I have set of data, which consist of continuous variables and categorical variables. I could use principle component analysis (PCA) on the continuous variables and with a visual approach determine which categorical variable to add in my predictive model. So my Question is, for a neural network is it possible to use [pca1, pca2, pca3, cat1, cat2] as input vector?
The categorical variables will be converted to numeric and scaled accordingly.
If u have two kinds of input features, categorical and continuous. The categorical data may be represented as one-hot code A, while the continuous data is just a vector B in N-dimension space. It seems that simply using concat(A, B) is not a good choice because A, B are totally different kinds of data. For example, unlike B, there is no numerical order in A .
If the categories are binary, then coding them as 0–1 is probably okay. But as soon as you get more than two categories, things get problematic. If the values are “Low”, “Intermediate”, and “High” (or more generally, if they at least have a natural order), then you can again make sense of coding them numerically as 1, 2, 3. But if the values are “Red”, “Green”, “Blue” (or more generally, something that has no intrinsic order), then simply coding them as integers won’t work. One possibility in the case is to put them equally spaced around a circle., since then the distance between any pair of them is the same. With N>3N>3 values , you may want to put them at the vertices of a regular simplex in NN-dimensional space. In other words, code them as (1,0,…,0), (0,1,0,…,0), …, (0, 0, .., 0, 1). Then the distance between any pair of values is the same.
Thanks for the quick replies everybody! @Ajit Kumar Roy. Thanks for the explaination. So I should use one-hot encoding to ensure that the distance between any pairs is the same. But I am not sure I understand how to feed the whole data set to the network as you mentioned 'using concat(A,B) is not a good choice'. In a practical sense, what would the input vector for one training example look like? [(0,0,0,1), (0,1,0,0) , pca1, pca2]. The vertices represent 2 different categorical variables. This is what I would do.
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