their errors) of the galaxies, we adopt those from fit extrapolation (j,h,k-m-ext) provided by the 2MASS database[^3], which are assumed to better trace the galactic luminosity (Jarrett et al. 2000; Blanton et al. 2005). All the magnitudes are converted to be in AB system following Blanton et al. (2005).

The SDSS-2MASS-GALEX matched sample
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We use the GALEX (Martin et al. 2005) survey GR4/GR5[^4] data to match with our selected sample from SDSS and 2MASS. The GALEX was launched in 2003 April, and will cover the whole sky in the FUV (1350 - 1750 Å) and NUV (1750 - 2800 Å) bands, with spatial resolutions of 6.0$^{\prime \prime }$ in the FUV and 4.5$^{\prime \prime }$ in the NUV. The central wavelengths of FUV and NUV are 1528Å  and 2271Å, respectively. In this paper, only the GALEX objects detected both in the NUV and FUV bands were used. The GALEX data products are made available to the general public via the MultiMission Archive at Space Telescope Science Institute (MAST). The GALEX survey design was done for five modes, in which two of them are more related to our work here, i.e., the All-sky Imaging Survey (AIS) with the goal to 