Interplanetary hydrogen atoms that penetrate into the heliosphere are illuminated by enhanced hydrogen Lyman alpha emission from solar active regions. Using the data obtained by the Solar Wind Anisotropies (SWAN) instrument on board the Solar and Heliospheric Observatory (SOHO), Bertaux et al. (2000) proposed a new method for earlier detection and monitoring of solar active regions on the far-side hemisphere. However, a quantitative relationship between the sky map of interplanetary Lyman alpha intensity and the enhanced emission from a solar active region was not discussed. Here, we analyze the interplanetary Lyman alpha intensity data obtained by the Ultraviolet Imaging Spectrometer (UVS) on board the Nozomi spacecraft. We develop a method to map the distribution of interplanetary Lyman alpha intensity into the Carrington coordinate system by assuming an interplanetary hydrogen screen at the location of maximum volume emission rate. Analysis period is from January 2000 to March 2000 near solar maximum. The solar activity during this analysis period is much higher as compared with the case study by Bertaux et al. (2000). The sky map of the Lyman alpha emission obtained by the UVS is shown to exhibit a high correlation with the solar extreme ultraviolet (EUV) intensity map obtained by the EUV Imaging Telescope (EIT) on board the SOHO satellite. The highest value of two-dimensional correlation coefficient is 0.80. An observed change in the periodicity of interplanetary Lyman alpha intensity is in good agreement with the growth of an active region on the Sun. It has been also confirmed that the far-side observations of UVS detected the growth of an active region in advance. This case study demonstrates that the location and intensity variation of activity on the far side of the Sun can be detected by far-side measurements of interplanetary Lyman alpha emission intensity. It is thus concluded that the developed method contributes to space weather forecasting on a scale of 2 weeks.