polarcbo.dynamic.KMeansCBO

class polarcbo.dynamic.KMeansCBO(x, V, noise, beta=1.0, noise_decay=0.0, diff_exp=1.0, kappa=1.0, tau=0.1, sigma=1.0, lamda=1.0, n_clusters=1)[source]

Bases: ParticleDynamic

KMeansCBO class

This class implements the KMeansCBO algorithm. It is a particle-based algorithm that uses the KMeans algorithm to cluster the particles and then uses the cluster centers as the mean of the particles in the cluster. The algorithm is initialized with a set of particles and a set of weights. The weights are used to initialize the KMeans algorithm. The algorithm then proceeds to update the particles according to the following rule:

\[x_{k+1} = x_k - \lambda \tau \nabla \log p(x_k) + \sigma \mathcal{N}(0,I)\]

where \(\lambda\) is the learning rate, \(\tau\) is the time step, \(\sigma\) is the noise parameter and \(\mathcal{N}(0,I)\) is a zero-mean isotropic Gaussian distribution.

Parameters:

x (array_like) – The initial positions of the particles. For a system of \(J\) particles, the i-th row of this array x[i,:] represents the position \(x_i\) of the i-th particle.
V (obejective) – The objective function \(V(x)\) of the system.
beta (float, optional) – The heat parameter \(\beta\) of the system. The default is 1.0.
tau (float, optional) – The time constant \(\tau\) of the noise model. The default is 0.01.
lamda (float, optional) – The default is 1.0.
sigma (float, optional) – The default is 1.0.
n_clusters (int, optional) – The number of clusters to form as well as the number of centroids to generate. The default is 1.