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Many types of shape descriptors have been proposed for 2D shape analysis, but most of them consist of component features that are not adapted to specific problems. This has two drawbacks. First, computation is wasted on the irrelevant components; second, the accuracy is impaired. This paper proposes an effective method that generates compact descriptors adapted to specific problems in hand, where each component of the new descriptor is a linear combination of the components in some classic descriptors. A progressive strategy is used to construct and select the most suitable linear combinations in successive rounds, where a variant of Adaboost is employed to ensure the optimum of the selected combinations in each round. Experiments show that our method effectively generates adaptive and compact descriptors for typical applications such as shape classification and retrieval.