There're three parameters in the Radial Basis Function Networks (RBFN). Centers of RBFs Width of RBFs Weights of RBFs It's a fact that Weights can be easily updated using a simple Gradient Descent. My question is: Can we optimize Centers and Widths of RBFs using Gradient Descent such that approximation will tend to be better. Any suggestion is welcome.

I want to use a Radial Basis Function Neural Network for my thesis. Is there any library that implements it? And in the negative case, which is the best library to implement it?

My data consists of a time series of values $\pm1$ and I am trying to apply a RBF NN as a function approximator. Essentially, the NN will take as input one data sample and predict the next sample (one step ahead prediction). However, my network is not getting trained. If I use floating point vales as in the data then the same code works. However for $\pm$ data, I am not able to figure out how to train the network …

I wanna estimate a rbf SVM to predict property prices. My data set has 11 features and roughly 57,000 rows. When I set C=10, R^2 is about 0.88 while MSE and RMSE are 0.1191 and 0.3451. The results are pretty good. Afterward, I estimate a SGD, using linear_model.SGDRegressor and loss='squared_epsilon_insensitive'. When I use adaptive learning rate, R^2 is reduced to 0.75 while MSE and RMSE are 0.2441 and 0.4940, respectively. When I use optimal learning rate, the results are even …

I have used 60 % data as training data and 40% data as test data. Exactly same instances of data are fed to SVM RBF kernel in Python and SVM Gaussian in MatLab. But the results of prediction in MatLab are horrible, all the data is belonging to the 5th class where I am getting 99% accuracy with good class-specific accuracies in Python. Please tell me where is the problem.

I know we can use Kernel trick in the primal form of SVM. So the hypothesis will be - and optimization objective - We can optimize the above equation using gradient descent, but in this equation suppose we use RBF kernel (which projects training data into infinite dimensions), then if the number of features are infinite, then dimension of 'w' will also be infinite and the optimization equation will learn 'w' using gradient descent, then how its supposed to learn …

I am trying to use Semi-Unsupervised clustering using reinforcement learning following this paper. Assume I have n data-points each of which has d dimensions. I also have c pairwise constraints of whether two elements are supposed to be in the same cluster or not. The paper states that "the original input dimension of the dataset is appended to a kernel space with a similarity metric to each pairwise point in the set of constraints" creating a d + 2c dimensional …

I'm working on a project where I have to dynamically cluster the position of objects with respect to one coordinate. So I'm essentially dealing with subsequent frames and each frame represents a one-dimensional dataset. The intuition behind clustering is to form clusters out of points that are in similar distance to other points within the cluster and can be naturally connected. I use spectral clustering due to its ability to cluster points by their connectedness and not the absolute location …

In Chapter 6 (Deep Forward Networks) on Page 193 of Deep Learning they talk about the design of Hidden Units. The Radial Basis Function is introduced as follows: $$ h_i = exp\big{(}-\frac{1}{\sigma_i^2}||W_{:,i} − x||^2\big{)} $$ What does the colon as Index for $W$ mean?

I want to compute a kernel matrix using RBF on my own. The training data is multidimensional. My query is whether we will apply $$e^{-\gamma(x-y)^2}$$ for each dimension and then sum the values across all dimension?

As you can see, I have some points (belonging to red and blue class), and I would to use an RBF kernel but I think that an RBF kernel can make points linearly separable only if they are located in perfect circular way. In this case I don't know how modify the kernel (or which parameters use) for respect the "oval" aspect that these data have.