I have several datasets i.e. matrices that have a 2 columns, one with a matlab date number and a second one with a double value. Here an example set of one of them
>> S20_EavesN0x2DEAir(1:20,:)
ans =
1.0e+05 *
7.345016409722222 0.000189375000000
7.345016618055555 0.000181875000000
7.345016833333333 0.000177500000000
7.345017041666667 0.000172500000000
7.345017256944445 0.000168750000000
7.345017465277778 0.000166875000000
7.345017680555555 0.000164375000000
7.345017888888889 0.000162500000000
7.345018104166667 0.000161250000000
7.345018312500001 0.000160625000000
7.345018527777778 0.000158750000000
7.345018736111110 0.000160000000000
7.345018951388888 0.000159375000000
7.345019159722222 0.000159375000000
7.345019375000000 0.000160625000000
7.345019583333333 0.000161875000000
7.345019798611111 0.000162500000000
7.345020006944444 0.000161875000000
7.345020222222222 0.000160625000000
7.345020430555556 0.000160000000000
Now that I have those different sensor values, I need to get them together into a matrix, so that I could perform clustering, neural net and so on, the only problem is, that the sensor data was taken with slightly different timings or timestamps and there is nothing I can do about that from a data collection point of view.
My first thought was interpolation to make one sensor data set fit another one, but that seems like a messy approach and I was thinking maybe I am missing something, a toolbox or function that would enable me to do this quicker without me fiddling around. To even complicate things more, the number of sensors grew over time, therefore I am looking at different start dates as well.
Someone a good idea on how to go about this? Thanks
I think your first thought about interpolation was the correct one, at least if you plan to use NNs. Another option would be to use approaches which are designed to deal with missing data, like http://en.wikipedia.org/wiki/Dempster%E2%80%93Shafer_theory for example.
It's hard to give an answer for the clustering part, because I have no idea what you're looking for in the data.
For the neural network, beside interpolating there are at least two other methods that come to mind:
training separate networks for each matrix
feeding them all together to the same network, with a flag specifying which matrix the data is coming from, i.e. something like: input (timestamp, flag_m1, flag_m2, ..., flag_mN) => target (value) where the flag_m* columns are mutually exclusive boolean values - i.e. flag_mK is 1 iff the line comes from matrix K, 0 otherwise.
These are the only things I can safely say with the amount of information you provided.
Related
I have a need to pass a vector of arguments to Rserve from tableau. Specifically, I am using IRR calculations in R (on Rserve), and i want to pass vector of cash-flows that are as columns in my table (instead of rows/measure). So, i want to collect all those CF in a vector and pass it on to Rserve. Passing them one at a time slows down IO.
SCRIPT_REAL("r_func(c(.arg1, .arg2, .arg3))",sum(cf1), sum(cf2), sum(cf3))
cf1..cfn are cashflows corresponding to various periods. Above code works well when cf are few but takes a long time when i have few hundereds. Further, time spent is not in calculation but IO when communicating with remote Rserve. If i have a local Rserve, this calculation happens under few seconds while on remote, it takes well over a minute.
Also, want to point out that tableau / Rserve, set one argument after another and that takes time. My expectation is that once i have a vector, it would be just 1 transfer and setting of arguments, and therefore this should speed up
The first step in understanding how Tableau interacts with R or Python, is understanding how Tableau's table calcs work.
Tableau Script_XXX() functions are table calculations which means that you invoke them on a vector of aggregate query results and the corresponding R or Python code needs to return a vector usually of the same size. (I think you may be able to return a scalar or smaller vector which gets replicated to appear like a vector of the same size as the argument -- but not certain)
You can control how your data is partitioned into vectors, and also the ordering of data in the vectors, by editing the table calc to specify the partitioning and addressing for that calc.
Partitioning determines how your aggregate query results are broken up into vectors for calculation purposes. Addressing determines how the elements of each vector are ordered. You can either do that based on the physical layout of the table structure, or (better) based on the specific dimensions.
See the Tableau on-line help for table calcs for more info, and look online training videos from Tableau or blog entries (especially from anyone named Bora)
One way to test your understanding of these concepts is create a Tableau table (i.e., a viz with a mark type of text) with several dimensions on row and column shelves. Then create calculated fields for INDEX() and SIZE() and display them on text. Finally, change the partitioning and addressing in different ways by editing those table calcs. Try several different permutations. When you can confidently predict what those functions will produce for different settings, then you're ready to do more complex tasks - such as talking to R.
It is also instructive to experiment with FIRST(), LAST(), LOOKUP(), WINDOW_SUM() etc -- and finally dig into PREVIOUS_VALUE(). Warning, PREVIOUS_VALUE() is a bit odd, and does not behave the way you probably assume it does. Still, it is a useful technique that can implement a recursive calculation, and is about as close to a for loop as Tableau gets.
I want to use pyfft to repeatedly compute the discrete Fourier transform of a subset of rows for a two-dimensional array. I do not know in advance which rows I need to transform, that depends on the output from the previous round. I do know that doing it for all rows is wasteful.
It is my understanding that a 'plan' in FFTW3 is associated with the type of transform (c2c, r2c, etc) and the input/output length, which is always a vector in the 1D case. In pyfftw it looks like a 'plan' is associated to the type of transform and the input/output shape, so my interpretation is that it uses the same FFTW3 plan for every row.
My question is: is it possible to use the same FFTW3 plan for some of the rows, without creating separate pyfftw.FFTW objects for all possible combinations of rows?
On a different note, I am wondering how pyfftw uses multiple cores: does it use multiple cores for each row (this appears natural in view of FFTW3 documentation) or does it farm out different rows to different cores (which was my initial assumption)?
If you can create a numpy array from a view, you can plan for it with pyFFTW - all valid numpy arrays should work just fine.
This means several things:
Your array needs to have regular strides, but those strides can be arbitrary.
ND arrays are planned as ND transforms, with the selected axes being used.
You can probably do something cunning with stride tricks and it will probably work (but might not do what you expect if you do something too nefarious like overlapping rows and then use threads).
One solution that I've used quite a bit is to copy the rows that you want to transform into an interim array, and transforming that. You might well find that's the fastest option (particularly when you can allow for getting the byte offset correct).
Obviously, this doesn't work if you always have a different number of rows. You might still find that if you plan for the largest number of rows that are transformed and then copy in a subset you still do faster than otherwise.
The problem you're going to come up against, even if you go down to the C level, is that the planning overhead might well dominate if you're changing your transform sizes often.
You could also try pyfftw.interfaces.numpy_fft which is normally faster that numpy and has the ability to cache repeated transform sizes.
Just starting to play around with Neural Networks for fun after playing with some basic linear regression. I am an English teacher so don't have a math background and trying to read a book on this stuff is way over my head. I thought this would be a better avenue to get some basic questions answered (even though I suspect there is no easy answer). Just looking for some general guidance put in layman's terms. I am using a trial version of an Excel Add-In called NEURO XL. I apologize if these questions are too "elementary."
My first project is related to predicting a student's Verbal score on the SAT based on a number of test scores, GPA, practice exam scores, etc. as well as some qualitative data (gender: M=1, F=0; took SAT prep class: Y=1, N=0; plays varsity sports: Y=1, N=0).
In total, I have 21 variables that I would like to feed into the network, with the output being the actual score (200-800).
I have 9000 records of data spanning many years/students. Here are my questions:
How many records of the 9000 should I use to train the network?
1a. Should I completely randomize the selection of this training data or be more involved and make sure I include a variety of output scores and a wide range of each of the input variables?
If I split the data into an even number, say 9x1000 (or however many) and created a network for each one, then tested the results of each of these 9 on the other 8 sets to see which had the lowest MSE across the samples, would this be a valid way to "choose" the best network if I wanted to predict the scores for my incoming students (not included in this data at all)?
Since the scores on the tests that I am using as inputs vary in scale (some are on 1-100, and others 1-20 for example), should I normalize all of the inputs to their respective z-scores? When is this recommended vs not recommended?
I am predicting the actual score, but in reality, I'm NOT that concerned about the exact score but more of a range. Would my network be more accurate if I grouped the output scores into buckets and then tried to predict this number instead of the actual score?
E.g.
750-800 = 10
700-740 = 9
etc.
Is there any benefit to doing this or should I just go ahead and try to predict the exact score?
What if ALL I cared about was whether or not the score was above or below 600. Would I then just make the output 0(below 600) or 1(above 600)?
5a. I read somewhere that it's not good to use 0 and 1, but instead 0.1 and 0.9 - why is that?
5b. What about -1(below 600), 0(exactly 600), 1(above 600), would this work?
5c. Would the network always output -1, 0, 1 - or would it output fractions that I would then have to roundup or rounddown to finalize the prediction?
Once I have found the "best" network from Question #3, would I then play around with the different parameters (number of epochs, number of neurons in hidden layer, momentum, learning rate, etc.) to optimize this further?
6a. What about the Activation Function? Will Log-sigmoid do the trick or should I try the other options my software has as well (threshold, hyperbolic tangent, zero-based log-sigmoid).
6b. What is the difference between log-sigmoid and zero-based log-sigmoid?
Thanks!
First a little bit of meta content about the question itself (and not about the answers to your questions).
I have to laugh a little that you say 'I apologize if these questions are too "elementary."' and then proceed to ask the single most thorough and well thought out question I've seen as someone's first post on SO.
I wouldn't be too worried that you'll have people looking down their noses at you for asking this stuff.
This is a pretty big question in terms of the depth and range of knowledge required, especially the statistical knowledge needed and familiarity with Neural Networks.
You may want to try breaking this up into several questions distributed across the different StackExchange sites.
Off the top of my head, some of it definitely belongs on the statistics StackExchange, Cross Validated: https://stats.stackexchange.com/
You might also want to try out https://datascience.stackexchange.com/ , a beta site specifically targeting machine learning and related areas.
That said, there is some of this that I think I can help to answer.
Anything I haven't answered is something I don't feel qualified to help you with.
Question 1
How many records of the 9000 should I use to train the network? 1a. Should I completely randomize the selection of this training data or be more involved and make sure I include a variety of output scores and a wide range of each of the input variables?
Randomizing the selection of training data is probably not a good idea.
Keep in mind that truly random data includes clusters.
A random selection of students could happen to consist solely of those who scored above a 30 on the ACT exams, which could potentially result in a bias in your result.
Likewise, if you only select students whose SAT scores were below 700, the classifier you build won't have any capacity to distinguish between a student expected to score 720 and a student expected to score 780 -- they'll look the same to the classifier because it was trained without the relevant information.
You want to ensure a representative sample of your different inputs and your different outputs.
Because you're dealing with input variables that may be correlated, you shouldn't try to do anything too complex in selecting this data, or you could mistakenly introduce another bias in your inputs.
Namely, you don't want to select a training data set that consists largely of outliers.
I would recommend trying to ensure that your inputs cover all possible values for all of the variables you are observing, and all possible results for the output (the SAT scores), without constraining how these requirements are satisfied.
I'm sure there are algorithms out there designed to do exactly this, but I don't know them myself -- possibly a good question in and of itself for Cross Validated.
Question 3
Since the scores on the tests that I am using as inputs vary in scale (some are on 1-100, and others 1-20 for example), should I normalize all of the inputs to their respective z-scores? When is this recommended vs not recommended?
My understanding is that this is not recommended as the input to a Nerual Network, but I may be wrong.
The convergence of the network should handle this for you.
Every node in the network will assign a weight to its inputs, multiply them by their weights, and sum those products as a core part of its computation.
That means that every node in the network is searching for some coefficients for each of their inputs.
To do this, all inputs will be converted to numeric values -- so conditions like gender will be translated into "0=MALE,1=FEMALE" or something similar.
For example, a node's metric might look like this at a given point in time:
2*ACT_SCORE + 0*GENDER + (-5)*VARISTY_SPORTS ...
The coefficients for each values are exactly what the network is searching for as it converges.
If you change the scale of a value, like ACT_SCORE, you just change the scale of the coefficient that will be found by the reciporical of that scaling factor.
The result should still be the same.
There are other concerns in terms of accuracy (computers have limited capacity to represent small fractions) and speed that may enter this, but not being familiar with NEURO XL, I can't say whether or not they apply for this technology.
Question 4
I am predicting the actual score, but in reality, I'm NOT that concerned about the exact score but more of a range. Would my network be more accurate if I grouped the output scores into buckets and then tried to predict this number instead of the actual score?
This will reduce accuracy, although you should converge to a solution much faster with fewer possible outputs (scores).
Neural Networks actually describe very high-dimensional functions in their input variables.
If you reduce the granularity of that function's output space, you essentially state that you don't care about local minima and maxima in that function, especially around the borders between your output scores.
As a result, you are sacrificing information that may be an essential component of the "true" function that you are searching for.
I hope this has been helpful, but you really should break this question down into its many components and ask them separately on different sites -- potentially some of them do belong here on StackOverflow as well.
I have a rather large(not too large but possibly 50+) set of conditions that must be placed on a set of data(or rather the data should be manipulated to fit the conditions).
For example, Suppose I have the a sequence of binary numbers of length n,
if n = 5 then a element in the data might be {0,1,1,0,0} or {0,0,0,1,1}, etc...
BUT there might be a set of conditions such as
x_3 + x_4 = 2
sum(x_even) <= 2
x_2*x_3 = x_4 mod 2
etc...
Because the conditions are quite complex in that they come from experiment(although they can be written down in logic form) and are hard to diagnose I would like instead to use a large sample set of valid data. i.e., Data I know satisfies the conditions and is a pretty large set. i.e., it is easier to collect the data then it is to deduce the conditions that the data must abide by.
Having said that, basically what I'm doing is very similar to neural networks. The difference is, I would like an actual algorithm, in some sense optimal, in some form of code that I can run instead of the network.
It might not be clear what I'm actually trying to do. What I have is a set of data in some raw format that is unique and unambiguous but not appropriate for my needs(in a sense the amount of data is too large).
I need to map the data into another set that actually is ambiguous to some degree but also has certain specific set of constraints that all the data follows(certain things just cannot happen while others are preferred).
The unique constraints and preferences are hard to figure out. That is, the mapping from the non-ambiguous set to the ambiguous set is hard to describe(which is why it is ambiguous). The goal, actually, is to have an unambiguous map by supplying the right constraints if at all possible.
So, on the vein of my initial example, I'm given(or supply) a set of elements and need some way to derive a list of constraints similar to what I've listed.
In a sense, I simply have a set of valid data and train it very similar to neural networks.
Then, after this "Training" I'm given the mapping function I can then use on any element in my dataset and it will produce a new element satisfying the constraint's, or if it can't, will give as close as possible an unambiguous result.
The main difference between neural networks and what I'm trying to achieve is I'd like to be able to use have an algorithm to code to be used instead of having to run a neural network. The difference here is the algorithm would probably be a lot less complex, not need potential retraining, and a lot faster.
Here is a simple example.
Suppose my "training set" are the binary sequences and mappings
01000 => 10000
00001 => 00010
01010 => 10100
00111 => 01110
then from the "Magical Algorithm Finder"(tm) I would get a mapping out like
f(x) = x rol 1 (rol = rotate left)
or whatever way one would want to express it.
Then I could simply apply f(x) to any other element, such as x = 011100 and could apply f to generate a hopefully unambiguous output.
Of course there are many such functions that will work on this example but the goal is to supply enough of the dataset to narrow it down to hopefully a few functions that make the most sense(at the very least will always map the training set correctly).
In my specific case I could easily convert my problem into mapping the set of binary digits of length m to the set of base B digits of length n. The constraints prevents some numbers from having an inverse. e.g., the mapping is injective but not surjective.
My algorithm could be a simple collection if statements acting on the digits if need be.
I think what you are looking for here is an application of Learning Classifier Systems, LCS -wiki. There are actually quite a few LCS open-source applications available, but you may need to experiment with the parameters in order to get a good result.
LCS/XCS/ZCS have the features that you are looking for including individual rules that could be heavily optimized, pressure to reduce the rule-set, and of course a human-readable/understandable set of rules. (Unlike a neural-net)
I am clustering a large set of points. Throughout the iterations, I want to avoid re-computing cluster properties if the assigned points are the same as the previous iteration. Each cluster keeps the IDs of its points. I don't want to compare them element wise, comparing the sum of the ID vector is risky (a small ID can be compensated with a large one), may be I should compare the sum of squares? Is there a hashing method in Matlab which I can use with confidence?
Example data:
a=[2,13,14,18,19,21,23,24,25,27]
b=[6,79,82,85,89,111,113,123,127,129]
c=[3,9,59,91,99,101,110,119,120,682]
d=[11,57,74,83,86,90,92,102,103,104]
So the problem is that if I just check the sum, it could be that cluster d for example, looses points 11,103 and gets 9,105. Then I would mistakenly think that there has been no change in the cluster.
This is one of those (very common) situations where the more we know about your data and application the better we are able to help. In the absence of better information than you provide, and in the spirit of exposing the weakness of answers such as this in that absence, here are a couple of suggestions you might reject.
One appropriate data structure for set operations is a bit-set, that is a set of length equal to the cardinality of the underlying universe of things in which each bit is set on or off according to the things membership of the (sub-set). You could implement this in Matlab in at least two ways:
a) (easy, but possibly consuming too much space): define a matrix with as many columns as there are points in your data, and one row for each cluster. Set the (cluster, point) value to true if point is a member of cluster. Set operations are then defined by vector operations. I don't have a clue about the relative (time) efficiency of setdiff versus rowA==rowB.
b) (more difficult): actually represent the clusters by bit sets. You'll have to use Matlab's bit-twiddling capabilities of course, but the pain might be worth the gain. Suppose that your universe comprises 1024 points, then you'll need an array of 16 uint64 values to represent the bit set for each cluster. The presence of, say, point 563 in a cluster requires that you set, for the bit set representing that cluster, bit 563 (which is probably bit 51 in the 9th element of the set) to 1.
And perhaps I should have started by writing that I don't think that this is a hashing sort of a problem, it's a set sort of a problem. Yeah, you could use a hash but then you'll have to program around the limitations of using a screwdriver on a nail (choose your preferred analogy).
If I understand correctly, to hash the ID's I would recommend using the matlab Java interface to use the Java hashing algorithms
http://docs.oracle.com/javase/1.4.2/docs/api/java/security/MessageDigest.html
You'll do something like:
hash = java.security.MessageDigest.getInstance('SHA');
Hope this helps.
I found the function
DataHash on FEX it is quiet fast for vectors and the strcmp on the keys is a lot faster than I expected.