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this example Notice the training rule will increase w, in this case, because (t - o), 7 , and Xi are all positive For example, if xi = 8, q = 01, t = 1 , and o = - 1 , then the weight update will be Awi = q(t - o)xi = O 1 ( 1 - (-1))08 = 016 On the other hand, if t = - 1 and o = 1, then weights associated with positive xi will be decreased rather than increased In fact, the above learning procedure can be proven to converge within a finite number of applications of the perceptron training rule to a weight vector that correctly classifies all training examples, provided the training examples are linearly separable and provided a sufficiently small 7 is used (see Minsky and Papert 1969) If the data are not linearly separable, convergence is not assured

.

6 Save and exit Interface Builder 7 Open MainWindowxib and add a UITabBarController to the document window Interface

Total consumer electronics sales reached $81 billion in 1999 and is expected to hit $85 billion in 2000 Total PC sales will hit a record $168 billion in 2000 with expected sales of 168 million units PC software accounted for $45 million in sales in 1999 and will surpass $52 billion in 2000, a 16 percent rise Of the $69 billion in revenues that the interactive entertainment industry generated in 1999, $13 billion came from PC games Here s a sampling of expectations at the beginning of the new millennium The following forecasts were made in 2000: DVD Forum: $16 billion in DVD-ROM/RAM drive sales in 2001, $4 billion in DVD audio players, and $8 billion in DVD video players/recorders Technicolor: The number of PCs equipped with DVD-ROM drives will reach more than 130 million units worldwide by 2001 Jon Peddie and Associates: DVD player sales in the US in 2004 will be nearly 20 million units IRMA: Thirteen million players will ship in the US in 2000, with 31 million sold in 2003 Two hundred and eighteen million DVDVideo titles will ship in 2000, with 360 million units in 2001 DVD-ROM and DVD-Audio will ship a combined 70 million discs in 2001 Screen Digest: Western Europe will have 54 million DVD players by the end of 2000, in 35 percent of TV households The total will rise to 47 million by 2003, or about 30 percent of TV households DVD spending will rise from $450 million in title purchases and $18 million in rentals ($470 million total) in 1999 to $49 billion in sales and $1 billion in rentals ($58 billion total) in 2003 VHS spending will fall from $61 billion in 1999 to $3 billion in 2003 Baskerville Communications: Worldwide spending on DVDs will surpass spending on videos by 2003 By 2010, 625 million DVD players will be in homes worldwide (55 percent of TV households), with spending on DVDs at $646 billion versus $25 billion for VHS Also by 2010, China will have the highest number of homes with DVD players at 127 million Sony: Ten million PlayStation 2 units will be shipped worldwide by the end of March 2001: four million in Japan, three million in the US, and three million in Europe InfoTech: Approximately 25 million DVD video recorders will be sold by 2005.

Although the perceptron rule finds a successful weight vector when the training examples are linearly separable, it can fail to converge if the examples are not linearly separable A second training rule, called the delta rule, is designed to overcome this difficulty If the training examples are not linearly separable, the delta rule converges toward a best-fit approximation to the target concept The key idea behind the delta rule is to use gradient descent to search the hypothesis space of possible weight vectors to find the weights that best fit the training examples This rule is important because gradient descent provides the basis for the BACKPROPAGATION algorithm, which can learn networks with many interconnected units It is also important because gradient descent can serve as the basis for learning algorithms that must search through hypothesis spaces containing many different types of continuously parameterized hypotheses The delta training rule is best understood by considering the task of training an unthresholdedperceptron; that is, a linear unit for which the output o is given by Thus, a linear unit corresponds to the first stage of a perceptron, without the threshold In order to derive a weight learning rule for linear units, let us begin by specifying a measure for the training error of a hypothesis (weight vector), relative to the training examples Although there are many ways to define this error, one common measure that will turn out to be especially convenient is

tab bar controller, select the Selected View Controller (Item 1), and change its class to FirstViewController in the First View Controller Identity Inspector Change its Nib Name to FirstViewController

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previous step Do not forget to set the NIB Name to SecondViewController in the Second View Controller Attributes Inspector