Moment approach to high-order accelerator beam optics - download pdf or read online

By Lysenko, W.P.; Los Alamos National Laboratory.; United States. Dept. of Energy.; United States. Dept. of Energy. Office of Scientific and Technical Information

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By Lysenko, W.P.; Los Alamos National Laboratory.; United States. Dept. of Energy.; United States. Dept. of Energy. Office of Scientific and Technical Information

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As can be seen in Fig. 8, augmenting the known data with zeros results in tight decision regions. Depending upon the desired classifier response, this may or may not be a preferred training method. 7 Decision boundaries for the modular neural network trained using Method 2. 8 Decision regions for modular network trained with augmented data (Method 3). signs for which the input data ranges are known and the designer is comfortable with the underlying statistics of the input features. 9 Decision regions for multiclass neural network trained on augmented data (Method 4).

2 Sum of squared difference metric In many applications the sum of squared difference (SSD) metric is used in place of the Euclidean distance to save processing time. For two vectors, x and y, of length N it is defined as N (xi − yi )2 . 3 Taxicab distance metric The taxicab, city block, or Manhattan distance metric is less computational than the Euclidean distance metric and is easier to implement in specialized hardware. For two vectors, x and y, of length N it is defined as N |xi − yi |. 4 Mahalanobis distance metric The Mahalanobis distance metric is a more advanced version of the Euclidean distance metric.

While samples do not generally need to be labeled for unsupervised approaches, the neural-network designer does need to know something about the data in order to interpret the results. , metadata) that might not be used as inputs to the unsupervised neural network but that can provide a better understanding of the groupings that it produces. 2 Feature Selection and Extraction Feature selection is key to developing a successful neural network. When the number of features is small and the number of samples is large, the designer can allow 26 Chapter 4 the neural network to choose the importance of each feature in making its decisions.

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Moment approach to high-order accelerator beam optics by Lysenko, W.P.; Los Alamos National Laboratory.; United States. Dept. of Energy.; United States. Dept. of Energy. Office of Scientific and Technical Information


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