An infrared ceiling sensor network system is reported in this study to realize behavior analysis and fall detection of a single person in the home environment. The sensors output multiple binary sequences from which we know the existence/non-existence of persons under the sensors. The short duration averages of the binary responses are shown to be able to be regarded as pixel values of a top-view camera, but more advantageous in the sense of preserving privacy. Using the "pixel values" as features, support vector machine classifiers succeeded in recognizing eight activities (walking, reading, etc.) performed by five subjects at an average recognition rate of 80.65%. In addition, we proposed a martingale framework for detecting falls in this system. The experimental results showed that we attained the best performance of 95.14% (F1 value), the FAR of 7.5% and the FRR of 2.0%. This accuracy is not sufficient in general but surprisingly high with such low-level information. In summary, it is shown that this system has the potential to be used in the home environment to provide personalized services and to detect abnormalities of elders who live alone.