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data as Gaussian rather than a Gaussian mixture (P 1) Furthermore, you can use the maximum-likelihood (ML) classi er (uniform prior probabilities) Support Vector Machine Classi er A support vector machine (SVM) is essentially a linear classi er operating in a higher dimensional space Consider a binary classi cation problem without loss of generality Let {w(x)}M be a set of nonlinear i 1 transformations mapping the N-dimensional input vector to an M-dimensional feature space (M N) A linear classi er, characterized by the weights w1 , w2 , , wM , P operates in this higher dimensional feature space g(x) M wj wj (x) b, where b j 1 is the bias parameter of the classi er The optimal weight vectors for this classi er can be represented in terms of a subset of training vectors, termed the support vecP tors wj Q ai wj (xi ), j 1, 2, .

, M Using the preceding representation for the i 1 P weight vectors, the linear classi er can be expressed as g(x) Q ai K(x, xi ) b, i 1 PM where K(x, xi ) j 1 wj (x)wj (xi ) is the symmetric kernel representing the SVM In the numerical examples presented in this chapter, we use a third-degree polynomial kernel: K(x mmaxi ) (xT xi 1)3 In practice, the SVM discriminant function g(x) is computed using the kernel representation, bypassing the nonlinear transformation into the higher dimensional space [13] The classi er design then corresponds to the choice of the kernel and the support vectors By appropriately choosing the kernel, an SVM can realize a neural network classi er as well Similar to neural networks, the training phase can take a long time However, once the classi er is trained, its application is relatively easy.

In general, a different SVM is trained for each class The output of each SVM can then be regarded as an estimate of the posterior probability for that class and the MAP decision rule can be directly applied 1443 Target Tracking Based on Cooperative Binary Detection.

(a) Maximize this over b to nd b and W . Thus, the wealth achieved in repeated horse races should grow to in nity like 2nW with probability 1. (b) Show that if instead we put all of our money on horse 1, the most likely winner, we will eventually go broke with probability 1. 6.2 Horse race with subfair odds. If the odds are bad (due to a track take), the gambler may wish to keep money in his pocket. Let b(0) be the amount in his pocket and let b(1), b(2), . . . , b(m) be the amount bet on horses 1, 2, . . . , m, with odds o(1), o(2), . . . , o(m), and win probabilities p(1), p(2), . . . , p(m). Thus, the resulting wealth is S(x) = b(0) + b(x)o(x), with probability p(x), x = 1, 2, . . . , m. (a) Find b maximizing E log S if 1/o(i) < 1.

Wireless sensor and actor networks (WSANs) [54] can be considered as an extension of traditional wireless sensor networks. They consist of two major components: sensor nodes and actor nodes. Sensor nodes are low-cost, low-power devices with limited sensing, computational, and communication capabilities. Actor nodes are resource-rich nodes equipped with more powerful processors, longer-range radio transceivers, and longer-lasting, or possibly renewable, power sources. They may also be able to navigate throughout the area covered by the sensor nodes. The number of sensor nodes generally outnumbers the number of actor nodes by a sizable quantity. There are several de ning characteristics of WSANs. These include:

Mix the paraformaldehyde with 25 ml of distilled water. Heat to 60 C on a stir plate. When moisture condenses on the sides of ask, add sodium hydroxide drop-wise and stir the solution until it clears. Cool solution in cold water bath. Filter and then add glutaraldehyde and 0.2 M buffer, pH range 7.2 7.4. Safety note. Use caution when preparing the solutions. Work in a wellventilated area; wear gloves and a lab coat.

A telephone subset consists of an earpiece, which we may call the receiver; the mouthpiece, which we may call the transmitter; and some control circuitry in the telephone cradle-stand. Figure 5.3 illustrates a telephone subset connected all the way through its subscriber loop to the local serving exchange. The control circuits are aptly shown.