On The Number Of Iterations For The Matching Pursuit Algorithm
| Autor: | Christopher M. Triggs, Bogdan Dumitrescu, Fangyao Li, Ciprian Doru Giurcaneanu |
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| Rok vydání: | 2018 |
| Předmět: |
Signal processing
Mathematical optimization Trace (linear algebra) Computer science Degrees of freedom (statistics) Linear model 020206 networking & telecommunications Feature selection 02 engineering and technology 01 natural sciences Upper and lower bounds 010104 statistics & probability 0202 electrical engineering electronic engineering information engineering 0101 mathematics Focus (optics) Linear combination Hat matrix Algorithm |
| Zdroj: | EUSIPCO |
| DOI: | 10.5281/zenodo.1159631 |
| Popis: | We address the problem of selecting, from a given dictionary, a subset of predictors whose linear combination provides the best description for the vector of measurements. To this end, we apply the well-known matching pursuit algorithm (MPA). Even if there are theoretical results on the performance of MPA, there is no widely accepted rule for stopping the algorithm. In this work, we focus on stopping rules based on information theoretic criteria (ITC). The key point is to evaluate the degrees of freedom (df) for the model produced at each iteration. This is traditionally done by computing the trace of the hat matrix which maps the data vector to its estimate. We prove some theoretical results concerning the hat matrix. One of them provides an upper bound on the increase of df from the m-th to the (m + 1)-th iteration. Based on the properties of the hat matrix, we propose novel ITC for selecting the number of iterations. All of them are obtained by modifying criteria designed for variable selection in the classical linear model. For assessing the performance of the novel criteria, we conduct a simulation study. |
| Databáze: | OpenAIRE |
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