A Quick Assessment of Topology Preservation for SOM Structures

Vidaurre, Diego; Muruzábal, Jorge

doi:10.1109/tnn.2007.895820

Cited by 16 publications

(9 citation statements)

References 12 publications

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“…For a short review on topology preservation, see [32]. In our problem, we have not a feature space where the patterns are placed, and we have only a dissimilarity matrix that reports the pattern organization.…”

Section: Map Evaluationmentioning

confidence: 99%

Soft Topographic Maps for Clustering and Classifying Bacteria Using Housekeeping Genes

Rosa

Rizzo

Urso

2011

Advances in Artificial Neural Systems

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The Self-Organizing Map (SOM) algorithm is widely used for building topographic maps of data represented in a vectorial space, but it does not operate with dissimilarity data. Soft Topographic Map (STM) algorithm is an extension of SOM to arbitrary distance measures, and it creates a map using a set of units, organized in a rectangular lattice, defining data neighbourhood relationships. In the last years, a new standard for identifying bacteria using genotypic information began to be developed. In this new approach, phylogenetic relationships of bacteria could be determined by comparing a stable part of the bacteria genetic code, the so-called "housekeeping genes." The goal of this work is to build a topographic representation of bacteria clusters, by means of self-organizing maps, starting from genotypic features regarding housekeeping genes.

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Section: Map Evaluationmentioning

confidence: 99%

Soft Topographic Maps for Clustering and Classifying Bacteria Using Housekeeping Genes

Rosa

Rizzo

Urso

2011

Advances in Artificial Neural Systems

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“…Second, can uniquely determine an orthogonal transformations matrix , where is introduced by . If 2 According to (6), it is clear that the optimal solution of inlaying transform matrix is irrelevant to c. Hence, we will not take into account the perturbation of c here. 3 For simplicity, in the following discussion, we sometimes use symbols without superscript to denote the corresponding variable at the (t 0 1)th step of inlaying.…”

Section: F An Analytical Justification Of the Approximately Optimal mentioning

confidence: 99%

“…6 It is more likely to get a biased result if we explicitly use an incomplete statistic to evaluate the topological and geometric preservation of different algorithms. Hence, we should avoid using the explicit structure criterion similar to known manifold learning algorithms.…”

Section: B a Quantitative Criterion Based On Kolmogorov Complexitymentioning

confidence: 99%

“…Nonlinear mapping techniques, such as self-organizing maps (SOM) [4]- [6], principal curves [7], [8], and topology preserving networks [9], do not involve a global cost function, tend to have many free parameters, and are limited in low-dimensional data sets [3]. To overcome these drawbacks, some classical manifold learning algorithms, e.g., isometric feature mapping (Isomap) [10], locally linear embedding (LLE) [11], and Laplacian eigenmap [12], have been developed.…”

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confidence: 99%

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Nonlinear Dimensionality Reduction by Locally Linear Inlaying

Hou

Zhang

et al. 2009

IEEE Trans. Neural Netw.

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High-dimensional data is involved in many fields of information processing. However, sometimes, the intrinsic structures of these data can be described by a few degrees of freedom. To discover these degrees of freedom or the low-dimensional nonlinear manifold underlying a high-dimensional space, many manifold learning algorithms have been proposed. Here we describe a novel algorithm, locally linear inlaying (LLI), which combines simple geometric intuitions and rigorously established optimality to compute the global embedding of a nonlinear manifold. Using a divide-and-conquer strategy, LLI gains some advantages in itself. First, its time complexity is linear in the number of data points, and hence LLI can be implemented efficiently. Second, LLI overcomes problems caused by the nonuniform sample distribution. Third, unlike existing algorithms such as isometric feature mapping (Isomap), local tangent space alignment (LTSA), and locally linear coordination (LLC), LLI is robust to noise. In addition, to evaluate the embedding results quantitatively, two criteria based on information theory and Kolmogorov complexity theory, respectively, are proposed. Furthermore, we demonstrated the efficiency and effectiveness of our proposal by synthetic and real-world data sets.

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“…In order to evaluate the topology preservation we use the Directional Product (DP ) [23], which is an improved and computationally less expensive implementation of Topographic Product. The maximum value of DP is 1.0 and higher values correspond to better topologies.…”

Section: Topology Evaluationmentioning

confidence: 99%

Clustering Quality and Topology Preservation in Fast Learning SOMs

Fiannaca

Fatta

Gaglio

et al. 2008

Artificial Neural Networks - ICANN 2008

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The Self-Organizing Map (SOM ) is a popular unsupervised neural network able to provide effective clustering and data visualization for data represented in multidimensional input spaces. In this paper we describe Fast Learning SOM (FLSOM ) which adopts a learning algorithm that improves the performance of the standard SOM with respect to the convergence time in the training phase. We show that FLSOM also improves the quality of the map by providing better clustering quality and topology preservation of multidimensional input data. Several tests have been carried out on different multidimensional datasets, which demonstrate better performances of the algorithm in comparison with the original SOM.

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A Quick Assessment of Topology Preservation for SOM Structures

Cited by 16 publications

References 12 publications

Soft Topographic Maps for Clustering and Classifying Bacteria Using Housekeeping Genes

Soft Topographic Maps for Clustering and Classifying Bacteria Using Housekeeping Genes

Nonlinear Dimensionality Reduction by Locally Linear Inlaying

Clustering Quality and Topology Preservation in Fast Learning SOMs

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