Fire Detection Algorithms Using Multimodal ... - Bilkent University

CHAPTER 6. WILDFIRE DETECTION 98as follows:D T (x, n)w ≥ 0 (6.33)In other words, weighted combination of decision values of sub-algorithms mustbe greater than 0, because the oracle states that y(x, n) = 1.Weights, w i (n) ≥ 0, are kept non-negative in the weight update step to detectsmoke. Each w i (n) ≥ 0 corresponds to a half-space which are closed and convex.Therefore, the POCS theory can be applied to this case as well. Whenever aweight happens to be negative, its projection onto the half-space w i (n) ≥ 0 istaken as 0.For y(x, n) = −1, we haveD T (x, n)w < 0 (6.34)In this case, the weight update equation for y(x, n) = 1 will be{w(n), if D T (x, n)w > 0w(n + 1) =(6.35)w(n) + µe(x,n) D(x, n), otherwise||D(x,n)|| 2where e(x, n) = Γ−D T (x, n)w(n) and Γ is any positive number. With this choice,w(n + 1) satisfies D T (x, n)w(n + 1) > 0 (for Γ = 0, the weights correspond toprojection onto the hyperplane D T (x, n)w(n + 1) = 0).For y(x, n) = −1, the weight update equation will bew(n + 1) ={w(n), if D T (x, n)w < 0e(x,n)w(n) + µ D(x, n),||D(x,n)|| 2otherwisewhere e(x, n) = Υ − D T (x, n)w(n) and Υ is any positive number.(6.36)It is almost impossible to know whether hyperplanes have a nonempty intersectionset for this computer vision application. However, half-spaces defined byEqs. 6.33 and 6.34 and they probably have a nonempty intersection set. As aresult, weight updates do not diverge [95].This set theoretic framework with tracking capability is especially usefulwhen the on-line active learning problem is of dynamic nature with drifting concepts[72]. In this problem, the nature of forestal recordings vary over time due