Lowe, D., & Tipping, M. E. (1996). Feed-forward neural networks and topographic mappings for exploratory data analysis. Neural Computing and Applications, 4, 83--95.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....that the precise degree of similarity (or dissimilarity) of two data points is to be enforced. In general, which set of assumptions is best depends on the problem at hand. In terms of implementation, the present algorithm owes a great deal to the shadow targets algorithm for Neuroscale [8, 15], whose eponymous data points enforce equivalence classes on sets of (otherwise) unsupervised data. That algorithm trades fidelity of representation against fidelity of equivalence classes much in the same way as Equation 4, although it does so in the context of a Kohonen neural network instead of ....

D. Lowe and M. E. Tipping. Feed-forward neural networks and topographic mappings for exploratory data analysis. Neural Computing and Applications, 4:83--95, 1996.

....distance between the i th datum and the j th datum in the input (output) space. This cost function, which is called stress, measures the change of the data distance structure induced by the dimensional reduction. The stress is also used in MDS. The cost function (1) is the most popular one [1][5] In this study, however, we try to preserve not only the distance structure, but also the cluster structure. In general, the dimensional reduction does not preserve the cluster structure especially when the number of reduced dimension is large. In this study, we incorporate prior knowledge ....

Lowe, D. and Tipping, M. E., Feed-forward neural networks and topographic mappings for exploratory data analysis, Neural Computing and Applications 4, 83--95, 1996.

....and section 4 the results obtained. The final section discusses the implications of this work, its strengths and limitations and open questions for future research. 2 Associating Perception with Global Position Figure 1 shows the general structure of the radial basis function network ([2]) used for associating perception with virtual coordinates. r (x coord. 1 r (y coord. 2 v 1 o j Radial Basis Function Layer w j Linear Layer i N Input Vector v 2 Figure 1: Radial basis function network used to associate perception with virtual coordinates. In our ....

D. Lowe and M. Tipping, "Feed-Forward Neural Networks and Topographic Mappings for Exploratory Data Analysis", Neural Computing and Applications 4, pp. 83-95, 1996.

....of 72 subject areas in all higher education institutions in the UK. Variables such as the number of active researchers, 6 postgraduate students and number of publications formed a 79 dimensional database that is used to assess research, on a scale of 1 to 5, in each subject area at each institute [9]. The last data set is the much analysed iris data [10] where the patterns are represented by four attributes (sepal and petal lengths and widths) Since in three of the databases (chromosome (d.p. chromosome (geometrical) and RAE) there are (around) one hundred patterns in each class, we also ....

Lowe D, Tipping ME. Feed-forward neural networks and topographic mappings for exploratory data analysis. Neural Computing and Applications 1996; 4: 83-95.

....the F s and the G s is roughly the same as the size of the F s, this serves to even up the contributions to the objective function from different size F s and G s. It has recently been argued that this approach produces better maps than for instance the SOM [Bezdek Pal 1995, Mao Jain 1995, Lowe Tipping 1996]. Note that the Sammon formula is not symmetric to interchange of F and G. 3.2.2 Demartines and H erault A measure related is the Sammon approach is that of [Demartines Herault 1995, Demartines Herault 1996] N X i=1 X j i (F(i; j) Gamma G(M(i) M(j) 2 h(G(M(i) M(j) 6) h is ....

....They conclude that the SOM generally performs significantly worse. 4 Comparing measures for the square to line problem Comparisons between the performance of various mapping algorithms on particular problems have been illuminating [Durbin Mitchison 1990, Bezdek Pal 1995, Mao Jain 1995, Lowe Tipping 1996]. Here we ask a different set of questions. How do different measures compare in rating the same maps Do the measures generally give a consistent ordering for different maps How well does this ordering compare with intuitive assessments How sensitive are these orderings to the measure of ....

Lowe, D. & Tipping, M. (1996). Feed-forward Neural Networks and Topographic Mappings for Exploratory Data Analysis. Neural Computing and Applications, 4, 83-95.

....which only dissimilarities are given. Dissimilarities between objects are monotonically related to Euclidean distances between the objects. Various types of MDS procedures and objective functions have been presented in the past. Recently MDS also got some attention from neural network researchers [2, 3]. However, in [3] the focus is on MDS as a dimensionality reduction technique, and the proposed method still assumes coordinate representations for all the objects. In [2] a mean field approach to the MDS problem is presented, which does not work as intuitively as the methods we will present. ....

....are given. Dissimilarities between objects are monotonically related to Euclidean distances between the objects. Various types of MDS procedures and objective functions have been presented in the past. Recently MDS also got some attention from neural network researchers [2, 3] However, in [3] the focus is on MDS as a dimensionality reduction technique, and the proposed method still assumes coordinate representations for all the objects. In [2] a mean field approach to the MDS problem is presented, which does not work as intuitively as the methods we will present. Moreover, excellent ....

Lowe, David and Michael E. Tipping, Feed-forward Neural Networks and Topographic Mappings for Exploratory Data Analysis, Neural Computing and Applications 4, 83--95, 1996.

....vectors. Generally, q p as dimension reduction is desired, with q = 2 in visualisation applications. The archetypal neural network topographic paradigm, Kohonen s selforganising map (SOM) is seen to offer less informative projections in many visualisation and exploratory analysis applications [6, 7, 11]. An alternative topographic paradigm, the Sammon mapping 1 [10] can offer better results. The mapping is generated by minimisation of an error, or STRESS , measure which explicitly 1 The Sammon mapping is also a very close relative of the statistic field of multidimensional scaling. ....

....located in the feature space without an expensive re optimisation procedure of the complete dataset. Because of this, there has been significant recent interest in development of distancepreserving mappings which incorporate a parameterised transformation from the data space to the feature space [5, 1, 8, 12, 6]. By defining y i = f(x i ; w) where w is a parameter vector, E may be differentiated with respect to the parameters, and the feature vectors indirectly adjusted so as to minimise the STRESS. In the NEUROSCALE model [6] the transformation f( Delta) is effected by a radial basis function ....

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D. Lowe and M. E. Tipping. Feed-forward neural networks and topographic mappings for exploratory data analysis. Neural Computing and Applications, 4:83--95, 1996.

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Lowe, D., & Tipping, M. E. (1996). Feed-forward neural networks and topographic mappings for exploratory data analysis. Neural Computing and Applications, 4, 83--95.

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D. Lowe and M. E. Tipping. Feed-forward neural networks and topographic mappings for exploratory data analysis. Neural Computing and Applications, 4:83--95, 1996.

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D. Lowe and M. Tipping. Feed-forward neural networks and topographic mappings for exploratory data analysis. Neural Computing and Applications, pages 83-95, 1996.

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D. Lowe and M. E. Tipping, "Feed-forward neural networks and topographic mappings for exploratory data analysis," Neural Computing and Applications 4, pp. 83--95, 1996.

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