Rent this article via DeepDyve. Karhunen J, Joutsensalo J. Generalisations of principal component analysis, optimisation problems, and neural networks. Neural Networks, ; 8 4 : — Google Scholar. Comon P, Golub GH. Tracking a few extreme singular values and vectors in signal processing.
Proceedings IEEE ; — Baldi P, Hornik K. Learning in linear neural networks: a survey. Palmieri F, Zhu J. Self-association and Hebbian learning in linear neural networks. Major limitations of PCA are that it provides a plexity and accuracy, have been proposed especially in the linear mapping only, and utilises merely the second-order stat- signal processing literature [2].
They provide a third broad group istics covariances of the data. On the other hand, these of methods for computing PCA which lies between the batch limitations greatly facilitate the computation of PCA compared alternatives and neural PCA learning algorithms.
Several of the to nonlinear techniques, and often make the same solution simpler adaptive algorithms can in fact be regarded as neural optimal in several different problems [1]. If the underlying data learning rules. Almost The same remark also concerns certain autoassociative multi- all the learning algorithms of PCA networks are based on the layer perception type data compressing networks.
Hebbian learning law and Oja's rule for extracting a single principal component. The authors do a good job in reviewing PCA networks are neural network realisations of principal the most widely known algorithms in a unified form. However, component analysis. Their learning algorithms are typically many important references, for example [3] and [4], are lacking. At the end of s, which is based on Diamantaras' thesis published in Most interest in PCA networks grew rapidly, together with a general of the references are from the year or before.
Admittedly, boom in neural networks. Many different, more or less related, the book contains some newer references, but mainly to the learning algorithms based on the seminal Oja's rule authors' own papers only. The experimental comparison of were proposed. This by Kung and Diamantaras is the only one devoted solely to is because an optimised learning parameter is used for APEX, this topic.
As such, it is a welcome review and standard while the learning parameter is constant for the other algor- reference of the field, which has matured to some extent during ithms. These include the effects of channel noise, asym- which has been expanded and updated considerably.
The metric PCA and nonlinear PCA, as well as signal enhancement authors have divided the book rather successsfully into eight against noise using the constrained and oriented PCA networks. The learning algorithm used for this purpose defines the orientation. The resulting classification might be expected to way the network weights are adjusted between successive be more accurate than other statistical ones because the training cycles or epochs.
Although many learning strategies training sample data are being used to provide estimates of the have been developed, the most widely used procedure is the shapes of distribution of membership of each class in the n- backpropagation learning algorithm, also known as the dimensional feature space as well as of the location of the generalised delta rule. The algorithm operates by searching an centre point of each class Mather, Each iteration in the gives good results if the frequency distribution of the data is in backpropagation algorithm has two basic movements: forward the multivariate normal distribution.
Unsupervised and backward. The forward propagation cycle starts with the classification methods can be used to find out whether training presentation of a set of input patterns to the network. The data represents the assumption of normal distribution. After backward error correction starts at the output layer and error is estimating the probabilities of each pixel being a member of fed backward through the intermediate layer towards the input the classes, the most likely class having the highest probability layer in order to adjust the weights and reduce the error.
The value is assigned to the pixel with a class label. If the highest process continues iteratively until the error is reduced to an probability value of a pixel is lower than a threshold to be set acceptable level. Although ANN-based classification methods are more robust 3.
Each processing node receives and sums a set of input accuracy. Network structure, therefore, has a direct and Mather were used. Thus, a ground truth image containing a total of Table 4. Image band combinations used in classification pixels was created.
Table 3 shows total number of pixels selected for each land cover type. As can be seen from According to these guidelines, weights in the network were the table, it was difficult to collect sample pixels for some randomly initialised in the range of [ It and momentum term were set to 0.
The symbol r is Urban a constant set by the noise level of the data. Typically, r is in Inland Water the range from 5 to Training processes for all network structures were controlled by taking Table 3.
In other words, learning process is stopped in-house software developed by the second author of this paper when the error on the validation set starts to rise. The was employed. The program randomly selects pixels from the generalisation capabilities of the trained networks were tested images by taking the ground truth image into account.
It also using the test pattern file. The results for all combinations allows the user to decide minimum and maximum number of including individual class accuracies were shown in Table 5. For minimum pixels were The table also includes the results of the Maximum Likelihood selected whilst pixels for maximum. For all band classification that is performed with exactly the same training combinations considered in this study training files included and test pixels.
The classification accuracies were estimated in pixels for each class pixels in total , validation files terms of Kappa coefficient, which is a more realistic statistical contained 40 pixels for each class, and testing files comprised measure of accuracy than overall accuracy since it incorporates pixels.
Network column in the table and principal component bands, several combinations of the shows the network structures established for the corresponding image data were produced by stacking image layers. In addition combination. C3 0. In order to estimate the number C5 0. The first is related to larger number higher than those produced by these images together with their of bare soil pixels in the image compared to the ML result. The principal components C3 and C4.
This shows the analysis of ground truth data showed that ANN classifier ineffectiveness of PCA bands for land cover type delineation.
The While the PCA bands do not introduce different distinctive second problem is about the incorrect classification of sea characteristics, they increase the dimensions and the pixels as inland water for pixels along the seashore. This is complexity of the data.
Therefore, they do not make any most likely resulted from the ground truth image due to the significant contribution to the results produced by the two possibility of selected pixels of inland water and water classifiers. Nonlinear component analysis as a kernel eigenvalue problem. Neural Computations, 10 5 , — Input space vs. Robust principal component analysis by self-organizing rules based on statistical physics approach.
Karhunen, J. Generalizations of principal component analysis, optimization problems, and neural networks. Neural Networks, 8 4 , — Bourlard, H. Auto-association by multilayer perceptrons and singular value decomposition. Biological Cybernetics, 59 4—5 , — Kramer, M. Nonlinear principal component analysis using autoassociative neural networks.
AIChE Journal, 37 2 , — Constrained principal component analysis via an orthogonal learning network. New Orleans, LA. Kambhatla, N. Fast non-linear dimension reduction. San Francisco, CA. An extension of neural gas to local PCA. Neurocomputing, 62 1 , — Hall, P.
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Journal of Climate and Applied Meteorology, 23 12 , — CGHAfor principal component extraction in the complex domain. Rattan, S.
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