I want implement a recommender system by Matlab, I choose MoveiLens Dataset , and svm algorithm.
I implement a function that returns two sets of Items. The first set is items that user Rate them more than 3 and second set is items that user Rate less than 4.
Rate is a matrix with 3 column, the first one is user Id,second one is Item Id, and third one is User Rate to this item .
function [like,dislike]=UsetLike(User,Rate)
k1=1;
k2=1;
for i=1:size(Rate,1)
if(Rate(i,1)==User)
if(Rate(i,3)>3)
like(k1)= Rate(i,2);
k1=k1+1;
end
if(Rate(i,3)<=3)
dislike(k2)= Rate(i,2);
k2=k2+1;
end
end
end
end
Then I write another function that train by svm such as this.
Feature is a matrix that in (i) row shows item (i) features, that has 19 features with 0 or 1 value.
function [svmModel]=TrainSVM(like,dislike,Feture)
group1=zeros(size(like,2),19);
group2=zeros(size(dislike,2),19);
for i=1: size(group1,1)
group1(i,:)= Feture(like(i),:);
end
for i=1: size(group2,1)
group2(i,:)= Feture(dislike(i),:);
end
Dataset=cat(1,group1,group2);
group=[repmat({'like'},1,size(group1,1)) repmat({'dislike'},1,size(group2,1) )]';
svmModel = svmtrain(Dataset, group, ...
'Autoscale',true, 'Showplot',false, 'Method','QP', ...
'BoxConstraint',2e-1, 'Kernel_Function','rbf', 'RBF_Sigma',1);
end
Now I want to know if my solution is right? As it was in mostly 3D space I can not precept it. What if I want to use Rate (1-5) instead of like or dislike?
In order to use the Rates (1-5) as an output signal you will need a modification called ranking SVM, as this is not just a multilabel classification, but rather a ranking problem.
Related
I try to do a 10 folds cross validation without using built-in function to train and recognize digit from 0-9 I have sample of 500 picture(50 for each digit to train and test.)
I try implement the answer MATLAB: 10 fold cross Validation without using existing functions and other websites but it didn't help that much. Mostly because I'm new to MATLAB so I don't know much about what I should do to tweak it.
This is the code I have so far.
c=zeros(10,size(x,2),size(x,3));
K=10;
k=10;
test= 1:50/K;
for fold =1:K
if(test(1)~=1)
train = x(1:test(1)-1,:,:);
if (test(5) ~=50)
train=[train ; x(test(end):50,:,:)];
end
else
train = x(test(1):50,:,:);
end
test = test+ones(1,50/K)*50/K;
end
for i =0:9
test=test+50/K*ones(1,5);
c(i+1,:,:)=cal_likelihood(x(1+i*50:50+i*50,:,:),50/k*(k-1));
end
Variable explanation
x is the 500x28x28 double where it keeps all 500 digit picture.
test is a test set.
train is a training set.
In order to do 10 folds cross validation I need to change training set like
1st fold : 1:5 for test,6:45 for train
2nd fold : 6:10 for test,1:5 11:50 for train and so on
The problem is I don't know how to shift the training set from one set to another like from 6:45 to 1:5 and 11:50. or Can I write a better loop than this?
PSS. If someone who answer this don't mind What does 500x28x28 double actually mean.
There are a few ways you could write this, some of which are easier to understand than others. Matlab is quite nice to write in as while expressions such as 1:3 evaluate to [1,2,3], the expression 1:0 evaluates to the empty set. So, it is very straightforward to generate the sets without having to use if statements.
I'd start off the loop as:
samples_per_digit=50;
block_sze=samples_per_digit/K;
for fold =1:K
test_ind = 1+(fold-1)*block_sze:fold*block_sze;
train_ind = [1:(fold-1)*block_sze, (fold*block_sze+1):samples_per_digit];
for i=0:9
train=x(train_ind+i*samples_per_digit,:,:);
test=x(test_ind+i*samples_per_digit,:,:);
% Perform training and validation in here for this fold of the digit i
You can verify that test_ind and train_ind correspond to the subsets of blocks of training and validation that you need. It is only in the innermost loop that these translate to the matrices corresponding to the digit images, using the value of i to compute the offset. Of course, if you wish, you can swap the order of the loops, computing all of the folds for a single digit. It all depends on how you wish to store your results.
I have been reading the documentation: here and here but it's really unclear for me and I don't see how to use pratically crossval to do a leave one out cross-validation.
vals = crossval(fun,X)
vals = crossval(fun,X,Y,...)
mse = crossval('mse',X,y,'Predfun',predfun)
mcr = crossval('mcr',X,y,'Predfun',predfun)
val = crossval(criterion,X1,X2,...,y,'Predfun',predfun)
vals = crossval(...,'name',value)
I really don't understand the funpart.
I have estimatimate chlorophyll rate with different index. Then I have done a linear regression between those index and the field taken chlorophyll rate. Now I want to validate them, one of my estimation is a column with 22 entries, so I want to use 21 of them as trainee and 1 as a test, and do 22 loops so that all the data have been used as test.
But I don't where should I put the regression model? If my regression is Y=aX+b,
do I re-use the a and b calculated before for the train part, or do I do a new linear regression with the train part then see what's the test will be with that?
I am not sure I totally understood how to make a leave one out model.
Then I want to know the result of the test by calculating the RMSE (and maybe the R²).
How do I code that using crossval?
I saw the answer to the question here but I don't have access to the crossvalind fonction with my license.
Well I finaly figure it out: so this is my script:
First I charged my data and the linear regression fonction
X=indicesCha_without_Cloud(:,3);
y=Cha_g_m2t_without_Cloud(:,3);
testval=#(XTRAIN,ytrain,XTEST)Linear_regression_indices( XTRAIN,ytrain,XTEST);
where in my case fun(in the Mathwork help) is testvaland Linear_regression_indices is a very simple fonction:
function [ Linear_regression_indices ] = Linear_regression_indices(XTRAIN,ytrain,XTEST )
Linear_regression_indices=(polyval(polyfit(XTRAIN,ytrain,1),XTEST));
end
There is 2 ways to do it and they both give the same result:
one by using simply the crossval fonction
cvMse = crossval('mse',X,y,'predfun',testval,'leaveout',1);
this will do as many fold as the data size, using each time one of the data as Xtest
the second one is using cvpartition
c = cvpartition(n,'LeaveOut') creates a random partition for leave-one-out cross validation on n observations. Leave-one-out is a special case of 'KFold', in which the number of folds equals the number of observations. link
c = cvpartition(y,'LeaveOut');
cvMse2=crossval('mse',X,y,'predfun',testval,'partition',c);
then the RMSE can be easily calculated
RMSE=sqrt(cvMse);
RMSE2=sqrt(cvMse2);
then I simply get my answer, in my case RMSE=0,3548
Objective
Currently I am trying to create an uncertain system based on a family of statespace models using ucover. For this I am basing my script on the documentation "Modeling a Family of Responses as an Uncertain System" which shows the technique for creating an uncertain system based on a single-input-single-output system (SISO) explicitly but makes it clear that this is fully useable for MIMO systems as well.
Technical details
Specifically it is stated with the documentation of ucover that it supports MIMO systems:
USYS = ucover(PARRAY,PNOM,ORD1,ORD2,UTYPE) returns an uncertain
system USYS with nominal value PNOM and whose range of behaviors
includes all LTI responses in the LTI array PARRAY. PNOM and PARRAY
can be SS, TF, ZPK, or FRD models. USYS is of class UFRD if PNOM
is an FRD model and of class USS otherwise.
ORD1 and ORD2 specify the order (number of states) of each diagonal
entry of W1 and W2. If PNOM has NU inputs and NY outputs, ORD1 and ORD2
should be vectors of length:
UTYPE ORD1 ORD2
InputMult NU-by-1 NU-by-1
OutputMult NY-by-1 NY-by-1
Additive NY-by-1 NU-by-1
In my case I am using both 2 inputs and 2 outputs so both ORD1 adn ORD2 should be 2 by 1. I am using 8 as the number of states used by W1 and W2 (just because, I will try adjusting that once this issue is sorted).
The Attempt
Based on the SISO example I have attempted to create a MIMO example, this is shown below
noInputs=2;
noOutputs=2;
noOfStates=4;
Anom=rand(noOfStates,noOfStates);
Bnom=rand(noOfStates,noInputs);
Cnom=rand(noOutputs,noOfStates);
Dnom=rand(noOutputs,noInputs);
Pnom=ss(Anom, Bnom, Cnom, Dnom);
p1 = Pnom*tf(1,[.06 1]); % extra lag
p2 = Pnom*tf([-.02 1],[.02 1]); % time delay
p3 = Pnom*tf(50^2,[1 2*.1*50 50^2]);
Parray = stack(1,p1,p2,p3);
Parrayg = frd(Parray,logspace(-1,3,60));
[P,Info] = ucover(Parrayg,Pnom,[8 8]',[8 8]','InputMult');
Wt = Info.W1;
bodemag((Pnom-Parray)/Pnom,'b--',Wt,'r'); grid
title('Relative Gaps vs. Magnitude of Wt')
The problem
Unlike the image in the documentation my uncertain model (when put through a bode plot) only shows a response on the lead diagonal. See the screenshot for what I mean:
Where blue is the individual models and red is the uncertain model
Question
How can I create an uncertain system based on a family of MIMO statespace models that correctly covers responses between all inputs and outputs?
If you use [8,8]' as your uncertainty order structure ord1,ord2, matlab will try to have two diagonal blocks in your uncertainty block each.
However matlab only supports diagonal weighting functions (due to some complications about nonconvex search) and what you are plotting is the diagonal weighting that will multiply the 2x2 full block LTI dynamic uncertainty. W1 affects the rows and W2 affects the columns of the uncertainty.
Hence you should check the samples of that uncertainty multiplied by the weights and then the plant. Then you can compare it with the uncertain model stack. Notice that your off-diagonal entries are practically zero (<1e-10) hence almost decoupled. But W1, W2 search looks for the H-infinity norm hence you don't get to see perfect covering at each block of the Bode plot. It combines the rows/columns of the required minimum uncertainty amount (see the examples on the help file). That's why you see 1 plot per each weight in the demos.
If you would like to model the each uncertainty affecting each block separately then you need to form a new augmented LFT such that the uncertainty is four 1x1(scalar) LTI dynamic uncertainty on the diagonal then you can have four entries in ord1 and ord2.
Since this is a MIMO system, you shouldn't compare things element-by-element. You are using the input-multiplicative form, so the uncertain system being created is of the form
Pnom*(I + W1*Delta*W2), where Delta is any stable (2-by-2, in this case) system, with ||Delta|| <= 1. So, to verify that the produced uncertain model "covers" your array of system, you should think of the equation
Parray = Pnom*(I + W1*Delta*W2)
and solve for Delta. Plot it (with SIGMA, say), and you will see that it is less than 1 in magnitude, for all frequencies. The Matlab code would be (multiply everything listed below, in order - my mulitplication symbol is not showing up in the posted answer...)
sigma(inv(W1)*inv(Pnom)*(Parrayg-Pnom)*inv(W2))
Now, using the syntax you specified, you are using weights W1 and W2 of the following form:
W1 = [W1_11 0;
0 W1_22]
and
W2 = [W2_11 0;
0 W2_22]
where you've specified 8th-order fits for all nonzero entries. Certainly for your example, this is overkill (although on a richer problem, it might be fine).
I would try much simpler, like
ucover(Parrag,Pnom,3,[],'InputMult')
That syntax will make an uncertain model of the form
Pnom*(I + w1*Delta)
where w1 is a scalar, 3rd order system. You could still see the covering by plotting SIGMA(Delta), namely
sigma((1/w1)*inv(Pnom)*(Parrayg-Pnom))
I hope that helps.
In order to create discrete or continuous time uncertain systems you can use uss associated with ureal.
Quick example
Define an uncertain propeller radius
% Propeller radius (m)
rp = ureal('rp',13.4e-2,'Range',[0.08 0.16]);
Define uncertain continuous time system
tenzo_unc = uss(A,Bw,Clocal,D,'statename',states,'inputname',inputs,'outputname',outputsLocal);
Simulate step response:
N = 5;
% Prende alcuni campioni del sistema incerto e calcola bound su incertezze
for i=1:1:N
sys{i} = usample(tenzo_unc);
step(sys{i})
hold on
cprintf('text','.');
end
Complete example
Quadcopter uncertain linearized model control with LQR. Code is available here
Step response
Closed Loop Step response
<script src="https://gist.github.com/GiovanniBalestrieri/f90a20780eb2496e730c8b74cf49dd0f.js"></script>
NB:
If you don't have the utility cprintf, include this script in your folder and use it.
I have 6 data sets, each data set is a 576by576 matrix. Each set of data represents measurements taken within 30 second intervals. e.g. set1 at t=0, set2 at time =30, ... ,set5 at 150 seconds.
You can look at these sets as frames if you will. I need to take first data point (1,1) from each data set -> (1,1,0), (1,1,3),(1,1,6),(1,1,9),(1,1,12),(1,1,15) and based on those 6 points find a fitting formula, then assign that general solution to the first spot of my solution matriz SM(1,1). I need to do this for every data point in the 6 sets until I have a 576by576 solution matriz.
if everything goes right I should be able to plot SM(0s)=set1, SM(30s)=set2,etc. but not only that. SM(45) should return a prediction of measurements at t=45 and so on and so forth. The purpose is to have one matrix than can predict data fluctuation from time t= 0 to 150 seconds.
Additional information:
1.- Each data point is independent form the rest of the data points in the same set.
2.- it is a none-linear fit
3.- all values are real
Does Matlab have an optimization tool for this kind of problem?
Should I treat the problem as 1D data fit and create a for loop that does the job 576^2 times?
(I don't even know where to begin)
Feel free to ask or edit anything if I wasn't clear enough. I am not sure that I've chosen the most precise title for this kind of problem.Thanks
Update:
Based on Guddu's answer I came up with this:
%% Loadint data Matrix A
A(:,:,1) = abs(set1);
A(:,:,2) = abs(set2);
A(:,:,3) = abs(set3);
A(:,:,4) = abs(set4);
A(:,:,5) = abs(set5);
A(:,:,6) = abs(set6);
%% Creating Solution Matrix B
t=0:30:150;
SM=zeros([576 576 150]);
for i=1:576
for j=1:576
y=squeeze(A(i,j,1:6));
f=fit(t',y,'smoothingspline');
data=feval(f,1:150);
SM(i,j,:)=data;
end
end
%% Plotting Frame at t=45
figure(1);
imshow(SM(:,:,45),[])
I am not sure if this is the most efficient way to do it, but it works. I am open to new ideas or suggestions. Thanks
i would suggest your main data matrix would be of size (6,576,576) -> a. first point (1,1) from each dataset would be a(1,1,1), a(2,1,1), a(3,1,1) .. a(6,1,1). as you have said each point (i,j) in each dataset from other point (k,l), i would suggest treat each position (i,j) for all datasets separately from other positions. so it would be looping 576*576 times. code could be something like this
t=0:30:150;
for i=1:576
for j=1:576
datavec=squeeze(a(1:6,i,j)); % Select (i,j) point from all 6 frames
% do the curve fitting and save in SM(i,j)
end
end
i am just curious what kind of non-linear function you want to fit to 6 points. this might not be the answer you want but it was kind of long to put in a comment
I am a total beginner in MATLAB and I hope to find some help here. I have some model prediction results for 80 individuals alltogether in one large matrix. I need to extract the data for each individual from the big matrix, assign them in a new variable/matrix, do some extra calculations and then plot certain information as needed.
To do so, I am trying to write a script with a loop function but in a complicated, or maybe more accurately: in a primitive way!
Simplified Example:
My matrix is called: All_Indi_Data .... its dimension is: 600 rows x 21 columns
%Column 1: grouping variable (e.g., code or ID with values 1,2,3,4,5, etc.);
%Column 2: independent var.;
%Column 3: t;
%Column 4: OBS;
%Column 5: PRED;
i= length (All_Indi_Data);
%% First Indi.
q=1; % indicating the ID of the indi for which I want to extract the data
j=1; % variable added to insure writing start from the first row
for r=1:i
if All_Indi_Data (r,1)==q
Indi_1 (j,1:21) = All_Indi_Data (r,1:21)
j=j+1
end
end
%% Second Indi.
q=q+1
j=1
for r=1:i
if All_Indi_Data (r,1)==q
Indi_2 (j,1:21) = All_Indi_Data (r,1:21)
j=j+1
end
end
.
.
.
1) My first question is: can I allocate these data in new variables (Indi_1, Indi_2, ect.) in a more simple way with or without the loop function?!!! I would appreciate your help a lot.
2) Is there any code or any way to plot these selected parts (according to the grouping variable, e.g. data for Indi_1) from the previously mentioned big matrix without wasting a lot of time and space (wto recopying the core part of the code again and again) for the script, and using the loop function?! in other words, I would like to detect - with loop function & the grouping variable- which values are of interest and then to plot them (e.g. data in colum 3 with data from column 4 for each individual, starting from the first to the last)?!
I hope that I described my problem clearly and hope to hear something from the expert guys :) ...
Thanks a lot in advance ..
Try the following code:
for idx=1:80
pos=find(All_Indi_Data(:,1)==idx);
eval(['Indi_' num2str(idx) '=All_Indi_Data(pos,:);']);
end
What I do is: in each iteration, I search for a value of the ID, indicated in the variable idx. Note that I do not use ´i´ as the name of a variable, because Matlab uses it and ´j´ and the imaginary unit for complex numbers and that could cause problems.
Then, using find I search for the position (or positions) of All_Indi_Data in which I can find the information of that individual. Now I have in the variable ´pos´ the indexes of the rows in which there is information for the individual of interest.
Finally, using eval I extract the data for each individual into a variable. Note that eval combined with a loop makes it easy to create lots of variables. I indicate the rows I want to extract with ´pos´ and, as I want all the columns, I use just ´:´ (you could use ´1:21´ too).
With another similar loop you can plot the information you want. For example:
for idx=1:80
eval(['x=Indi_' num2str(idx) ';']);
% Now I have in X the information for this individual
%Plot the columns of x I want
plot(x(:, 3), x(:,4));
pause; %stay here until a press a key
end