Can I compute the function f(x) = sqr(x) using opencv ANN ?
I need to train my ann by using set of integers and their square values.
I need to get squared value of a integer as output from ann model.
If we can do that using opencv ann, what will be the number input neurons, output neurons and how to specify the classes etc.. ??
You mention class specification, but I don't think that this is a class categorization problem. I think it would be better to treat the input as X, and the output as sqr(X). Then this becomes a general function approximation problem.
There is an issue with this particular problem however. Neural networks aren't well suited for functions with unbounded input/output. The output of a neural network is usually limited to the range of its activation function, and the input value is usually scaled to some reasonable range. Assuming you are using the default activation (symmetrical sigmoid), your output is limited to (-1, 1). If you have a limited range of integers you want to use, you can still do this, but you'll have to scale the inputs and outputs accordingly.
If you use this method, there will be one input node, and one output node, corresponding to the scaled versions of X and sqr(X) respectively. OpenCV will try to take care of scaling for you automatically. It's probably best for you to trust this, UNLESS you are planning on providing multiple different sets of training data. The different sets may have different distributions, hence a different scale.
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I am creating an ANN which has 3 input neurons which take inputs from the device "s accelerometer in the form of x , y , z. These values are positive as well as negative depending upon the acceleration. I am not able to get an suitable activation to normalize these values. Also , I am not getting desired predictions. Any help will be valuable. :-)
You should normalize your data before. I would advise using standard score, which looks as following:
collect training sets for each of the input variables
calculate mean (m) and standard deviation (std) for each of the sets
normalize as (x-m)/z
If you are working on a regression problem, don't forget to normalize target values as well.
you can also use other normalization techniques if you think they would work better for your case. Some of them you can see here.
Choice of the activation function, in this case, should not affect much, you can just play with different types and see which results in a better performance.
I'm currently working on a classification problem with tensorflow, and i'm new to the world of machine learning, but I don't get something.
I have successfully tried to train models that output the y tensor like this:
y = [0,0,1,0]
But I can't understand the principal behind it...
Why not just train the same model to output classes such as y = 3 or y = 4
This seems much more flexible, because I can imagine having a multi-classification problem with 2 million possible classes, and it would be much more efficient to output a number between 0-2,000,000 than to output a tensor of 2,000,000 items for every result.
What am I missing?
Ideally, you could train you model to classify input instances and producing a single output. Something like
y=1 means input=dog, y=2 means input=airplane. An approach like that, however, brings a lot of problems:
How do I interpret the output y=1.5?
Why I'm trying the regress a number like I'm working with continuous data while I'm, in reality, working with discrete data?
In fact, what are you doing is treating a multi-class classification problem like a regression problem.
This is locally wrong (unless you're doing binary classification, in that case, a positive and a negative output are everything you need).
To avoid these (and other) issues, we use a final layer of neurons and we associate an high-activation to the right class.
The one-hot encoding represents the fact that you want to force your network to have a single high-activation output when a certain input is present.
This, every input=dog will have 1, 0, 0 as output and so on.
In this way, you're correctly treating a discrete classification problem, producing a discrete output and well interpretable (in fact you'll always extract the output neuron with the highest activation using tf.argmax, even though your network hasn't learned to produce the perfect one-hot encoding you'll be able to extract without doubt the most likely correct output )
The answer is in how that final tensor, or single value, are calculated. In an NN, your y=3 would be build by a weighted sum over the values of the previous layer.
Trying to train towards single values would then imply a linear relationship between the category IDs where none exists: For the true value y=4, the output y=3 would be considered better than y=1 even though the categories are random, and may be 1: dogs, 3: cars, 4: cats
Neural networks use gradient descent to optimize a loss function. In turn, this loss function needs to be differentiable.
A discrete output would be (indeed is) a perfectly valid and valuable output for a classification network. Problem is, we don't know how to optimize this net efficiently.
Instead, we rely on a continuous loss function. This loss function is usually based on something that is more or less related to the probability of each label -- and for this, you need a network output that has one value per label.
Typically, the output that you describe is then deduced from this soft, continuous output by taking the argmax of these pseudo-probabilities.
I am using word2vec model for training a neural network and building a neural embedding for finding the similar words on the vector space. But my question is about dimensions in the word and context embeddings (matrices), which we initialise them by random numbers(vectors) at the beginning of the training, like this https://iksinc.wordpress.com/2015/04/13/words-as-vectors/
Lets say we want to display {book,paper,notebook,novel} words on a graph, first of all we should build a matrix with this dimensions 4x2 or 4x3 or 4x4 etc, I know the first dimension of the matrix its the size of our vocabulary |v|. But the second dimension of the matrix (number of vector's dimensions), for example this is a vector for word “book" [0.3,0.01,0.04], what are these numbers? do they have any meaning? for example the 0.3 number related to the relation between word “book" and “paper” in the vocabulary, the 0.01 is the relation between book and notebook, etc.
Just like TF-IDF, or Co-Occurence matrices that each dimension (column) Y has a meaning - its a word or document related to the word in row X.
The word2vec model uses a network architecture to represent the input word(s) and most likely associated output word(s).
Assuming there is one hidden layer (as in the example linked in the question), the two matrices introduced represent the weights and biases that allow the network to compute its internal representation of the function mapping the input vector (e.g. “cat” in the linked example) to the output vector (e.g. “climbed”).
The weights of the network are a sub-symbolic representation of the mapping between the input and the output – any single weight doesn’t necessarily represent anything meaningful on its own. It’s the connection weights between all units (i.e. the interactions of all the weights) in the network that gives rise to the network’s representation of the function mapping. This is why neural networks are often referred to as “black box” models – it can be very difficult to interpret why they make particular decisions and how they learn. As such, it's very difficult to say what the vector [0.3,0.01,0.04] represents exactly.
Network weights are traditionally initialised to random values for two main reasons:
It prevents a bias being introduced to the model before training begins
It allows the network to start from different points in the search space after initialisation (helping reduce the impact of local minima)
A network’s ability to learn can be very sensitive to the way its weights are initialised. There are more advanced ways of initialising weights today e.g. this paper (see section: Weights initialization scaling coefficient).
The way in which weights are initialised and the dimension of the hidden layer are often referred to as hyper-parameters and are typically chosen according to heuristics and prior knowledge of the problem space.
I have wondered the same thing and put in a vector like (1 0 0 0 0 0...) to see what terms it was nearest to. The answer is that the results returned didn't seem to cluster around any particular meaning, but were just kind of random. This was using Mikolov's 300-dimensional vectors trained on Google News.
Look up NNSE semantic vectors for a vector space where the individual dimensions do seem to carry specific human-graspable meanings.
I need help in figuring out a suitable activation function. Im training my neural network to detect a piano note. So in this case I can have only one output. Either the note is there (1) or the note is not present (0).
Say I introduce a threshold value of 0.5 and say that if the output is greater than 0.5 the desired note is present and if its less than 0.5 the note isn't present, what type of activation function can I use. I assume it should be hard limit, but I'm wondering if sigmoid can also be used.
To exploit their full power, neural networks require continuous, differentable activation functions. Thresholding is not a good choice for multilayer neural networks. Sigmoid is quite generic function, which can be applied in most of the cases. When you are doing a binary classification (0/1 values), the most common approach is to define one output neuron, and simply choose a class 1 iff its output is bigger than a threshold (typically 0.5).
EDIT
As you are working with quite simple data (two input dimensions and two output classes) it seems a best option to actually abandon neural networks and start with data visualization. 2d data can be simply plotted on the plane (with different colors for different classes). Once you do it, you can investigate how hard is it to separate one class from another. If data is located in the way, that you can simply put a line separating them - linear support vector machine would be much better choice (as it will guarantee one global optimum). If data seems really complex, and the decision boundary has to be some curve (or even set of curves) I would suggest going for RBF SVM, or at least regularized form of neural network (so its training is at least quite repeatable). If you decide on neural network - situation is quite similar - if data is simply to separate on the plane - you can use simple (linear/threshold) activation functions. If it is not linearly separable - use sigmoid or hyperbolic tangent which will ensure non linearity in the decision boundary.
UPDATE
Many things changed through last two years. In particular (as suggested in the comment, #Ulysee) there is a growing interest in functions differentable "almost everywhere" such as ReLU. These functions have valid derivative in most of its domain, so the probability that we will ever need to derivate in these point is zero. Consequently, we can still use classical methods and for sake of completness put a zero derivative if we need to compute ReLU'(0). There are also fully differentiable approximations of ReLU, such as softplus function
The wikipedia article has some useful "soft" continuous threshold functions - see Figure Gjl-t(x).svg.
en.wikipedia.org/wiki/Sigmoid_function.
Following Occam's Razor, the simpler model using one output node is a good starting point for binary classification, where one class label is mapped to the output node when activated, and the other class label for when the output node is not activated.
I am trying to pre-process biological data to train a neural network and despite an extensive search and repetitive presentation of the various normalization methods I am none the wiser as to which method should be used when. In particular I have a number of input variables which are positively skewed and have been trying to establish whether there is a normalisation method that is most appropriate.
I was also worried about whether the nature of these inputs would affect performance of the network and as such have experimented with data transformations (log transformation in particular). However some inputs have many zeros but may also be small decimal values and seem to be highly affected by a log(x + 1) (or any number from 1 to 0.0000001 for that matter) with the resulting distribution failing to approach normal (either remains skewed or becomes bimodal with a sharp peak at the min value).
Is any of this relevant to neural networks? ie. should I be using specific feature transformation / normalization methods to account for the skewed data or should I just ignore it and pick a normalization method and push ahead?
Any advice on the matter would be greatly appreciated!
Thanks!
As features in your input vector are of different nature, you should use different normalization algorithms for every feature. Network should be feeded by uniformed data on every input for better performance.
As you wrote that some data is skewed, I suppose you can run some algoritm to "normalize" it. If applying logarithm does not work, perhaps other functions and methods such as rank transforms can be tried out.
If the small decimal values do entirely occur in a specific feature, then just normalize it in specific way, so that they get transformed into your work range: either [0, 1] or [-1, +1] I suppose.
If some inputs have many zeros, consider removing them from main neural network, and create additional neural network which will operate on vectors with non-zeroed features. Alternatively, you may try to run Principal Component Analysis (for example, via Autoassociative memory network with structure N-M-N, M < N) to reduce input space dimension and so eliminate zeroed components (they will be actually taken into account in the new combined inputs somehow). BTW, new M inputs will be automatically normalized. Then you can pass new vectors to your actual worker neural network.
This is an interesting question. Normalization is meant to keep features' values in one scale to facilitate the optimization process.
I would suggest the following:
1- Check if you need to normalize your data. If, for example, the means of the variables or features are within same scale of values, you may progress with no normalization. MSVMpack uses some normalization check condition for their SVM implementation. If, however, you need to do so, you are still advised to run the models on the data without Normalization.
2- If you know the actual maximum or minimum values of a feature, use them to normalize the feature. I think this kind of normalization would preserve the skewedness in values.
3- Try decimal value normalization with other features if applicable.
Finally, you are still advised to apply different normalization techniques and compare the MSE for evey technique including z-score which may harm the skewedness of your data.
I hope that I have answered your question and gave some support.