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Abstract:
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The novelty of object data analysis is that it allows for studying the contents of image data, by representing key features extracted from them, as points on metric spaces called object spaces. Oftentimes an object space is nonlinear, therefore, it has to be embedded into a Euclidean space. In this paper, we introduce an extrinsic approach for object data on manifolds using statistical depth concept. We employ the classical spherical depth and extend it to general spaces via embeddings. It enables us to measure the depth of data on nonlinear manifold. The uniform consistency and limiting distribution of an empirical extrinsic spherical depth function on manifold are studied. We illustrate our approach in both simulated data and real data examples.
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