Modelo de Mezcla Gaussiana (GMM)
Una Gaussiana Modelo de Mezcla (GMM) is a probabilistic model that assumes that the data is generated from a mixture of several Gaussian distributions, each representing a different cluster or group within the data. GMMs are widely used in statistics and aprendizaje automático for tasks such as clustering, estimación de densidad, and classification.
Cada distribución gaussiana in a GMM is defined by its mean (the center of the distribution) and covariance (which describes the shape and orientation of the distribution). The overall model is a weighted sum of these Gaussian components, where the weights indicate the proportion of the data that belongs to each cluster.
Matemáticamente, el probability la función de densidad de un GMM puede expresarse como:
P(x) = Σ (πk * N(x | μk, Σk))
Aquí, πk represents the weight de la k-ésima componente gaussiana, y N(x | μk, Σk) denotes the probability density of the data point x under the k-th Gaussian with mean μk y covarianza Σk.
To fit a GMM to data, algorithms such as the Expectation-Maximization (EM) algorithm are commonly used. The EM algorithm iteratively updates the parameters of the Gaussian components to maximize the likelihood of the datos observados.
GMMs are particularly useful in scenarios where the data exhibits cluster-like structures and can be applied in various fields, including finance, procesamiento de imágenes, and bioinformatics.