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forced to minimize the error at (1200,2). This causes the linear consequent hyperplanes to go through the point (1200,2). A promising strategy to circumvent this problem lies in the adaptation of only those parameters that correspond to signi cantly active rules, that is, rules that possess normalized membership function values Y ~act higher than a certain x threshold near 0. This guarantees that rules that represent areas not lying near a constant process state remain unchanged and, hence, are not disturbed. In FLEXFIS, this can be accomplished by replacing Step 9 in Algorithm 1 with the following condition: x Step 9: If Yi ~ k 1 ! thresh, perform recursive weighted least squares for the consequent parameters of the ith rule by. . . . This is demonstrated in the right images in Figure 5.4, where a threshold of 0.1 was used. In fact, setting the threshold is a crucial point for a well-performing adaptation: If it is set too close to 0, the unlearning effect remains; if it is set too close to 1, the consequent parameters are hardly updated and may not be able to follow new comming trends in the data. Another point of view of the unlearning effect is when considering classi cation problems, where the data distribution of the classes gets quite unbalanced during the incremental learning process, so that one or more classes become signi cantly more frequent than some others. In this case, the danger is high that the less-frequent classes are simply overwhelmed and do not contribute to a cluster or a rule with majority any longer, causing a bad classi cation accuracy for these classes [50]. In order to overcome this unpleasant effect, we propose a timing of update strategy, where it is not the case that each single new incoming instance is taken into the evolving process of the fuzzy classi ers, but only in the following three situations (here, for two classes): 1. Whenever there is a disagreement between the classi er s decision and the true class ( ! extending the classi er to this new state). 2. Whenever the relative proportion of samples seen so far and falling into all the classes is equally balanced ( ! re ning the classi er with additional samples is usually advantageous). 3. Whenever the relative proportion of samples seen so far and belonging to the current class into which the sample falls is lower than the relative proportion of the most signi cant class (class with highest number of representatives in order to incorporate more samples from less frequent classes and boost up the performance for these).
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If there isnoinitiallycollecteddata set, wecansuppose that vectorx1 representsthe rst data point of the data stream xk, k 1, 2,. . .. We associate the rst cluster center with that point v1 x1 and initialize its inverse covariance matrix and determinant, and the counter M1 of the vectors belonging to the cluster:
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peratures of up to 75 C. This causes denaturation of the proteins, which then form unwanted small lumps in the sausage meat and partly lose their ability to bind water.
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logical phenomena. The chapter is divided into eight sections that carry the reader from the theoretical underpinnings of the methodology through applied examples of time series applications to new applications and directions within time series analysis. The second section provides a general overview and describes the most prevalent methodology used in time series analysis. This section provides an introduction to the major concepts, issues, and terminology. The major classes of research questions that can be addressed by time series analysis are also discussed. These include process analysis, intervention analysis, and the analysis of treatment effects over time. Some general guidelines are suggested to aid in determining when a time series study and analysis might offer speci c advantages over alternative methodologies. The third section presents a more complete and technical discussion of the class of time series known as autoregressive integrated moving average (ARIMA) models. These models
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where (x) = 0 e t t x 1 dt denotes the gamma function. For simplicity, we consider the case of two stocks, in which case d (b) = 1 1 db, b(1 b) 0 b 1, (16.158)
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Figure 9.2. Color development in fermented sausages.
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Yr. 0007 $12,000 8,000 4,000 $24,000 $ 5,000 4,000 8,000 $17,000 $ 7,000
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Note: You can adjust the degree of automatic smoothing and straightening by choosing preferences for drawing settings. See Choosing drawing settings on page 75.
This one s nifty but subtle. With the sidebar hidden, drag the dot slowly and at a steady speed. When the sidebar is just big enough to allow all its items to appear fully, with no ellipses at the ends of words, the sidebar will stick for a few pixels even as you drag, pinning the sidebar at its optimal size. If you keep dragging, eventually the sidebar will unstick and let you make it bigger. If the sidebar is wider than necessary to display all items, you can use this trick in the other direction, as you drag to make the sidebar smaller. It doesn t work exactly as you would hope, reversing the pinning effect. Instead, when you drag within a few pixels of the optimal width, the sidebar edge suddenly jumps to the left to hit the sticky point, where it stays until your dragging catches up with it.
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