Incremental Support Vector Regression

The incremental support vector regression algorithm updates the trained SVR function whenever a new training input is added to the training set. The basic idea is to change Lagrange multiplier parameters, corresponding to the new input in a finite number of discrete steps until it meets the Karush-Kuhn-Tucker (KKT) conditions [3]:


where

On-line Support Vector Regression Updating

Figure 1 and figure 2 shows the on-line learning procedure of the support vector regression. X-axis is the intensity of data and Y-axis is the probability of pixels belonging to the background. In Figure 1, training data are labeled as red cycles. They scatter in a small range. After training, their probability distribution is estimated as a single hump (red dash curve). When a new data labeled as black star is coming, the probability distribution is on-line learned and becomes two different humps (black curve). Figure 2 shows the change of a multi-peak distribution without and with the new input. It can be seen that the probability distribution will move from left to right along the movement direction of new incoming data and support vector regression-based background model has the learning ability to adapt the new incoming data.

Figure 1. On-line updating of support vector regression.

Figure 2. On-line updating of support vector regression.