outcome makes sense or is just garbage depends on how general your model is. Many techniques can learn very good models that explain the observed data very well, but which are not generalizable and will return unuseful results when you feed new data into the model. You need to find a model that both explains the given data as well as potentially unobserved data which is a non-trivial process. Usually people estimate the generalization error of that model by splitting the known data into two partitions: one with which the model is learned and another one on which the learned models are tested. You then want to select that model which is accurate on both data. You can also check out the answer I gave on another question here which also treats the topic of machine learning: https://stackoverflow.com/a/3764893/189767
I don't think you're "overlooking something massively obvious", but rather you're faced with a problem that is not trivial to solve.
Btw, you can also use genetic programming (GP) in HeuristicLab. The model of GP is a mathematical formula and in HeuristicLab you can export that model to e.g. MatLab.
Ad Fibonacci, the closed formula for Fibonacci numbers is F(n) = (phi^n - psi^n) / sqrt(5) where phi and psi are special magic numbers according to wikipedia. If you want to find that with GP you need one variable (n), three constants, and the power function. However, it's very likely that you find a vastly different formula that is similar in output. The problem in machine learning is that very different models can produce the same output. The recursive form requires that you include the values of the past two n into the data set. This is similar to learning a model for a time series regression problem.
I am trying to use SVM for News article classification.
I created a table that contains the features (unique words found in the documents) as rows.
I created weight vectors mapping with these features. i.e if the article has a word that is part of the feature vector table that location is marked as 1 or else 0.
Ex:- Training sample generated...
1 1:1 2:1 3:1 4:1 5:1 6:1 7:1 8:1 9:1
10:1 11:1 12:1 13:1 14:1 15:1 16:1
17:1 18:1 19:1 20:1 21:1 22:1 23:1
24:1 25:1 26:1 27:1 28:1 29:1 30:1
As this is the first document all the features are present.
I am using 1, 0 as class labels.
I am using svm.Net for classification.
I gave 300 weight vectors manually classified as training data and the model generated is taking all the vectors as support vectors, which is surely overfitting.
My total features (unique words/row count in feature vector DB table) is 7610.
What could be the reason?
Because of this over fitting my project is now in pretty bad shape. It is classifying every article available as a positive article.
In LibSVM binary classification is there any restriction on the class label?
I am using 0, 1 instead of -1 and +1. Is that a problem?
You need to do some type of parameter search, also if the classes are unbalanced the classifier might get artificially high accuracies without doing much. This guide is good at teaching basic, practical things, you should probably read it
As pointed out, a parameter search is probably a good idea before doing anything else.
I would also investigate the different kernels available to you. The fact that you input data is binary might be problematic for the RBF kernel (or might render it's usage sub-optimal, compared to another kernel). I have no idea which kernel could be better suited, though. Try a linear kernel, and look around for more suggestions/idea :)
For more information and perhaps better answers, look on stats.stackexchange.com.
I would definitely try using -1 and +1 for your labels, that's the standard way to do it.
Also, how much data do you have? Since you're working in 7610-dimensional space, you could potentially have that many support vectors, where a different vector is "supporting" the hyperplane in each dimension.
With that many features, you might want to try some type of feature selection method like principle component analysis.
Imagine you wanted to serialize and deserialize stackoverflow posts including their tags as space efficiently as possible (in binary), but also for performance when doing tag lookups. Is there a good datastructure for that kind of scenario?
Stackoverflow has about 28532 different tags, you could create a table with all tags and assign them an integer, Furthermore you could sort them by frequency so that the most common tags have the lowest numbers. Still storing them simply like a string in the format "1 32 45" seems a bit inefficent borth from a searching and storing perspective
Another idea would be to save tags as a variable bitarray which is attractive from a lookup and serializing perspective. Since the most common tags are first you potentially could fit tags into a small amount of memory.
The problem would be of course that uncommon tags would yield huge bitarrays. Is there any standard for "compressing" bitarrays for large spans of 0's? Or should one use some other structure completely?
EDIT
I'm not looking for a DB solution or a solution where I need to keep entire tables in memory, but a structure for filtering individual items
Not to undermine your question but 28k records is really not all that many. Are you perhaps optimizing prematurely?
I would first stick to using 'regular' indices on a DB table. The harshing heuristics they use are typically very efficient and not trivial to beat (or if you can is it really worth the effort in time and are the gains large enough?).
Also depending on where you actually do the tag query, is the user really noticing the 200ms time gain you optimized for?
First measure then optimize :-)
EDIT
Without a DB I would probably have a master table holding all tags together with an ID (if possible hold it in memory). Keep a regular sorted list of IDs together with each post.
Not sure how much storage based on commonality would help. A sorted list in which you can do a regular binary search may prove fast enough; measure :-)
Here you would need to iterate all posts for every tag query though.
If this ends up being to slow you could resort to storing a pocket of post identifiers for each tag. This data structure may become somewhat large though and may require a file to seek and read against.
For a smaller table you could resort to build one based on a hashed value (with duplicates). This way you could use it to quickly get down to a smaller candidate list of posts that need further checking to see if they match or not.
You need second table with 2 fields: tag_id question_id
That's it. Then you create indexes on tag_id, question_id and question_id, tag_id - that would be covering index so all your queries would be very fast.
I have a feeling you abstracted your question too much; you didn't say very much about how you want to access the datastructure, which is very important.
That being said, I suggest to count the number of occurances for each tag and then use Huffman coding to come up with the shortest encoding which can be used for the tags. This is not entirely perfect, but I'd stick with it until you've demonstrate that it's inappropriate. You can then associate the codes with each question.
If you want to efficiently lookup questions within a specific tag, you will need some kind of index. Maybe, all Tag objects could have an array of references (references, pointers, nummeric-id, etc) to all the questions that are tagged with this particular tag. This way you simply need to find the tag object and you have an array pointing to all the questions of that tag.
I know this question have been asked a lot of time.
I want a suggestion on which algorithm is suitable for approximate string matching.
The application is specifically for company name matching only and nothing else.
The biggest challenge is probably the company end name part and short named part
Example:
1. companyA pty ltd vs companyA pty. ltd. vs companyA
2. WES Engineering vs W.E.S. Engineering (extremely rare occurance)
Do you think Levenshtein Edit Distance is adequate?
I'm using C#
Regards,
Max
There are various string distance metrics you could use.
I would recommend Jaro-Winkler. Unlike edit-distance where the result of a comparison is in discrete units of edits, JW gives you a 0-1 score. It is especially suited for proper names. Also look at this nice tutorial and this SO question.
I haven't worked with C# but here are some implementations of JW I found online:
Impl 1 (They have a DOT NET version too if you look at the file list)
Impl 2
If you want to do a bit more sophisticated matching, you can try to do some custom normalization of word forms commonly occurring in company names such as ltd/limited, inc/incorporated, corp/corporation to account for case insensitivity, abbreviations etc. This way if you compute
distance (normalize("foo corp."),
normalize("FOO CORPORATION") )
you should get the result to be 0 rather than 14 (which is what you would get if you computed levenshtein edit-distance).
Yes, Levenshtein distance is suitable for this. It will work for all those you have listed at least.
You could also possibly use Soundex, but I don't think you'll need it.
In these simple examples, just removing all non-alpha-numeric characters gives you a match, and is the easiest to do as you can pre-compute the data on each side, then do a straight equals match which will be a lot faster than cross multiplying and calculating the edit distance.
I have provided my answer already in another question.
https://stackoverflow.com/a/30120166/2282794
I have worked on really large scale system with similar name matching requirements that you have talked about.
Name matching is not very straightforward and the order of first and last names might be different.
Simple fuzzy name matching algorithms fail miserably in such scenarios.
If we just want to talk about the Approximate String matching algorithms, then there are many. Few of them are: Jaro-Winkler, Edit distance(Levenshtein), Jaccard similarity, Soundex/Phonetics based algorithms etc. A simple googling would give us all the details.
You can implement all of them in C#
Irony is, they work while you try to match two given input strings. Alright theoretically and to demonstrate the way fuzzy or approximate string matching works.
However, grossly understated point is, how do we use the same in production settings. Not everybody that I know of who were scouting for an approximate string matching algorithm knew how they could solve the same in the production environment.
I might have just talked about Lucene which is specific to Java but there is Lucene for .Net also.
https://lucenenet.apache.org/