Validation of Nonlinear PCA

Scholz, Matthias

doi:10.1007/s11063-012-9220-6

Cited by 67 publications

(40 citation statements)

References 23 publications

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“…43) and compared these fits to a prediction derived from the contours of the shapes (shape skeleton; green lines). As can be seen, the red response fits deviate substantially from the green predictions based on local geometry.…”

Section: Resultsmentioning

confidence: 99%

Visual perception of shape altered by inferred causal history

Spröte

Schmidt

Fleming

2016

Sci Rep

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One of the main functions of vision is to represent object shape. Most theories of shape perception focus exclusively on geometrical computations (e.g., curvatures, symmetries, axis structure). Here, however, we find that shape representations are also profoundly influenced by an object’s causal origins: the processes in its past that formed it. Observers placed dots on objects to report their perceived symmetry axes. When objects appeared ‘complete’—created entirely by a single generative process—responses closely approximated the object’s geometrical axes. However, when objects appeared ‘bitten’—as if parts had been removed by a distinct causal process—the responses deviated significantly from the geometrical axes, as if the bitten regions were suppressed from the computation of symmetry. This suppression of bitten regions was also found when observers were not asked about symmetry axes but about the perceived front and back of objects. The findings suggest that visual shape representations are more sophisticated than previously appreciated. Objects are not only parsed according to what features they have, but also to how or why they have those features.

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Section: Resultsmentioning

confidence: 99%

Visual perception of shape altered by inferred causal history

Spröte

Schmidt

Fleming

2016

Sci Rep

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“…This results in a 18-dimensional time-varying signal. We use a 3-layer autoencoder to reduce the dimension of the data from 18 dimensions to 2, using the nonlinear PCA toolbox for Matlab [21]. The network has one hidden layer with 6 nodes and an output layer has 2 nodes.…”

Section: Experiments and Resultsmentioning

confidence: 99%

Ranking the parameters of deep neural networks using the fisher information

Tao

Berisha

Woolf

et al. 2016

2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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The large number of parameters in deep neural networks (DNNs) often makes them prohibitive for low-power devices, such as field-programmable gate arrays (FPGA). In this paper, we propose a method to determine the relative importance of all network parameters by measuring the amount of information that the network output carries about each of the parameters -the Fisher Information. Based on the importance ranking, we design a complexity reduction scheme that discards unimportant parameters and assigns more quantization bits to more important parameters. For evaluation, we construct a deep autoencoder and learn a non-linear dimensionality reduction scheme for accelerometer data measuring the gait of individuals with Parkinson's disease. Experimental results confirm that the proposed ranking method can help reduce the complexity of the network with minimal impact on performance.

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“…Ed (y) = 0, including isotropic pdfs, for which nonlinear methods must be used [24,25], such as the nonlinear-PCA (NL-PCA) [26] which has been applied to climatic data [27][28][29][30][31].…”

Section: Note That There Are Examples Of Non-gaussian Pdfs Verifyingmentioning

confidence: 99%

Independent Subspace Analysis of the Sea Surface Temperature Variability: Non-Gaussian Sources and Sensitivity to Sampling and Dimensionality

Pires

Hannachi

2017

Complexity

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We propose an expansion of multivariate time-series data into maximally independent source subspaces. The search is made among rotations of prewhitened data which maximize non-Gaussianity of candidate sources. We use a tensorial invariant approximation of the multivariate negentropy in terms of a linear combination of squared coskewness and cokurtosis. By solving a high-order singular value decomposition problem, we extract the axes associated with most non-Gaussianity. Moreover, an estimate of the Gaussian subspace is provided by the trailing singular vectors. The independent subspaces are obtained through the search of "quasiindependent" components within the estimated non-Gaussian subspace, followed by the identification of groups with significant joint negentropies. Sources result essentially from the coherency of extremes of the data components. The method is then applied to the global sea surface temperature anomalies, equatorward of 65 ∘ , after being tested with non-Gaussian surrogates consistent with the data anomalies. The main emerging independent components and subspaces, supposedly generated by independent forcing, include different variability modes, namely, The East-Pacific, the Central Pacific, and the Atlantic Niños, the Atlantic Multidecadal Oscillation, along with the subtropical dipoles in the Indian, South Pacific, and South-Atlantic oceans. Benefits and usefulness of independent subspaces are then discussed.

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Validation of Nonlinear PCA

Cited by 67 publications

References 23 publications

Visual perception of shape altered by inferred causal history

Visual perception of shape altered by inferred causal history

Ranking the parameters of deep neural networks using the fisher information

Independent Subspace Analysis of the Sea Surface Temperature Variability: Non-Gaussian Sources and Sensitivity to Sampling and Dimensionality

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