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Alternative c-means is a robustified version of k-means-type clustering that uses a robust distance measure instead of the conventional Euclidean distance based on an Mestimation concept. This paper proposes a linear clustering model for estimating intrinsic linear sub-structures in a robust way based on a similar manner to alternative c-means. In order to replace the least square measure with alternative c-means-type robust measure, the clustering criteria of distances between data samples and linear prototypes are calculated by the lower rank approximation concept. In numerical experiments, the model is compared with the conventional noise clustering model, where noise samples are dumped into the additional noise cluster while they are still assigned to normal clusters in the alternative c-means-type model. Several experimental results demonstrate the robust feature of the proposed model from both view points of noise sensitivity and cluster validation.