I have a set of training data, each item in this set consists of 4 numerical values and 1 nominal-value which is the name of the method that these values have been calculated with. (There are 8 methods)
I'm training a Neural Network with these. To get rid of the nominal-value I simply assigned a value from 1 to 8 to each method and used one input to pass it to Neural Network and 4 other inputs for numerical-values. It is sort of working, but the result is not as amazing as I want.
So my question is could it be because of this simple assignment of numbers to nominal-values? or maybe it is because of mixing two different categories of inputs which are not really at the same level (numbers and method types)
Since you don't provide much detail, my answer can't be very specific.
Generally speaking neural networks tend to perform worse when coding nominal values as numeric values since the transformation will impose a (probably) false ordering on the variables. Mixing inputs with very varied levels also tend to worsen the performance.
However, given the little information provided here there is no way of telling if this is the reason that the networks performance is "not as amazing" as you want. It could just as well be the case that you don't have enough training data, or that your training data contains a lot of noise. Perhaps you need to pre-scale your data, perhaps there is an error in your network code, perhaps you have chosen ill-suited values of constants for your learning algorithm...
The reasons a neural network doesn't perform as expected are many and diverse (on of them beeing unreasonably high expectations). Without much more information there is no way of knowing what the problem is in your case.
As a general note, a better way for coding nominal values would be a binary vector. In your case, in addition to the 4 continuous-valued inputs, you'd have 8 binary input neurons, where only one is activated (1) and the other 7 are inactive.
The way you did it implies an artificial relationship between the computation methods, which is almost certainly an artifact. For example, 1 and 2 are numerically (and from your network's point of view!) nearer than 1 and 8. But are the methods nr. 1 and 2 really more similar, or related, than the methods 1 and 8?
Mapping categories to numerical values is not a good practice in statistics. Especially in the case of neural networks. Bear in mind that neural networks tend to map similar inputs to similar outputs. If you map category A to 1 and category B to 2 (both as inputs), the NN will try to output similar values for both categories, even if they have nothing to do with each other.
A sparser representation is preferred. If you have 4 categories, map them like this:
A -> 0001
B -> 0010
etc
Take a look at the "Subject: How should categories be encoded?" in this link: ftp://ftp.sas.com/pub/neural/FAQ2.html#A_cat
The previous answers are right - do not map nominal values into arbitrary numeric ones. However, if the attribute has an ordinal nature ("Low", "Medium", High" for example), you can replace the nominal values by ascending numeric values. Note that this may not be the optimal solution - since there is no guarantee for example that "High"=3 by the nature of your data. Instead, use one-hot bit encoding as suggested. The reason for this is that a neural network is very similar to regression in the sense that multiple numeric values go through some kind of an aggregating function - but this happens multiple times. Each input is also multiplied by a weight. So when you enter a numeric value, it undergoes a series of mathematical manipulations that adjusts its weights in the network. So if you use numeric values for non-nomial data - nominal values that were mapped to closer numeric values will be treated about the same in the best case, in the worst case - it can harm your model.
来源：https://stackoverflow.com/questions/9008174/nominal-value-inputs-for-neural-network