Generally a vector in R^N can be represented in a (1x1xN) shape. Therefore the N features (N = 208) have no spatial relationship since each feature has a dimension of 1x1. Therefore the convolutions in a CNN will take place over 1x1 weights, which sums to a scalar multiplication and add (i.e., similar to a "vanilla" densely connected neural network).

With this rationale, you can design a CNN as an expensive regressor, and it will work!

If you use Python, you can check code examples using Keras.

I use Matlab. Thank you for your explanation.

It does not make much sense to use a convolutional network if you have nothing to "convolve" on. As mentioned earlier by Faris, the features in your 1-dimensional vector have no spatial relationship, so why not using a traditional NN, shallow or deep, or even an Autoencoder type of architecture? For the current standards, 208 input values is not large at all.

Dr. Costa, thanks for your feedback. In fact, 208 values at the input are not a large number but enough to talk about noisy data. Of the 208 input values, you can build not only one vector but, for example, a 13x16 image. Does the use of CNN become justified for the input data so presented?

Hi Grzegorz, it still does not make sense to me since reshaping a 1D vector to 2D does not give the data any spatial meaning. A good solution for your problem would be using a stack of Autoencoders, that can be as deep as you need (depth depends on how non linear your system must be). Autoencoders create a compact representation of your data and serve as good denoising tools (since they have to get rid of non important information in order to generate a compressed representation, they tend to get rid of noise first). From this compact representation, you can easily do your regression task similarly to any other NN.

Example of using Autoencoders in Matlab:

https://www.mathworks.com/help/nnet/ug/construct-deep-network-using-autoencoders.html

I agree with Bruno's answer. Reshaping the data gives it a false spatial meaning (i.e., inviting a property of the data that is not likely true or relevant). CNNs are best suited for images, but they are not the only deep neural networks out there. You can make a "vanilla" or artificial neural network as deep and as wide as you want and still have a deep regressor for 1D data points.

Hi Bruno. Thanks for the information. I've seen this Matlab page and have already stacked several autoencoders. A certain problem in Matlab is that the full connected layer (SoftmaxLayer) is adapted for classification. I have a real number in the output, so I would have to write the code myself. For now, I have tested such a system: inputs(208)-encoder(100)-encoder(70)-encoder(50)-encoder(20)-MLP(1). Separately I trained MultiLayer Perceptron (MLP: 20-[10hidden neurons] -1). I was hoping that if 208 input values were replaced by 20, I would remove the noise. Unfortunately, it works poorly. I am looking for a way to improve it.

You wrote "depth depends on how non-linear your system must be". How to get rid of "linearity"? And how to choose the number of depth/convolutions afterwards?

PS

It seems that the number of my questions is growing exponentially. I'm sorry, I do not expect all of them to be answered.

Hi Faris. Thanks for your feedback. I listen to all suggestions with attention and I am grateful for the time devoted to me.

You are so welcome Grzegorz. Best wishes of success in your research :-).

Hi Grzegorz, I believe you are correct regarding Matlab's implementation only allowing softmax at the output. You probably have to code the fine tuning part yourself to allow a regression loss function to be applied for the backpropagation. I would suggest then starting with a regular NN, that can be as deep or as wide as you need (as suggested by Faris). There's no strict process to determine the architecture and training process of your network, but a good rule of thumb would be:

1) High bias (i.e. accuracy is low during training)? Use a bigger network (deeper or wider) or train longer. Once you have low bias...

2) High variance (i.e. accuracy is acceptable during training but low during testing)? Collect more data or use regularization.

If you still get poor results, it may be the case that your data is so noisy that it looks random and a correct output cannot be drawn from that. It happens, sometimes.

I hope that was helpful somehow. Good luck.

Bruno

Thanx Bruno. Especially for these two thumb rules.