We have proposed a new method for fMRI data analysis which is called Functional Feature Embedded Space Mapping (FFESM). Our work mainly focuses on the experimental design with periodic stimuli which can be described by a number of Fourier coefficients in the frequency domain. A nonlinear dimension reduction technique Isomap is applied to the high dimensional features obtained from frequency domain of the fMRI data for the first time. Finally, the presence of activated time series is identified by the clustering method in which the information theoretic criterion of minimum description length (MDL) is used to estimate the number of clusters. The feasibility of our algorithm is demonstrated by real human experiments. Although we focus on analyzing periodic fMRI data, the approach can be extended to analyze non-periodic fMRI data (event-related fMRI) by replacing the Fourier analysis with a wavelet analysis.