To combine the strengths of generative and discriminative approaches for image classification, we characterize our proposed CoDT features of a HEp-2 cell image by a gradient vector derived from a generative model of the training data to model the generation process of the features, and then we feed the output image representations into a discriminative classifier for the identification of HEp-2 cells.

Let X = {x_{n}, n = 1,2,N} be a set of samples from the CoDT feature space of one HEp-2 cell image. The probability density distribution of the CoDT feature, which is used to model the generative process of elements in the feature space, is described by a GMM. Let X = {w_{t}, p_{t}, %t, t = 1,2,..., T} denote the parameters of the GMM, where w_{t}, /u_{t} and X_{t} respectively denotes the mixture weight, mean vector and covariance matrix of Gaussian t. Then we can formulate

and p_{t} (x_{n} |X) is the Gaussian t defined as

where D is the dimension of the CoDT feature. Actually, the GMM, which models the generation process of the CoDT features, can be regarded as a probabilistic codebook/vocabulary [21]. The parameters of GMM can be adaptively estimated by the Expectation Maximization (EM) algorithm [22] based on the training CoDT feature space. Briefly, EM algorithm can be implemented by the following two steps: Expectation step (E step): the posteriori probability for each training data x_{n} is given by

Maximization step (M step): the means, variances and mixture weights are updated by

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Each Gaussian component can be treated as a micro-texton word of the micro- texton vocabulary while w_{t} corresponds to the relative frequency of word t, represents the mean of the word and E_{t} is the variation around the mean. In the followings, the covariance matrices are assumed to be diagonal and denoted by o_{t} = diag(E_{t}).