Although I'm not familiar with training (relational?) neural networks, I'm quite sure that your question can be answered reasonably only if you give an idea of the range of the continuous values to be discretized. A formal solution always is : discretize x to that of the discrete values to which it is closest. So in your case. x>0.5 goes to +1, x by >= and < by

A fast and safe way is using equal frequency.

Although I'm not familiar with training (relational?) neural networks, I'm quite sure that your question can be answered reasonably only if you give an idea of the range of the continuous values to be discretized. A formal solution always is : discretize x to that of the discrete values to which it is closest. So in your case. x>0.5 goes to +1, x by >= and < by

Like in the above answers I would suggest to use some thresholds Upper and Lower and classify your data as 1 if Data > Upper, 0 if Lower < Data < Upper and -1 if Data

Let's assume the frequency dentity of the values is a gaussian centered at 0. The problem boils down to find a threshold between 0 and 1, as a function of the standard deviation of the gaussian.

I'm thinking about Ulrich Mutze's suggestion. I'm not sure how accurate the net will be after discretization but I guess there may be a substantial reduction. So instead of a sudden discretization maybe you could construct a function with a parameter lambda that is

(1) f(x, lambda) = x 　for lambda=0 and

(2) f(x, lambda) = Ulrich's discretization 　for lambda->infinity, and

(3) a "smoothed step function" 　for lambda>0.

Then you could continuously train your network while slowly increasing the lambda. This will have discrete weights at the end, and may be optimal (or at least better than a "sudden" discretization), too. This is just an idea, I hope it helps.

If the original continuous values are in the interval [a, b], then you can do a mapping of this interval to the interval [-3/2 ; 3/2] which then can be conveniently subdivided in three parts of equal length 1.

Values between -3/2 and -1/2 will go to the class -1

Values between -1/2 and 1/2 will go to the class 0

Values between 1/2 and 3/2 will go to the class 1

In other words, the class becomes the center of the subdivision.

You are essentially trying to map a continuous variable to the three discrete values -1,0,+1 ? One way would be to define a threshold value V, and measure the candidate value. You can assign a -1, 0, or +1 depending one whether the candiadte is less than, equal to, or greater than the threshold. This is of course not reversible, i.e. you cant get back the actual value of the candidate, from the discretised values. Does this suit your end application (RNN) ?

You could also train a network with three output values, [1 0 0 ] for 0, [0 1 0 ] for 1 etc and take the max output. Discrete outputs means it's essentially a classification problem. Not necessarily better than a simple threshold though.

If you consider a continuous function on in interval then the mean value of that function you will get by integral of this function divided by its length. After that you can use rounding method like Mutze has suggested.

And what about clustering your data ? use kmeans or any clustering algorithm that requiere the number of cluster to be given and use 3 as cluster number. Then the cluster with the center closest to -1 become -1, the one closest to 0 become 0 and so on...

.

Hello,

if your final goal is to have a trained RNN with weights values in {-1, 0, 1}, you might consider training your RNN with an additional term in the cost function "mildly punishing" weight values away from this set (some kind of regularization, except that you have tree poles for the regularizer instead of only one ({0}) as usual) and increase this term at the end of the training ("annealing").

Yes, you get a handful of additional parameters to set to implement that ...

.

You can use the 1st, 2nd and 3rth quartile.

Thank you all for your valuable inputs & insights.

Hello, for this type of coding I suggest you use the method of coding threshold. In this case you should set two threshold values​​. Upper one (Vt) and a lower (Vl), with these values ​​pudes encode data as follows:

if x>Vt then

c=1;

else if x< Vl then

c=-1

else

c=0;

end

where x are the data analog c the encoded data

The problem You described, is how to divide set of attributes to three buckets – defeat, draw, win. There are some methods to do that.

Naive - based on equal interval length or equal number. First divided whole range into parts of equal length.

Length=(umin-umax)/n in your case n=3

with bounds

Have a look at this software:

http://cgi.csc.liv.ac.uk/~frans/KDD/Software/LUCS-KDD-DN/lucs-kdd_DN.html

It does a smart analysis of the data to take into account distributions.

"instead of dividing the range into equally sized divisions the range was divided so as the take account of the probability that a particular value was associated with a particular class"

You just have to quantize it depending on your application . Decide on the thresholds and form three groups for the three discrete values you have, they dont have to be equisized, dependents on the data and the application.

I would also recommend you the Fayyad and Irani method if you have a target/response variable that is discrete. But if your target variable in not discrete, you can use the method by discretizing the target variable using expert knowledge or equal frequency. If you wish something more in the line of Fayyad and Irani method, then, sorry for the self-citing, but I developed myself a method to use Fayyad method when the target variable is continuous:

https://www.researchgate.net/publication/215739042_Fish_recruitment_prediction_using_robust_supervised_classification_methods?ev=prf_pub

You can download a Java implementation from:

http://www.sc.ehu.es/ccwbayes/members/jafernandes/

About the method of Fayyad and Irani you have it implemented in WEKA:

http://www.cs.waikato.ac.nz/ml/weka/

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