Ortogonal Pursuit de Correspondência (OMP) is a algoritmo ganancioso used in the field of aprendizado de máquina and processamento de sinais for solving sparse approximation problems. It aims to find a representação esparsa of a signal or data vector in a given dictionary of basis functions. The algorithm is particularly useful when the number of available measurements is much smaller than the number of potential basis functions, making it a popular choice in various applications such as compressed sensing and seleção de variáveis.
The core idea of OMP is to iteratively select the best matching elements from the dictionary that contribute most significantly to the approximation of the target signal. The process begins with an initial guess (often a zero vector) and, at each iteration, identifies the dictionary element that correlates most with the current residual (the difference between the actual signal and its approximation). This selected element is then added to the approximation set.
Uma vez que um elemento é escolhido, o OMP atualiza a aproximação projetando o sinal no subespaço gerado pelos elementos selecionados. O resíduo é então recalculado, e o processo se repete até que um número especificado de elementos tenha sido selecionado ou até que o resíduo esteja abaixo de um determinado limiar. Isso torna o OMP eficiente em termos de cálculo, pois reduz o tamanho do problema a cada passo.
OMP is particularly valuable in applications where interpretability and simplicity are crucial, as it results in a sparse representation that highlights the most significant features of the data. However, it is important to note that OMP can be sensitive to noise and may not always guarantee the solução ótima, particularly in highly correlated dictionaries.