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Speaker verification becomes increasingly important due to the popularity of speech assistants and smart home. i-vectors are used broadly for this topic, which use factor analysis to model the shift of average parameter in Gaussian Mixture Models. Recently by the progress of deep learning, high-level non-linearity improves results in many areas. In this paper we proposed a new framework of i-vectors which uses stochastic gradient descent to solve the problem of i-vectors. From our preliminary results stochastic gradient descent can get same performance as expectation-maximization algorithm. However, by backpropagation the assumption can be more flexible, so both linear and non-linear assumption is possible in our framework. From our result, both maximum a posteriori estimation and maximum likelihood lead to slightly better result than conventional i-vectors and both linear and non-linear system has similar performance.