4 Unsupervised Learning Neural Networks

QR-Code Scanner In .NETUsing Barcode Control SDK for .NET framework Control to generate, create, read, scan barcode image in VS .NET applications.

In the above, dk,p is the Euclidean distance as de ned in equation (420), I is the total 1 number of input units, and gk (0) = 0 Thus, bk (0) = I , which initially gives each output unit an equal chance to be the winner; bk (t) is the conscience factor de ned for each output unit The more an output unit wins, the larger the value of gk (t) becomes, and bk (t) becomes larger negative Consequently, a factor |bk (t)| is added to the distance dk,p Usually, for normalized inputs, = 00001 and = 10

Quick Response Code Maker In Visual Studio .NETUsing Barcode encoder for Visual Studio .NET Control to generate, create QR Code image in .NET applications.

Self-Organizing Feature Maps

Scan QR Code In Visual Studio .NETUsing Barcode reader for .NET Control to read, scan read, scan image in Visual Studio .NET applications.

Kohonen developed the self-organizing feature map (SOM) [474, 475, 476], as motivated by the self-organization characteristics of the human cerebral cortex Studies of the cerebral cortex showed that the motor cortex, somatosensory cortex, visual cortex and auditory cortex are represented by topologically ordered maps These topological maps form to represent the structures sensed in the sensory input signals The self-organizing feature map is a multidimensional scaling method to project an I-dimensional input space to a discrete output space, e ectively performing a compression of input space onto a set of codebook vectors The output space is usually a two-dimensional grid The SOM uses the grid to approximate the probability density function of the input space, while still maintaining the topological structure of input space That is, if two vectors are close to one another in input space, so is the case for the map representation The SOM closely resembles the learning vector quantizer discussed in the previous section The di erence between the two unsupervised algorithms is that neurons are usually organized on a rectangular grid for SOM, and neighbors are updated to also perform an ordering of the neurons In the process, SOMs e ectively cluster the input vectors through a competitive learning process, while maintaining the topological structure of the input space Section 451 explains the standard stochastic SOM training rule, while a batch version is discussed in Section 452 A growing approach to SOM is given in Section 453 Di erent approaches to speed up the training of SOMs are overviewed in Section 454 Section 455 explains the formation of clusters for visualization purposes Section 456 discusses in brief di erent ways how the SOM can be used after training

Barcode Creation In .NETUsing Barcode creator for .NET Control to generate, create bar code image in Visual Studio .NET applications.

Stochastic Training Rule

Bar Code Reader In .NETUsing Barcode recognizer for Visual Studio .NET Control to read, scan read, scan image in .NET framework applications.

SOM training is based on a competitive learning strategy Assume I-dimensional input vectors zp , where the subscript p denotes a single training pattern The rst step of the training process is to de ne a map structure, usually a two-dimensional grid (refer to Figure 43) The map is usually square, but can be of any rectangular shape The number of elements (neurons) in the map is less than the number of training patterns Ideally, the number of neurons should be equal to the number of independent training patterns

Print QR In C#.NETUsing Barcode printer for .NET framework Control to generate, create QR Code JIS X 0510 image in VS .NET applications.

45 Self-Organizing Feature Maps

Encoding QR Code ISO/IEC18004 In .NET FrameworkUsing Barcode generator for ASP.NET Control to generate, create Quick Response Code image in ASP.NET applications.

Input Vector

Denso QR Bar Code Encoder In VB.NETUsing Barcode maker for VS .NET Control to generate, create QR Code image in .NET framework applications.

Figure 43 Self-organizing Map Each neuron on the map is associated with and I-dimensional weight vector that forms the centroid of one cluster Larger cluster groupings are formed by grouping together similar neighboring neurons Initialization of the codebook vectors can occur in various ways: Assign random values to each weight wkj = (wkj1 , wkj2 , , wKJI ), with K the number of rows and J the number of columns of the map The initial values are bounded by the range of the corresponding input parameter While random initialization of weight vectors is simple to implement, this form of initialization introduces large variance components into the map which increases training time Assign to the codebook vectors randomly selected input patterns That is, wkj = zp with p U (1, PT ) This approach may lead to premature convergence, unless weights are perturbed with small random values Find the principal components of the input space, and initialize the codebook vectors to re ect these principal components A di erent technique of weight initialization is due to Su et al [818], where the objective is to de ne a large enough hyper cube to cover all the training patterns [818] The algorithm starts by nding the four extreme points of the map by determining the four extreme training patterns Firstly, two patterns are found with the largest inter-pattern Euclidean distance A third pattern is (425)

Code 39 Full ASCII Drawer In .NET FrameworkUsing Barcode printer for Visual Studio .NET Control to generate, create Code 39 Extended image in Visual Studio .NET applications.

4 Unsupervised Learning Neural Networks located at the furthest point from these two patterns, and the fourth pattern with largest Euclidean distance from these three patterns These four patterns form the corners of the map Weight values of the remaining neurons are found through interpolation of the four selected patterns, in the following way: Weights of boundary neurons are initialized as w1j wKj wk1 wkJ = = = = w1J w11 (j 1) + w11 J 1 wKJ wK1 (j 1) + wK1 J 1 wK1 w11 (k 1) + w11 K 1 wKJ w1J (k 1) + w1J K 1 (426) (427) (428) (429)

Bar Code Drawer In .NET FrameworkUsing Barcode creator for .NET framework Control to generate, create bar code image in VS .NET applications.

for all j = 2, , J 1 and k = 2, , K 1 The remaining codebook vectors are initialized as wkj = wkJ wk1 (j 1) + wk1 J 1 (430)

Generating Bar Code In VS .NETUsing Barcode encoder for .NET framework Control to generate, create bar code image in .NET applications.

for all j = 2, , J 1 and k = 2, , K 1 The standard training algorithm for SOMs is stochastic, where codebook vectors are updated after each pattern is presented to the network For each neuron, the associated codebook vector is updated as wkj (t + 1) = wkj (t) + hmn,kj (t)[zp wkj (t)] (431)

Industrial 2 Of 5 Drawer In Visual Studio .NETUsing Barcode generator for VS .NET Control to generate, create Standard 2 of 5 image in Visual Studio .NET applications.

where mn is the row and column index of the winning neuron The winning neuron is found by computing the Euclidean distance from each codebook vector to the input vector, and selecting the neuron closest to the input vector That is, ||wmn zp ||2 = min{||wkj zp ||2 } 2

Encoding Data Matrix ECC200 In .NET FrameworkUsing Barcode generator for ASP.NET Control to generate, create Data Matrix image in ASP.NET applications.

(432)

UCC - 12 Encoder In VB.NETUsing Barcode creation for .NET Control to generate, create EAN128 image in Visual Studio .NET applications.

The function hmn,kj (t) in equation (431) is referred to as the neighborhood function Thus, only those neurons within the neighborhood of the winning neuron mn have their codebook vectors updated For convergence, it is necessary that hmn,kj (t) 0 when t The neighborhood function is usually a function of the distance between the coordinates of the neurons as represented on the map, ie hmn,kj (t) = h(||cmn ckj ||2 , t) 2 (433)

Printing Code39 In Visual Studio .NETUsing Barcode drawer for ASP.NET Control to generate, create Code 39 Extended image in ASP.NET applications.

with the coordinates cmn , ckj R2 With increasing value of ||cmn ckj ||2 (that is, 2 neuron kj is further away from the winning neuron mn), hmn,kj 0 The neighborhood can be de ned as a square or hexagon However, the smooth Gaussian kernel is mostly used: hmn,kj (t) = (t)e

Drawing Universal Product Code Version A In Visual C#.NETUsing Barcode generation for .NET Control to generate, create UPC-A Supplement 2 image in Visual Studio .NET applications.

||cmn ckj ||2 2 2 2 (t)

Create Barcode In Visual Studio .NETUsing Barcode creation for ASP.NET Control to generate, create bar code image in ASP.NET applications.

(434)

DataMatrix Creator In JavaUsing Barcode drawer for Java Control to generate, create Data Matrix image in Java applications.

Drawing GS1 - 13 In JavaUsing Barcode generator for Java Control to generate, create UPC - 13 image in Java applications.