I have been using the patternnet classifier to classify between 2 different classes - labeled 0, 1.
I'm trying to use MATLAB to generate Roc Curve graphs for some data produced using patternnet but I am having trouble understanding the parameters it needs to run.
[xTr, yTr, TTr, aucTr] = perfcurve(t, results.Data.y, 1);
I assume that:
t is the vector of labels generated that states into which class my data belongs (mine consists of 0 and 1 and is 2x834 in size)
scores is the variable created by patternnet called ‘results.Data.y' (2x834 in size)
posclass is 1.
But scores should be a vector (1x834 in size) and I don't know which row to choose?
Detail about the perfcurve function is available here :
http://in.mathworks.com/help/stats/perfcurve.html
The examples are pretty helpful.
Regarding your specific case, t is not the predicted vector, but the vector you create yourself to label your test data, which obviously would be 1xn (where n = 834 for your case.)
Your score matrix would be m*n, where m is the number of classes in your data (which is 2 for your case).
Since you're saying 1 is your positive class, you'll chose the column which contains the score of your positive class.
Something like :
[xTr, yTr, TTr, aucTr] = perfcurve(t, results.Data.y(:,1), 1);
plot(xTr, yTr);
Related
Greetins,
How can I calculate how many distance calculations would need to be performed to classify the IRIS dataset using Nearest Mean Classifier.
I know that IRIS dataset has 4 features and every record is classified according to 3 different labels.
According to some textbooks, the calculation can be carried out as follow:
However, I am lost on these different notations and what does this equation mean. For example, what is s^2 is in the equation?
The notation is standard with most machine learning textbooks. s in this case is the sample standard deviation for the training set. It is quite common to assume that each class has the same standard deviation, which is why every class is assigned the same value.
However you shouldn't be paying attention to that. The most important point is when the priors are equal. This is a fair assumption which means that you expect that the distribution of each class in your dataset are roughly equal. By doing this, the classifier simply boils down to finding the smallest distance from a training sample x to each of the other classes represented by their mean vectors.
How you'd compute this is quite simple. In your training set, you have a set of training examples with each example belonging to a particular class. For the case of the iris dataset, you have three classes. You find the mean feature vector for each class, which would be stored as m1, m2 and m3 respectively. After, to classify a new feature vector, simply find the smallest distance from this vector to each of the mean vectors. Whichever one has the smallest distance is the class you'd assign.
Since you chose MATLAB as the language, allow me to demonstrate with the actual iris dataset.
load fisheriris; % Load iris dataset
[~,~,id] = unique(species); % Assign for each example a unique ID
means = zeros(3, 4); % Store the mean vectors for each class
for i = 1 : 3 % Find the mean vectors per class
means(i,:) = mean(meas(id == i, :), 1); % Find the mean vector for class 1
end
x = meas(10, :); % Choose a random row from the dataset
% Determine which class has the smallest distance and thus figure out the class
[~,c] = min(sum(bsxfun(#minus, x, means).^2, 2));
The code is fairly straight forward. Load in the dataset and since the labels are in a cell array, it's handy to create a new set of labels that are enumerated as 1, 2 and 3 so that it's easy to isolate out the training examples per class and compute their mean vectors. That's what's happening in the for loop. Once that's done, I choose a random data point from the training set then compute the distance from this point to each of the mean vectors. We choose the class that gives us the smallest distance.
If you wanted to do this for the entire dataset, you can but that will require some permutation of the dimensions to do so.
data = permute(meas, [1 3 2]);
means_p = permute(means, [3 1 2]);
P = sum(bsxfun(#minus, data, means_p).^2, 3);
[~,c] = min(P, [], 2);
data and means_p are the transformed features and mean vectors in a way that is a 3D matrix with a singleton dimension. The third line of code computes the distances vectorized so that it finally generates a 2D matrix with each row i calculating the distance from the training example i to each of the mean vectors. We finally find the class with the smallest distance for each example.
To get a sense of the accuracy, we can simply compute the fraction of the total number of times we classified correctly:
>> sum(c == id) / numel(id)
ans =
0.9267
With this simple nearest mean classifier, we have an accuracy of 92.67%... not bad, but you can do better. Finally, to answer your question, you would need K * d distance calculations, with K being the number of examples and d being the number of classes. You can clearly see that this is required by examining the logic and code above.
Can anyone help me to understand how can I extract features from an image using Partial least squares (PLS) regression function "plsregress()" in Matlab?
Before this, I have used PCA function in Matlab "princomp()" to extract features from the image, what I have understood is, for example if we have 20 images, each one 50×50pixels. The first step is
(1) construct the input matrix, where each row represent one image, that is mean the size of the input matrix is [20 , 50×50] = [20,2500].
(2) when we call the pca() in matlab we get:
[eigenvectors score variances] = princomp(inputMatrix);
the eigenvectors which represent the Principle components' coefficients (features) , the score of the Principal components and the variances (eigenvalues) of each principal component.
(3) To construct the dataset in the test stage, I have used the a test dataset which is a matrix consist of one image, its size is [50,50] and I have used the principal components ( eigenvectors) with the higher variances (for example the first 5 components) to reconstruct the dataset.
First, I have used this equation to calculate the score of test dataset
test_score = test_dataset * eigenvalues(: ,1:5);
newtest_data = test_score * eigenvalues(:, 1:5)' ; // reconstructing dataset using 5 PCs.
My question is, how can I perform same steps but by using Partial Least Square (PLS) regression?
I have been using the LibSVM classifier to classify between 3 different classes - labeled 2, 1, -1
I'm trying to use MATLAB to generate Roc Curve graphs for some data produced using LibSVM but am having trouble understanding the parameters it needs to run.
I assume that:
labels is the vector of labels generated that states into which class my data belongs (mine consists on 1, -1 and 2 and is 60x1 in size)
scores is the variable created by LibSVM called 'accuracy_score' (60x3 in size)
But I don't know what posclass is?
I would also appreciate finding out if my assumptions are correct, and if not, why not?
See here for a clear explanation:
Given the following instruction:
[X,Y] = perfcurve(labels,scores,posclass);
labels are the true labels of the data, scores are the output scores from your classifier (before the threshold) and posclass is the positive class in your labels.
see documentation of percurve, posclass is the label of positive class, in your case it has to be either 1,-1 or 2
http://www.mathworks.com/help/stats/perfcurve.html
ROC curve have "false positive rate" on x axis and "true positive rate on y axis". By specifying the posclass, you are specifying with respect to which class you are calculating false positive rate and true positive rate.
e.g. if you specify posclass as 2, you consider that when the true label is 2, predicting either 1 or -1 is considered a false prediction (false negative).
Edit:
The accuaracy_score you metioned (in my version of the documentation(3.17, in matlab folder), it is called decision_values/prob_estimates) have 3 column, each column correspond to the probability of the data belonging to one class.
e.g.
model=svmtrain(train_label,train_data);
[predicted_label, accuracy, decision_values]=predict(test_label,test_dat,model);
model.Label contains the class labels, individual columns in decision_values contains probability of the the test case belong to class specified in model.Label.(see http://www.csie.ntu.edu.tw/~b91082/SVM/README).
to use purfcurve to compute ROC for class m:
[X,Y] = perfcurve(truelabels, decision_values(:,m)*model.Label(m),model.Label(m));
It is essential to do decision_values(:,m)*model.Label(m) especially when you class label is a negative number.
I'm working on doing a logistic regression using MATLAB for a simple classification problem. My covariate is one continuous variable ranging between 0 and 1, while my categorical response is a binary variable of 0 (incorrect) or 1 (correct).
I'm looking to run a logistic regression to establish a predictor that would output the probability of some input observation (e.g. the continuous variable as described above) being correct or incorrect. Although this is a fairly simple scenario, I'm having some trouble running this in MATLAB.
My approach is as follows: I have one column vector X that contains the values of the continuous variable, and another equally-sized column vector Y that contains the known classification of each value of X (e.g. 0 or 1). I'm using the following code:
[b,dev,stats] = glmfit(X,Y,'binomial','link','logit');
However, this gives me nonsensical results with a p = 1.000, coefficients (b) that are extremely high (-650.5, 1320.1), and associated standard error values on the order of 1e6.
I then tried using an additional parameter to specify the size of my binomial sample:
glm = GeneralizedLinearModel.fit(X,Y,'distr','binomial','BinomialSize',size(Y,1));
This gave me results that were more in line with what I expected. I extracted the coefficients, used glmval to create estimates (Y_fit = glmval(b,[0:0.01:1],'logit');), and created an array for the fitting (X_fit = linspace(0,1)). When I overlaid the plots of the original data and the model using figure, plot(X,Y,'o',X_fit,Y_fit'-'), the resulting plot of the model essentially looked like the lower 1/4th of the 'S' shaped plot that is typical with logistic regression plots.
My questions are as follows:
1) Why did my use of glmfit give strange results?
2) How should I go about addressing my initial question: given some input value, what's the probability that its classification is correct?
3) How do I get confidence intervals for my model parameters? glmval should be able to input the stats output from glmfit, but my use of glmfit is not giving correct results.
Any comments and input would be very useful, thanks!
UPDATE (3/18/14)
I found that mnrval seems to give reasonable results. I can use [b_fit,dev,stats] = mnrfit(X,Y+1); where Y+1 simply makes my binary classifier into a nominal one.
I can loop through [pihat,lower,upper] = mnrval(b_fit,loopVal(ii),stats); to get various pihat probability values, where loopVal = linspace(0,1) or some appropriate input range and `ii = 1:length(loopVal)'.
The stats parameter has a great correlation coefficient (0.9973), but the p values for b_fit are 0.0847 and 0.0845, which I'm not quite sure how to interpret. Any thoughts? Also, why would mrnfit work over glmfit in my example? I should note that the p-values for the coefficients when using GeneralizedLinearModel.fit were both p<<0.001, and the coefficient estimates were quite different as well.
Finally, how does one interpret the dev output from the mnrfit function? The MATLAB document states that it is "the deviance of the fit at the solution vector. The deviance is a generalization of the residual sum of squares." Is this useful as a stand-alone value, or is this only compared to dev values from other models?
It sounds like your data may be linearly separable. In short, that means since your input data is one dimensional, that there is some value of x such that all values of x < xDiv belong to one class (say y = 0) and all values of x > xDiv belong to the other class (y = 1).
If your data were two-dimensional this means you could draw a line through your two-dimensional space X such that all instances of a particular class are on one side of the line.
This is bad news for logistic regression (LR) as LR isn't really meant to deal with problems where the data are linearly separable.
Logistic regression is trying to fit a function of the following form:
This will only return values of y = 0 or y = 1 when the expression within the exponential in the denominator is at negative infinity or infinity.
Now, because your data is linearly separable, and Matlab's LR function attempts to find a maximum likelihood fit for the data, you will get extreme weight values.
This isn't necessarily a solution, but try flipping the labels on just one of your data points (so for some index t where y(t) == 0 set y(t) = 1). This will cause your data to no longer be linearly separable and the learned weight values will be dragged dramatically closer to zero.
I write a classifier (Gaussian Mixture Model) to classify five human actions. For every observation the classifier compute the posterior probability to belong to a cluster.
I want to valutate the performance of my system parameterized with a threshold, with values from 0 to 100. For every threshold values, for every observation, if the probability of belonging to one of cluster is greater than threshold I accept the result of the classifier otherwise I discard it.
For every threshold values I compute the number of true-positive, true-negative, false-positive, false-negative.
Than I compute the two function: sensitivity and specificity as
sensitivity = TP/(TP+FN);
specificity=TN/(TN+FP);
In matlab:
plot(1-specificity,sensitivity);
to have the ROC curve. But the result isn't what I expect.
This is the plot of the functions of discards, errors, corrects, sensitivity and specificity varying the threshold of one action.
This is the plot of ROC curve of one action
This is the stem of ROC curve for the same action
I am wrong, but i don't know where. Perhaps I do wrong the calculating of FP, FN, TP, TN especially when the result of the classifier is minor of the threshold, so I have a discard. What I have to incremente when there is a discard?
Background
I am answering this because I need to work through the content, and a question like this is a great excuse. Thank you for the good opportunity.
I use data from the built-in fisher iris data:
http://archive.ics.uci.edu/ml/datasets/Iris
I also use code snippets from the Mathworks tutorial on the classification, and for plotroc
http://www.mathworks.com/products/demos/statistics/classdemo.html
http://www.mathworks.com/help/nnet/ref/plotroc.html?searchHighlight=plotroc
Problem Description
There is clearer boundary within the domain to classify "setosa" but there is overlap for "versicoloir" vs. "virginica". This is a two dimensional plot, and some of the other information has been discarded to produce it. The ambiguity in the classification boundaries is a useful thing in this case.
%load data
load fisheriris
%show raw data
figure(1); clf
gscatter(meas(:,1), meas(:,2), species,'rgb','osd');
xlabel('Sepal length');
ylabel('Sepal width');
axis equal
axis tight
title('Raw Data')
Analysis
Lets say that we want to determine the bounds for a linear classifier that defines "virginica" versus "non-virginica". We could look at "self vs. not-self" for other classes, but they would have their own
So now we make some linear discriminants and plot the ROC for them:
%load data
load fisheriris
load iris_dataset
irisInputs=meas(:,1:2)';
irisTargets=irisTargets(3,:);
ldaClass1 = classify(meas(:,1:2),meas(:,1:2),irisTargets,'linear')';
ldaClass2 = classify(meas(:,1:2),meas(:,1:2),irisTargets,'diaglinear')';
ldaClass3 = classify(meas(:,1:2),meas(:,1:2),irisTargets,'quadratic')';
ldaClass4 = classify(meas(:,1:2),meas(:,1:2),irisTargets,'diagquadratic')';
ldaClass5 = classify(meas(:,1:2),meas(:,1:2),irisTargets,'mahalanobis')';
myinput=repmat(irisTargets,5,1);
myoutput=[ldaClass1;ldaClass2;ldaClass3;ldaClass4;ldaClass5];
whos
plotroc(myinput,myoutput)
The result is shown in the following, though it took deleting repeat copies of the diagonal:
You can note in the code that I stack "myinput" and "myoutput" and feed them as inputs into the "plotroc" function. You should take the results of your classifier as targets and actuals and you can get similar results. This compares the actual output of your classifier versus the ideal output of your target values. Those are the input to plotroc.
So this will give you "built-in" ROC, which is useful for quick work, but does not make you learn every step in detail.
Questions you can ask at this point include:
which classifier is best? How do I determine what best is in this case?
What is the convex hull of the classifiers? Is there some mixture of classifiers that is more informative than any pure method? Bagging perhaps?
You are trying to draw the curves of precision vs recall, depending on the classifier threshold parameter. The definition of precision and recall are:
Precision = TP/(TP+FP)
Recall = TP/(TP+FN)
You can check the definition of these parameters in:
http://en.wikipedia.org/wiki/Precision_and_recall
There are some curves here:
http://www.cs.cornell.edu/courses/cs578/2003fa/performance_measures.pdf
Are you dividing your dataset in training set, cross validation set and test set? (if you do not divide the data, it is normal that your precision-recall curve seems weird)
EDITED: I think that there are two possible sources for your problem:
When you train a classifier for 5 classes, usually you have to train 5 distinctive classifiers. One classifier for (class A = class 1, class B = class 2, 3, 4 or 5), then a second classfier for (class A = class 2, class B = class 1, 3, 4 or 5), ... and the fifth for class A = class 5, class B = class 1, 2, 3 or 4).
As you said to select the output for your "compound" classifier, you have to pass your new (test) datapoint through the five classifiers, and you choose the one with the biggest probability.
Then, you should have 5 thresholds to define weighting values that my prioritize selecting one classifier over the others. You should check how the matlab implementations uses the thresholds, but their effect is that you don't choose the class with more probability, but the class with better weighted probability.
As you say, maybe you are not calculating well TP, TN, FP, FN. Your test data should have datapoints belonging to all the classes. Then you have testdata(i,:) and classtestdata(i) are the feature vector and "ground truth" class of datapoint i. When you evaluate the classifier you obtain classifierOutput(i) = 1 or 2 or 3 or 4 or 5. Then you should calculate the "confusion matrix", which is the way to calculate TP, TN, FP, FN when you have multiple classes (> 2):
http://en.wikipedia.org/wiki/Confusion_matrix
http://www.mathworks.com/help/stats/confusionmat.html
(note the relation between TP, TN, FP, FN that you are calculating for the multiclass problem)
I think that you can obtain the TP, TN, FP, FN data of each subclassifier (remember that you are calculating 5 separate classifiers, even if you do not realize it) from the confusion matrix. I am not sure but you can draw the precision recall curve for each subclassifier.
Also check these slides: http://www.slideserve.com/MikeCarlo/multi-class-and-structured-classification
I don't know what the ROC curve is, I will check it because machine learning is a really interesting subject for me.
Hope this helps,