A Gaussian Mixture Model Classifier Using Supervised And Unsupervised Learning
نویسندگان
چکیده
Topic category: 7. Image and Multi-dimensional Signal Processing 9. Statistical Signal & Array Processing This paper presents an algorithm for a maximum likelihood estimation (MLE) classiier, using Gaussian mixture models (GMMs), incorporating a combination of supervised and unsupervised training. This will enable the use of data for which no ground truth class labels are available, to improve classiier performance. The applications motivation for this work is to improve the performance of military unattended ground sensors (UGS), used for the detection of hostile intruders in remote regions. There is considerable scope for the application of multi-sensor data fusion techniques to UGS systems. The algorithm presented in this paper uses GMMs to represent classes of targets in an UGS system. See 1], 2], 3], 4], 5] for previous work relevant to this paper. Parameter values for the GMMs are obtained using MLE. The novel feature of this work is the use of combined supervised and unsupervised training for a single classiier. The likelihood function is as follows: (1) where the factors represent respectively the likelihood for data with class labels (discriminative training) and the likelihood for data without class labels (non-discriminative or density training). Y 1 is the set of class labels for the feature data X 1 ; X 2 is another set of unlabelled feature data. The parameter vectors 1 and 2 contain the means and covariance matrices for the labelled and unlabelled data respectively. P c 0 c=1 P nc i=1 (ci p(x j j 1 ; i; c))P (cj 1)] (2) P (X 2 j 2) = N2 Y j=1 p(x j j 2) (3) where: yji is the coeecient for the i th element of the class indicated by class label y j. Equations 1 and 3 give the likelihood functions for the discriminative and non-discriminative training. The logarithm of L is maximised using gradient descent or expectation-maximisation. The global maximum likelihood for the mixture parameters is then the sum of the components of L coming from the discrim-inative and non-discriminative training. This discriminative or supervised training approach maximises the likelihood of the parameters w:r:t: the class labels of the labelled data, in contrast to the non-discriminative or unsupervised training used in systems such as AutoClass, which maximise the likelihood w:r:t: the feature densities. The algorithm is evaluated on a suitable data set, and its performance is compared with that of a non-discriminatively-trained classiier. This algorithm will …
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