A nonlinear projection method based on Kohonen's topology preserving maps

Kraaijveld, Martin; Mao, Jianchang; Jain, Anil K.

doi:10.1109/72.377962

Cited by 184 publications

(68 citation statements)

References 24 publications

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“…2. The first force, , represents the updating force from the winner to the input , which is the same as that used by the winner in (6). It adapts the neurons toward the input in a direction that is orthogonal to the tangent plane of the winner.…”

Section: A Visom Structure and Derivationmentioning

confidence: 99%

“…A winning neuron can be found according to its distance to the input, i.e., Then the SOM updates the weight of the winning neuron according to (6) where is the learning rate at time . In the SOM, the weights of the neurons in a neighborhood of the winner are updated by (7) where is the neighborhood function, which is monotonically decreasing with .…”

Section: A Visom Structure and Derivationmentioning

confidence: 99%

“…The algorithm has found a wide range of applications in VQ, pattern classification, data mining and visualization, knowledge discovery, and information retrieval. When the SOM is used for visualization, however, as the inter-neuron distances are not directly visible or measurable on the map, one has to use a coloring scheme such as the U-matrix [5], [6], or interpolation [10], to mark relative distances between the weights of neighboring neurons referred in the input space. Even so, the structures of data clusters may not be apparent and often appear distorted.…”

Section: Introductionmentioning

confidence: 99%

“…Kohonen's SOM is an abstract mathematical model of the mapping between nerve sensory (especially retina) and cerebral cortex (especially visual cortex) [3], [4]. As the inputs to the SOM are often drawn from a high-dimensional space, the algorithm has been used as a visualization tool for dimensional reduction (e.g., [5], [6]). One of greatest properties of the SOM is that it is a topology preserving mapping, i.e., close points in the input space will be mapped to nearby neurons in the map space.…”

Section: Introductionmentioning

confidence: 99%

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ViSOM - a novel method for multivariate data projection and structure visualization

Yin

2002

IEEE Trans. Neural Netw.

173

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Abstract-When used for visualization of high-dimensional data, the self-organizing map (SOM) requires a coloring scheme such as the U-matrix to mark the distances between neurons. Even so, the structures of the data clusters may not be apparent and their shapes are often distorted. In this paper, a visualization-induced SOM (ViSOM) is proposed to overcome these shortcomings. The algorithm constrains and regularizes the inter-neuron distance with a parameter that controls the resolution of the map. The mapping preserves the inter-point distances of the input data on the map as well as the topology. It produces a graded mesh in the data space such that the distances between mapped data points on the map resemble those in the original space, like in the Sammon mapping. However, unlike the Sammon mapping, the ViSOM can accommodate both training data and new arrivals and is much simpler in computational complexity. Several experimental results and comparisons with other methods are presented.

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Section: A Visom Structure and Derivationmentioning

confidence: 99%

Section: A Visom Structure and Derivationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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ViSOM - a novel method for multivariate data projection and structure visualization

Yin

2002

IEEE Trans. Neural Netw.

173

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“…SOFM is a neural network based on "competitive learning", that is, the neurons of output layer will compete with each other so as to get activated opportunity [7,8]. Generally, in competitive learning neural network, the winner will be selected from competitive phase, and the weight vector of the winner will be adjusted in the reward phase, which is as shown in equation (1)-(2).…”

Section: Using the Topological Network Of Sofm To Realize The Structumentioning

confidence: 99%

An Approach for Fuzzy Modeling based on Self-Organizing Feature Maps Neural Network

Chen¹,

Chiang²,

Chen³

et al. 2014

Appl. Math. Inf. Sci.

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Abstract:Exploration of large and high-dimensional data sets is one of the main problems in data analysis. Self-organizing feature maps (SOFM) is a powerful technique for clustering analysis and data mining. Competitive learning in the SOFM training process focuses on finding a neuron that its weight vector is most similar to that of an input vector. SOFM can be used to map large data sets to a simpler, usually one or two-dimensional topological structure. In this paper, we present a new approach to acquisition of initial fuzzy rules using SOFM learning algorithm, not only for its vector feature, but also for its topological. In general, fuzzy modeling requires two stages: structure identification and parameter learning. First, the algorithm partitions the input space into some local regions by using SOFM, then it determines the decision boundaries for local input regions, and finally, based on the decision boundaries, it learns the fuzzy rule for each local region by recursive least squares algorithm. The simulation results show that the proposed method can provide good model structure for fuzzy modeling and has high computing efficiency.

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Coupling self‐organizing maps with a Naïve Bayesian classifier: Stream classification studies using multiple assessment data

Fytilis

Rizzo

2013

Water Resources Research

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Organizing or clustering data into natural groups is one of the most fundamental aspects of understanding and mining information. The recent explosion in sensor networks and data storage associated with hydrological monitoring has created a huge potential for automating data analysis and classification of large, high‐dimensional data sets. In this work, we develop a new classification tool that couples a Naïve Bayesian classifier with a neural network clustering algorithm (i.e., Kohonen Self‐Organizing Map (SOM)). The combined Bayesian‐SOM algorithm reduces classification error by leveraging the Bayesian's ability to accommodate parameter uncertainty with the SOM's ability to reduce high‐dimensional data to lower dimensions. The resulting algorithm is data‐driven, nonparametric and is as computationally efficient as a Naïve Bayesian classifier due to its parallel architecture. We apply, evaluate and test the Bayesian‐SOM network using two real‐world hydrological data sets. The first uses genetic data to classify the state of disease in native fish populations in the upper Madison River, MT, USA. The second uses stream geomorphic and water quality data measured at ∼2500 Vermont stream reaches to predict habitat conditions. The new classification tool has substantial benefits over traditional classification methods due to its ability to dynamically update prior information, assess the uncertainty/confidence of the posterior probability values, and visualize both the input data and resulting probabilistic clusters onto two‐dimensional maps to better assess nonlinear mappings between the two.

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A nonlinear projection method based on Kohonen's topology preserving maps

Cited by 184 publications

References 24 publications

ViSOM - a novel method for multivariate data projection and structure visualization

ViSOM - a novel method for multivariate data projection and structure visualization

An Approach for Fuzzy Modeling based on Self-Organizing Feature Maps Neural Network

Coupling self‐organizing maps with a Naïve Bayesian classifier: Stream classification studies using multiple assessment data

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