Symmetric Monotonic Regression: Techniques and Applications in Sensor Networks

Inter-sensor modeling of data streams is an important problem and an enabler for numerous sensor network tasks such as faulty data detection, missing data recovery, and compression. We have developed a new symmetric monotonic regression (SMR) technique for predicting data at one sensor using data from another sensor or a set of sensors that simultaneously guarantees isotonicity and minimizes an arbitrary form of error for predicting stream X from stream Y and vice versa. Using a simple and fast algorithm, we also developed a lower bound regression (LBR) approach for evaluating the achievable accuracy of regression between the readings at two sensors. SMR often performs very close to the lower bound on a set of collected real-life sensor data. We show how LBR barrier can be outperformed by conducting prediction using either data from multiple sensors or by considering information extracted (multiple consecutive time samples) of the explanatory stream. The effectiveness of SMR is demonstrated on a sensor node sleeping coordination problem by reducing energy consumption by more than an order of magnitude with respect to the best previously published technique.