With the popularity of smart phones and the development of mobile computing, indoor positioning services have triggered large scale of technology innovation and commercial cooperation. In the field of Wi-Fi based fingerprinting positioning system, for one thing, we deploy space division method based on Random Forest for dividing the fingerprinting radio map into sub regions freely and classifying candidate points accurately. For another thing, we propose a dimension reduction method, which integrates Maximum Likelihood Estimation for estimating intrinsic dimensionality and Kernel Principal Component Analysis for feature extraction, to tremendously reduce the size of a radio map, thereby saving terminal storage and alleviating error margin. Compared with linear feature extraction methods and manifold learning techniques, the proposed method shows a better performance in low dimension. The experimental results demonstrate that the proposed indoor positioning system, which is based on the given space division and dimension reduction techniques, could achieve 98% space division accuracy, 85% confidence probability with 2m positioning error and reduce 74% size of the radio map in addition to its noise suppression ability.