Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets

Demartines, Pierre; Hérault, Jeanny

doi:10.1109/72.554199

Cited by 533 publications

(334 citation statements)

References 9 publications

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“…In particular, we mention the following seven techniques: (1) Sammon mapping (Sammon, 1969), (2) curvilinear components analysis (CCA; Demartines and Hérault, 1997), (3) Stochastic Neighbor Embedding (SNE; Hinton and Roweis, 2002), (4) Isomap (Tenenbaum et al, 2000), (5) Maximum Variance Unfolding (MVU; Weinberger et al, 2004), (6) Locally Linear Embedding (LLE; Roweis and Saul, 2000), and (7) Laplacian Eigenmaps (Belkin and Niyogi, 2002). Despite the strong performance of these techniques on artificial data sets, they are often not very successful at visualizing real, high-dimensional data.…”

Section: Introductionmentioning

confidence: 99%

How to Use t-SNE Effectively

Wattenberg

Viégas

Johnson

2016

Distill

704

489

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We present a new technique called "t-SNE" that visualizes high-dimensional data by giving each datapoint a location in a two or three-dimensional map. The technique is a variation of Stochastic Neighbor Embedding (Hinton and Roweis, 2002) that is much easier to optimize, and produces significantly better visualizations by reducing the tendency to crowd points together in the center of the map. t-SNE is better than existing techniques at creating a single map that reveals structure at many different scales. This is particularly important for high-dimensional data that lie on several different, but related, low-dimensional manifolds, such as images of objects from multiple classes seen from multiple viewpoints. For visualizing the structure of very large data sets, we show how t-SNE can use random walks on neighborhood graphs to allow the implicit structure of all of the data to influence the way in which a subset of the data is displayed. We illustrate the performance of t-SNE on a wide variety of data sets and compare it with many other non-parametric visualization techniques, including Sammon mapping, Isomap, and Locally Linear Embedding. The visualizations produced by t-SNE are significantly better than those produced by the other techniques on almost all of the data sets.

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Section: Introductionmentioning

confidence: 99%

How to Use t-SNE Effectively

Wattenberg

Viégas

Johnson

2016

Distill

704

489

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“…In this study, some unsupervised statistical and neural projection models, namely Principal Component Analysis (PCA) [9], Curvilinear Component Analysis (CCA) [10], and Cooperative Maximum Likelihood Hebbian Learning (CMLHL) [11] have been applied, comparing their results. PCA [9] is a standard statistical technique for compressing multidimensional data; it can be shown to give the best linear compression of the data in terms of least mean square error.…”

Section: Unsupervised Projection Modelsmentioning

confidence: 99%

“…CCA [10] is a nonlinear dimensionality reduction method. It was developed as an improvement on the Self Organizing Map (SOM) [12], trying to circumvent the limitations inherent in some linear models such as PCA.…”

Section: Unsupervised Projection Modelsmentioning

confidence: 99%

Unsupervised Visualization of SQL Attacks by Means of the SCMAS Architecture

Herrero

Pinzón

Corchado

et al. 2010

Advances in Intelligent and Soft Computing

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Abstract. This paper presents an improvement of the SCMAS architecture aimed at securing SQL-run databases. The main goal of such architecture is the detection and prevention of SQL injection attacks. The improvement consists in the incorporation of unsupervised projection models for the visual inspection of SQL traffic. Through the obtained projections, SQL injection queries can be identified and subsequent actions can be taken. The proposed approach has been tested on a real dataset, and the obtained results are shown.

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“…Another method based on curvilinear component analysis (CCA) [16] uses similar ideas to this work in term of finding mappings between data space and unfolded spaces. This task is done in two stages of learning the unfolding transformation by a neural network, and then nonlinear projection of the input space through the mapping.…”

Section: Introductionmentioning

confidence: 99%

Manifold learning and unwrapping using density ridges

Shaker¹

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xii 3.6 Unwrapped mnist-0 digits with a selection of images of the actual digits on top. Orientation and thickness of digits smoothly vary across horizontal and vertical directions, respectively. . 34 3.7 Unfolding mnist-0 digits using two benchmark manifold learning methods. Unlike the proposed method, no smooth variation of structure is preserved using these methods. . . . . 35 3.8 Unfolding mnist-2 digits using the proposed method and t-SNE. Similar to Figure 3.7(b) for mnist-0, no smooth variation of structure is preserved using t-SNE, while proposed method shows smooth change of thickness and shape in horizontal and vertical coordinates, respectively. 36 3.9 Unfolding mnist-9 digits using the proposed method, which shows smooth change of thickness Sylvain Bouix, who were also my mentors, for all of their guidance through this process; your discussion, ideas, and feedback have been absolutely invaluable.

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Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets

Cited by 533 publications

References 9 publications

How to Use t-SNE Effectively

How to Use t-SNE Effectively

Unsupervised Visualization of SQL Attacks by Means of the SCMAS Architecture

Manifold learning and unwrapping using density ridges

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