Given a Matrix, I'm interested in the Eigenvalues and the corresponding Eigenvector.
Using Jama, I can get the Eigenvalues and the Eigenvectors, yet the correlation between the two is not defined: I want to map each Eigenvector to the corresponding Eigenvalue.
Can you please recommend me of a way to do so? I tried to implement it myself but it got nasty.
Thanks :)
I am trying to look for an authorized answer, yet for now, According to experiments and observation I performed, the eigenvectors and evigenValues seem to be corresponding.
Usually they are presented in corresponding order. But you can always multiply an eigenvector by the matrix and seeing what multiplier it applies to the vector. That's also your eigenvalue directly.
I asked the developer of the Weka by mail regrading the above issue and they confirm the assumption -
The eigenvectors are indeed provided in the same order as the eigenvalues.
Use a hashmap to store them? I'm not sure this answer is relevant given the question is a bit vague..
Related
I have 3 points [x0 y0], [x1 y1], [x2 y2] with strict conditional x0<x1<x2, y0<y1<y2. All this points lay on some exponentional functions y=ae^(bx)+c. I need to find a,b,c... It's not possible to solve system of 3 equations precisely, therefore I need to approximate it. Is there some math library in java that will help me solve this problem? I find something similar on mathcad
https://help.ptc.com/mathcad/en/index.html#page/PTC_Mathcad_Help/exponential_regression.html but not find in java.
Other way - how to solve system of 3 equations and 3 values approximately.
ae^(bx_0)+c=y_0
ae^(bx_1)+c=y_1
ae^(bx_2)+c=y_2
You have to solve a system of non-linear equations, for which only an approximate solution is possible but can be done using the Newton Raphson's Multivariate method.
The algorithm is, quite frankly, a notational pain but you can go through it here -
http://fourier.eng.hmc.edu/e176/lectures/NM/node21.html.
What is happening essentially is you have a function whose derivative lead you to an 'equilibrium' from an initial random point (which you guess as a possible root)
If you are not willing to write the code yourself this repo can give you a starter of sorts - https://github.com/prasser/newtonraphson.
But AFAIK, no ready library exists for this purpose. You can use Wolfram's Mathematica or MATLAB/OCTAVE for ready libraries though.
That said, here are a few other (more complicated) things you can look into
https://en.wikipedia.org/wiki/Levenberg%E2%80%93Marquardt_algorithm
https://www1.fpl.fs.fed.us/optimization.html
http://icl.cs.utk.edu/f2j/
http://optalgtoolkit.sourceforge.net/
http://scribblethink.org/Computer/Javanumeric/index.html
https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.fmin_l_bfgs_b.html
Hope this helps!
Suppose I input to WEKA some dataset and set a normalization filter for the attributes so the values be between 0 and 1. Then suppose the normalization is done by dividing on the maximum value, and then the model is built. Then what happens if I deploy the model and in the new instances to be classified an instance has a feature value that is larger than the maximum in the training set. How such a situation is handled? Does it just take 1 or does it then take more than 1? Or does it throw an exception?
The documentation doesn't specify this for filters in general.So it must depend on the filter. I looked at the source code of weka.filters.unsupervised.attribute.Normalize which I assume you are using, and I don't see any bounds checking in it.
The actual scaling code is in the Normalize.convertInstance() method:
value = (vals[j] - m_MinArray[j]) / (m_MaxArray[j] - m_MinArray[j])
* m_Scale + m_Translation;
Barring any (unlikely) additional checks outside this method I'd say that it will scale to a value greater than 1 in the situation that you describe. To be 100% sure your best bet is to write a testcase, invoke the filter yourself, and find out. With libraries that haven't specified their working in the Javadoc, you never know what the next release will do. So if you greatly depend on a particular behaviour, it's not a bad idea to write an automated test that regression-tests the behaviour of the library.
I have the same questions as you said. I did as follows and may this method can help you:
I suppose you use the weka.filters.unsupervised.attribute.Normalize to normalize your data.
as Erwin Bolwidt said, weka use
value = (vals[j] - m_MinArray[j]) / (m_MaxArray[j] - m_MinArray[j])
* m_Scale + m_Translation;
to normalize your attribute.
Don't forget that the Normalize class has this two method:
public double[] getMinArray()
public double[] getMaxArray()
Which Returns the calculated minimum/maximum values for the attributes in the data.
And you can store the minimum/maximum values. And then use the formula to normalize your data by yourself.
Remember you can set the attribute in Instance class, and you can classify your result by Evaluation.evaluationForSingleInstance
I 'll give you the link later, may this help you.
Thank you
Could anybody, please, point me on the algorithm of how matrix multiplication can be done (Identifying the order of multiplying). I tried really different way which I could design, but nothing works as expected, unfortunately :( For example I have one of the following matrix chains to multiply:
((((0(((((((((((((((1 2)3)4)5)6)7)8)9)10)11)12)13)14)15)16))17)18)19
((((((((((((0 1)2)3)4)5)6)7)8)9)10)(11(12(13(14(15(16(1718))))))))19
(((((0 1)(2(((3 4)(5 6))(((7 8)(9(10 11)))((((12 13)14)15)16)))))17)18)19
(((((((0 1)2)3)4)5)(6(7(8(9(10(11(12 13))))))))(((((14 15)16)17)18)19)
Can somebody share a universal algorithm for all the cases?
NOTE:
1.I need multiplication only.
2.Matrices have different dimension, so they are not square. (Naturally, Matrices' dimensions agree)
3.Maybe this topic can be helpful, but I really have no idea how it can be applied here.
Thanks in advance to everybody who is trying to help!
What you are looking for is called "Matrix chain multiplication". http://en.wikipedia.org/wiki/Matrix_chain_multiplication
For a project that I'm currently working on I am dealing with a list of lists of integers, something of the form:
{[1,2];[5];[3,6,7]}
The idea here is that I'm trying to resolve an n-dimensional array into a list of the local maxima that occur in whatever particular axis I happen to be looking at. My question is this: I would like to get out a list of what would essentially be points in this n-dimensional space that contains every possible combination of entries of this list. For example, I would want the above to return:
{[1,5,3];[1,5,6];[1,5,7];[2,5,3];[2,5,6];[2,5,7]}
With the ordering not actually mattering to me. My first idea in how to approach this would be to boil this down to a tree where each path represents a possible combination and outputting every possible path, but I'm really not sure if this is the best way of going about it, and I am unfamiliar enough with Java's tree classes to be unsure if this would actually be straightforward to implement or not. Ideas?
Ah, my mistake, totally a duplicate.
I'm making a chat responder for a game and i want know if there is a way you can compare two strings and see if they are approximatley equal to each other for example:
if someone typed:
"Strength level?"
it would do a function..
then if someone else typed:
"Str level?"
it would do that same function, but i want it so that if someone made a typo or something like that it would automatically detect what they're trying to type for example:
"Strength tlevel?"
would also make the function get called.
is what I'm asking here something simple or will it require me to make a big giant irritating function to check the Strings?
if you've been baffled by my explanation (Not really one of my strong points) then this is basically what I'm asking.
How can I check if two strings are similar to each other?
See this question and answer: Getting the closest string match
Using some heuristics and the Levenshtein distance algorithm, you can compute the similarity of two strings and take a guess at whether they're equal.
Your only option other than that would be a dictionary of accepted words similar to the one you're looking for.
You can use Levenshtein distance.
I believe you should use one of Edit distance algorithms to solve your problem. Here is for example Levenstein distance algorithm implementation in java. You may use it to compare words in the sentences and if sum of their edit distances would be less than for example 10% of sentence length consider them equals.
Perhaps what you need is a large dictionary for similar words and common spelling mistakes, for which you would use for each word to "translate" to one single entry or key.
This would be useful for custom words, so you could add "str" in the same key as "strength".
However, you could also make a few automated methods, i.e. when your word isn't found in the dictionary, to loop recursively for 1 letter difference (either missing or replaced) and can recurse into deeper levels, i.e. 2 missing letters etc.
I found a few projects that do text to phonemes translations, don't know which one is best
http://mary.dfki.de/
http://www2.eng.cam.ac.uk/~tpl/asp/source/Phoneme.java
http://java.dzone.com/announcements/announcing-phonemic-10
If you want to find similar word beginnings, you can use a stemmer. Stemmers reduce words to a common beginning. The most known algorithm if the Port Stemmer (http://tartarus.org/~martin/PorterStemmer).
Levenshtein, as pointed above, is great, but computational heavy for distances greater than one or two.