General Linear model analysis is usually done for fMRI data. I have applied the same analysis to MRI data and found the clusters which are linearly related to columns of behavioral scores(design matrix). I wanted to know if this analysis will give me the correct results or not. Please let me know if anyone has an idea about it, I can share more required information.
I am doing this clustering so that I can find the interesting regions in the brain MRI to create a mask and then pass it to CNN for better classification results.
I'm trying to get a better understanding of neural networks by trying to programm a Convolution Neural Network by myself.
So far, I'm going to make it pretty simple by not using max-pooling and using simple ReLu-activation. I'm aware of the disadvantages of this setup, but the point is not making the best image detector in the world.
Now, I'm stuck understanding the details of the error calculation, propagating it back and how it interplays with the used activation-function for calculating the new weights.
I read this document (A Beginner's Guide To Understand CNN), but it doesn't help me understand much. The formula for calculating the error already confuses me.
This sum-function doesn't have defined start- and ending points, so i basically can't read it. Maybe you can simply provide me with the correct one?
After that, the author assumes a variable L that is just "that value" (i assume he means E_total?) and gives an example for how to define the new weight:
where W is the weights of a particular layer.
This confuses me, as i always stood under the impression the activation-function (ReLu in my case) played a role in how to calculate the new weight. Also, this seems to imply i simply use the error for all layers. Doesn't the error value i propagate back into the next layer somehow depends on what i calculated in the previous one?
Maybe all of this is just uncomplete and you can point me into the direction that helps me best for my case.
Thanks in advance.
You do not backpropagate errors, but gradients. The activation function plays a role in caculating the new weight, depending on whether or not the weight in question is before or after said activation, and whether or not it is connected. If a weight w is after your non-linearity layer f, then the gradient dL/dw wont depend on f. But if w is before f, then, if they are connected, then dL/dw will depend on f. For example, suppose w is the weight vector of a fully connected layer, and assume that f directly follows this layer. Then,
dL/dw=(dL/df)*df/dw //notations might change according to the shape
//of the tensors/matrices/vectors you chose, but
//this is just the chain rule
As for your cost function, it is correct. Many people write these formulas in this non-formal style so that you get the idea, but that you can adapt it to your own tensor shapes. By the way, this sort of MSE function is better suited to continous label spaces. You might want to use softmax or an svm loss for image classification (I'll come back to that). Anyway, as you requested a correct form for this function, here is an example. Imagine you have a neural network that predicts a vector field of some kind (like surface normals). Assume that it takes a 2d pixel x_i and predicts a 3d vector v_i for that pixel. Now, in your training data, x_i will already have a ground truth 3d vector (i.e label), that we'll call y_i. Then, your cost function will be (the index i runs on all data samples):
sum_i{(y_i-v_i)^t (y_i-vi)}=sum_i{||y_i-v_i||^2}
But as I said, this cost function works if the labels form a continuous space (here , R^3). This is also called a regression problem.
Here's an example if you are interested in (image) classification. I'll explain it with a softmax loss, the intuition for other losses is more or less similar. Assume we have n classes, and imagine that in your training set, for each data point x_i, you have a label c_i that indicates the correct class. Now, your neural network should produce scores for each possible label, that we'll note s_1,..,s_n. Let's note the score of the correct class of a training sample x_i as s_{c_i}. Now, if we use a softmax function, the intuition is to transform the scores into a probability distribution, and maximise the probability of the correct classes. That is , we maximse the function
sum_i { exp(s_{c_i}) / sum_j(exp(s_j))}
where i runs over all training samples, and j=1,..n on all class labels.
Finally, I don't think the guide you are reading is a good starting point. I recommend this excellent course instead (essentially the Andrew Karpathy parts at least).
I am training a CNN for predicting joints on hands. The problem is that my net always converges to the mean value of the training set, and I can only get identical results for different test images. Do you know how to prevent this?
I think you must be using the MSECriterion()? It is the standard l2 (minimum square error) loss. While the CNN tries to predict results, there are multiple modes through which the result can be correct. And what l2 loss does is that it converges to an average of all these modes as that is the most feasible way it can intuitively approach to attain less-penalized results.
The MSE-based solution
appears overly smooth due to the pixel-wise average of
possible solutions in the pixel space
To pick the optimum mode of answer, you can look into adversarial loss LINK. This loss picks the optimum mode based on what it thinks is realistic in terms of the data it has seen.
For further clarification, look at figure 3 in this paper: SRGAN
I was using tensorflow. Was trying to do some regression using simple CNN with one neuron in output layer. Was optimizing mean square error:
cost = tf.reduce_mean(tf.abs(y_prediction - y_output_placeholder))
optimizer = tf.train.AdamOptimizer(learning_rate=LEARNING_RATE).minimize(cost)
My problem was I made output placeholder of true values with different shape than output predictions of the net.
placeholder's shape was [None]
predictions's shape was [None, 1].
When I changed placeholder's shape to match the one of prediction output problem was solved.
i wanna use SOM toolbox (http://www.cis.hut.fi/somtoolbox/theory/somalgorithm.shtml) for predicting missing values or outliers . but i can't find any function for it.
i wrote a code for visualizaition and getting BMU(Best maching unit) but i'don't know how to use it in prediction. could you help me?
thank you in advance .
If still interests you here goes one solution.
Train your network with a training set with all the inputs that you will further on analyze. After learning, you give the new test data to classify with only the inputs that you have. The network give you back which was the best matching unit (for the features you have), and with this you can access to which of the features you do not have/outliers the BMU corresponds to.
This of course leads to a different learning and prediction implementation. The learning you implement straightforward as suggested in many tutorials. The prediction you need to make the SOM ignore NaN and calculate the BMU based on only the other values. After that, with the BMU you can get the corresponding features and use that to predict missing values or outliers.
I have 50 images and created a database of the green channel of each image by separating them into two classes (Skin and wound) and storing the their respective green channel value.
Also, I have 1600 wound pixel values and 3000 skin pixel values.
Now I have to use bayes classification in matlab to classify the skin and wound pixels in a new (test) image using the data base that I have. I have tried the in-built command diaglinear but results are poor resulting in lot of misclassification.
Also, I dont know if it's a normal distribution or not so can't use gaussian estimation for finding the conditional probability density function for the data.
Is there any way to perform pixel wise classification?
If there is any part of the question that is unclear, please ask.
I'm looking for help. Thanks in advance.
If you realy want to use pixel wise classification (quite simple, but why not?) try exploring pixel value distributions with hist()/imhist(). It might give you a clue about a gaussianity...
Second, you might fit your values to the some appropriate curves (gaussians?) manually with fit() if you have curve fitting toolbox (or again do it manualy). Then multiply the curves by probabilities of the wound/skin if you like it to be MAP classifier, and finally find their intersection. Voela! you have your descition value V.
if Xi skin
else -> wound