Neural networks - input values

Question

I have a question that may be trivial but it's not described anywhere i've looked. I'm studying neural networks and everywhere i look there's some theory and some trivial example with some 0s and 1s as an input. I'm wondering: do i have to put only one value as an input value for one neuron, or can it be a vector of, let's say, 3 values (RGB colour for example)?

Answer 1

Generally, the input for a single neuron is a value between 0 and 1. That convention is not just for ease of implementation but because normalizing the input values to the same range ensures that each input carries similar weighting. (If you have some images with 8 bit color with pixel values between 0 and 7 and some images with 16 bit color with pixel values between 0 and 255 you probably wouldn't want to favor the 24 bit color images just because the numerical values are higher. Similarly, you will probably want your images to be the same dimensions.)

As far as using pixel values as inputs, it is very common to try to gather a higher level representation of the image than its pixels (more info). For example, given a 5 x 5 (normalized) gray scale image:

[1 1 1 1 1]
[0 0 1 0 0] 
[0 0 1 0 0] 
[0 0 1 0 0] 
[0 0 1 0 0]

We could use a the following feature matrices to help discover horizontal, vertical, and diagonal features of the images. See python haar face detection for more information.

[1 1]  [0 0]  [1 0]  [0 1]  [1 0], [0 1]
[0 0], [1 1], [1 0], [0 1], [0 1], [1 0]

To build the input vector, v, for this image, take the first 2x2 feature matrix and "apply" it with element-wise multiplication to the first position in the image. Applying,

[1 1] (the first feature matrix) to [1 1] (the first position in the image)
[0 0]                               [0 0] 

will result in 2 because 1*1 + 1*1 + 0*0 + 0*0 = 2. Append 2 to the back of your input vector for this image. Then move this feature matrix to the next position, one to the right, and apply it again, adding the result to the input vector. Do this repeatedly for each position of the feature matrix and for each of the feature matrices. This will build your input vector for a single image. Be sure that you build the vectors in the same order for each image.

In this case the image is black and white, but with RGB values you could extend the algorithm to do the same computation but add 3 values to the input vector for each pixel--one for each color. This should provide you with one input vector per image and a single input to each neuron. The vectors will then need to be normalized before running through the network.

Answer 2

Use light wavelength normalized to visible spectrum as the input.

There are some approximate equations on the net. Search for RGB to wavelength conversion or use HSL color model and extract Hue component and possibly use Saturation and Lightness as well. Well...

Answer 3

The above answers are technically correct, but don't explain the simple truth: there is never a situation where you'd need to give a vector of numbers to a single neuron.

From a practical standpoint this is because (as one of the earlier solutions has shown) you can just have a neuron for each number in a vector and then have all of those be the input to a single neuron. This should get you your desired behavior after training, as the second layer neuron can effectively make use of the entire vector.

From a mathematical standpoint, there is a fundamental theorem of coding theory that states that any vector of numbers can be represented as a single number. Thus, if you really don't want an extra layer of neurons, you could simply encode the RGB values into a single number and input that to the neuron. Though, this coding function would probably make most learning problems more difficult, so I doubt this solution would be worth it in most cases.

To summarize: artificial neural networks are used without giving a vector to an input unit, but lose no computational power because of this.

Answer 4

It can be whatever you want, as long as you write your inner function accordingly.

The examples you mention use [0;1] as their domain, but you can use R, R², or whatever you want, as long as the function you use in your neurons is defined on this domain.

In your case, you can define your functions on R3 to allow for RGB values to be handled

A trivial example : use (x1, y1, z1),(x2,y2,z2)->(ax1+x2,by1+y2,cz1+z2) as your function to transform two colors into one, a b and c being your learning coefs, which you will determine during the learning phase.

Very detailed information (including the answer to your question) is available on Wikipedia.

Answer 5

Normally a single neuron takes as its input multiple real numbers and outputs a real number, which typically is calculated as applying the sigmoid function to the sum of the real numbers (scaled, and then plus or minus a constant offset).

If you want to put in, say, two RGB vectors (2 x 3 reals), you need to decide how you want to combine the values. If you add all the elements together and apply the sigmoid function, it is equivalent to getting in six reals "flat". On the other hand, if you process the R elements, then the G elements, and the B elements, all individually (e.g. sum or subtract the pairs), you have in practice three independent neurons.

So in short, no, a single neuron does not take in vector values.

Answer 6

When dealing with multi-dimensional data, I believe a two layer neural network is said to give better result.

In your case:

R[0..1] => (N1)----\
                    \
G[0..1] => (N2)-----(N4) => Result[0..1]
                    /
B[0..1] => (N3)----/

As you can see, the N4 neurone can handle 3 entries.

The [0..1] interval is a convention but a good one imo. That way, you can easily code a set of generic neuron classes that can take an arbitrary number of entries (I had template C++ classes with the number of entries as template parameter personally). So you code the logic of your neurons once, then you toy with the structure of the network and/or combinations of functions within your neurons.