The Linear Separability Problem: Some Testing Methods

Elizondo, David

doi:10.1109/tnn.2005.860871

Cited by 88 publications

(41 citation statements)

References 15 publications

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“…If synaptic strengths w ij exist that respect these constraints for all times t and neurons i, the sequence is called linearly separable. There exist many methods to test linear separability (Elizondo, 2006).…”

Section: Methodsmentioning

confidence: 99%

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Matching Recall and Storage in Sequence Learning with Spiking Neural Networks

Brea

Senn

Pfister

2013

Journal of Neuroscience

122

137

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Storing and recalling spiking sequences is a general problem the brain needs to solve. It is, however, unclear what type of biologically plausible learning rule is suited to learn a wide class of spatiotemporal activity patterns in a robust way. Here we consider a recurrent network of stochastic spiking neurons composed of both visible and hidden neurons. We derive a generic learning rule that is matched to the neural dynamics by minimizing an upper bound on the Kullback-Leibler divergence from the target distribution to the model distribution. The derived learning rule is consistent with spike-timing dependent plasticity in that a presynaptic spike preceding a postsynaptic spike elicits potentiation while otherwise depression emerges. Furthermore, the learning rule for synapses that target visible neurons can be matched to the recently proposed voltage-triplet rule. The learning rule for synapses that target hidden neurons is modulated by a global factor, which shares properties with astrocytes and gives rise to testable predictions.

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Section: Methodsmentioning

confidence: 99%

“…Linear separability, which is the criterion for learnability, was tested with the linear programming method provided by Mathematica (Elizondo, 2006). For the asymmetric Hebb rule, w ij ϭ 1/T ⌺ t (2 x i (t ϩ 1) Ϫ 1)(2 x j (t) Ϫ 1), we tested, whether these weights lead to perfect recall of the sequence.…”

Section: Methodsmentioning

confidence: 99%

Matching Recall and Storage in Sequence Learning with Spiking Neural Networks

Brea

Senn

Pfister

2013

Journal of Neuroscience

122

137

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show abstract

“…Undoubtedly, these approaches will be beneficial in terms of diagnostic correctness [33][34][35] . An exploratory analysis of neural networks in our dataset already increased the overall accuracy to 82% after 10-fold cross-validation [33] .…”

Section: Discussionmentioning

confidence: 99%

Automated Interpretation of Pulmonary Function Tests in Adults with Respiratory Complaints

et al. 2017

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Background: The use of pulmonary function tests is primarily based on expert opinion and international guidelines. Current interpretation strategies are using predefined cutoffs for the description of a typical pattern. Objectives: We aimed to explore the predicted disease outcome based on the American Thoracic Society/European Respiratory Society (ATS/ERS) interpreting strategy. Subsequently, we investigated whether an unbiased machine learning framework integrating lung function with clinical variables may provide alternative decision trees resulting in a more accurate diagnosis. Methods: Our study included data from 968 subjects admitted for the first time to a pulmonary practice. The final clinical diagnosis was based on the combination of complete pulmonary function with the investigations that were decided at the physician's discretion. Clinical diagnoses were separated into 10 different groups and validated by an expert panel. Results: The ATS/ERS algorithm resulted in a correct diagnostic label in 38% of the subjects. Chronic obstructive pulmonary disease (COPD) was detected with an acceptable accuracy (74%), whereas all other diseases were poorly identified. The new data-based decision tree improved the general accuracy to 68% after 10-fold cross-validation when detecting the most common lung diseases, with a significantly higher positive predictive value and sensitivity for COPD, asthma, interstitial lung disease, and neuromuscular disorder (83/78, 66/82, 52/59, and 100/54%, respectively). Conclusions: Our data show that the current algorithms for lung function interpretation can be improved by a computer-based choice of lung function and clinical variables and their decision-making thresholds.

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“…These methods are described in detail in [4]. Several heuristic methods, to reduce the calculation time while testing for linear separability, are presented in [3].…”

Section: Methods For Testing Linear Separabilitymentioning

confidence: 99%

Dimensionality Reduction and Microarray Data

Elizondo

Passow

Birkenhead

et al. 2008

Lecture Notes in Computational Science and Enginee

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Summary. Microarrays are being currently used for the expression levels of thousands of genes simultaneously. They present new analytical challenges because they have a very high input dimension and a very low sample size. It is highly complex to analyse multi-dimensional data with complex geometry and to identify lowdimensional "principal objects" that relate to the optimal projection while losing the least amount of information. Several methods have been proposed for dimensionality reduction of microarray data. Some of these methods include principal component analysis and principal manifolds. This article presents a comparison study of the performance of the linear principal component analysis and the non linear local tangent space alignment principal manifold methods on such a problem. Two microarray data sets will be used in this study. A classification model will be created using fully dimensional and dimensionality reduced data sets. To measure the amount of information lost with the two dimensionality reduction methods, the level of performance of each of the methods will be measured in terms of level of generalisation obtained by the classification models on previously unseen data sets. These results will be compared with the ones obtained using the fully dimensional data sets.

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The Linear Separability Problem: Some Testing Methods

Cited by 88 publications

References 15 publications

Matching Recall and Storage in Sequence Learning with Spiking Neural Networks

Matching Recall and Storage in Sequence Learning with Spiking Neural Networks

Automated Interpretation of Pulmonary Function Tests in Adults with Respiratory Complaints

Dimensionality Reduction and Microarray Data

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