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While feature extraction based on two-dimensional principal component analysis (2DPCA) is widely used in image recognition, such a method usually fails to handle the noise and outliers, because adopted F-norm square actually exaggerates the effect of outliers. To tackle the aforementioned problem, we present a novel algorithm called Area-2DPCA, which uses F-norm to characterize the variance and reconstruction error. By doing so, the project directions, which minimize the summation of the area between projection directions and reconstruct error of each data, can be found. Moreover, the Area-2DPCA sets different weighted coefficients to each residual error. To find the solution of our model, a non-greedy algorithm, which has a closed form solution in each step, is presented. The extensive experimental results demonstrate the superiority of our proposed model, compared with the state-of-the-art.