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With rapid development of socio-economics, the task of discovering functional zones becomes critical to better understand the interactions between social activities and spatial locations. In this paper, we propose a framework to discover the real functional zones from the biased and extremely sparse Point of Interests (POIs). To cope with the bias and sparsity of POIs, the unbiased inner influences between spatial locations and human activities are introduced to learn a balanced and dense latent region representation. In addition, a spatial location based clustering method is also included to enrich the spatial information for latent region representation and enhance the region functionality consistency for the fine-grained region segmentation. Moreover, to properly annotate the various and fine-grained region functionalities, we estimate the functionality of the regions and rank them by the differences between the normalized POI distributions to reduce the inconsistency caused by the fine-grained segmentation. Thus, our whole framework is able to properly address the biased categories in sparse POI data and explore the true functional zones with a fine-grained level. To validate the proposed framework, a case study is evaluated by using very large real-world users GPS and POIs data from city of Raleigh. The results demonstrate that the proposed framework can better identify functional zones than the benchmarks, and, therefore, enhance understanding of urban structures with a finer granularity under practical conditions.