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Margin Analysis of the LVQ Algorithm 02

Margin Analysis of the LVQ Algorithm

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Annual Conference on neural Information Processing Systems

作者： Koby Crammer Ran Gilad-Bachrach Amir Navot Naftali Tishby School of Computer Science and Engineering and Interdisciplinary Center for Neural Computation The Hebrew University Jerusalem Israel

ISBN: (纸本)0262025507

Prototypes based algorithms are commonly used to reduce the computational complexity of Nearest-Neighbour (NN) classifiers. In this paper we discuss theoretical and algorithmical aspects of such algorithms. On the theory side, we present margin based generalization bounds that suggest that these kinds of classifiers can be more accurate then the 1-NN rule. Furthermore, we derived a training algorithm that selects a good set of prototypes using large margin principles. We also show that the 20 years old Learning Vector Quantization (LVQ) algorithm emerges naturally from our framework.

关键词： algorithms PROTOTYPE Classifiers Tumor margin status complexity classes Generalization

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Extracting Relevant Structures with Side Information 02

Extracting Relevant Structures with Side Information

引用

Annual Conference on neural Information Processing Systems

作者： Gal Chechik Naftali Tishby School of Computer Science and Engineering and The Interdisciplinary Center for Neural Computation The Hebrew University of Jerusalem 91904 Israel

ISBN: (纸本)0262025507

The problem of extracting the relevant aspects of data, in face of multiple conflicting structures, is inherent to modeling of complex data. Extracting structure in one random variable that is relevant for another variable has been principally addressed recently via the information bottleneck method. However, such auxiliary variables often contain more information man is actually required due to structures that are irrelevant for the task. In many other cases it is in fact easier to specify what is irrelevant than what is, for the task at hand. Identifying the relevant structures, however, can thus be considerably improved by also minimizing the information about another, irrelevant, variable. In this paper we give a general formulation of this problem and derive its formal, as well as algorithmic, solution. Its operation is demonstrated in a synthetic example and in two real world problems in the context of text categorization and face images. While the original information bottleneck problem is related to rate distortion theory, with the distortion measure replaced by the relevant information, extracting relevant features while removing Irrelevant ones is related to rate distortion with side information.

关键词： Distortion measurement information side information Rate distortion theory Text categorization World problems Rate distortion Random variable Variable Traffic Bottlenecks

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Cross-dataset Clustering: Revealing Corresponding Themes Across Multiple Corpora 6

Cross-dataset Clustering: Revealing Corresponding Themes Acr...

引用

6th Conference on Natural Language Learning, CoNLL 2002

作者： Dagan, Ido Marx, Zvika Shamir, Eli Department of Computer Science Bar-Ilan University Ramat-Gan52900 Israel LingoMotors Inc United States Center for Neural Computation The Hebrew University CS Dept. Bar-Ilan University Ramat-Gan52900 Israel School of Computer Science and Engineering The Hebrew University Jerusalem91904 Israel

We present a method for identifying corresponding themes across several corpora that are focused on related, but distinct, domains. This task is approached through simultaneous clustering of keyword sets extracted from the analyzed corpora. Our algorithm extends the information-bottleneck soft clustering method for a suitable setting consisting of several datasets. Experimentation with topical corpora reveals similar aspects of three distinct religions. The evaluation is by way of comparison to clusters constructed manually by an expert. © 2002 Proceedings of the Annual Meeting of the Association for computational Linguistics. All Rights Reserved.

关键词： Cluster analysis

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Universality and individuality in a neural code

Universality and individuality in a neural code

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14th Annual neural Information Processing Systems Conference, NIPS 2000

作者： Schneidman, Elad Brenner, Naama Tishby, Naftali De Ruyter Van Steveninck, Rob R. Bialek, William School of Computer Science and Engineering Center for Neural Computation Jerusalem 91904 Israel Department of Neurobiology Hebrew University Jerusalem 91904 Israel NEC Research Institute 4 Independence Way Princeton NJ 08540 United States

ISBN: (纸本)0262122413

The problem of neural coding is to understand how sequences of action potentials (spikes) are related to sensory stimuli, motor outputs, or (ultimately) thoughts and intentions. One clear question is whether the same coding rules are used by different neurons, or by corresponding neurons in different individuals. We present a quantitative formulation of this problem using ideas from information theory, and apply this approach to the analysis of experiments in the fly visual system. We find significant individual differences in the structure of the code, particularly in the way that temporal patterns of spikes are used to convey information beyond that available from variations in spike rate. On the other hand, all the flies in our ensemble exhibit a high coding efficiency, so that every spike carries the same amount of information in all the individuals. Thus the neural code has a quantifiable mixture of individuality and universality.

关键词： Electrophysiology

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Group redundancy measures reveal redundancy reduction in the auditory pathway 01

Group redundancy measures reveal redundancy reduction in the...

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Proceedings of the 14th International Conference on neural Information Processing Systems: Natural and Synthetic

作者： Gal Chechik Amir Globerson Naftali Tishby Michael J. Anderson Eric D. Young Israel Nelken School of Computer Science and Engineering and The Interdisciplinary Center for Neural Computation Hebrew University of Jerusalem Israel Department of Biomedical Engineering Johns Hopkins University Baltimore MD Department of Physiology Hadassah Medical School and The Interdisciplinary Center for Neural Computation Hebrew University of Jerusalem Israel

The way groups of auditory neurons interact to code acoustic information is investigated using an information theoretic approach. We develop measures of redundancy among groups of neurons, and apply them to the study of collaborative coding efficiency in two processing stations in the auditory pathway: the inferior colliculus (IC) and the primary auditory cortex (AI). Under two schemes for the coding of the acoustic content, acoustic segments coding and stimulus identity coding, we show differences both in information content and group redundancies between IC and AI neurons. These results provide for the first time a direct evidence for redundancy reduction along the ascending auditory pathway, as has been hypothesized for theoretical considerations [Barlow 1959,2001]. The redundancy effects under the single-spikes coding scheme are significant. only for groups larger than ten cells, and cannot be revealed with the redundancy measures that use only pairs of cells. The results suggest that, the auditory system transforms low level representations that contain redundancies due to the statistical structure of natural stimuli, into a representation in which cortical neurons extract rare and independent component of complex acoustic signals, that are useful for auditory scene analysis.

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Data clustering by Markovian relaxation and the Information Bottleneck Method 00

Data clustering by Markovian relaxation and the Information ...

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Annual Conference on neural Information Processing Systems

作者： Noam Slonim Naftali Tishby School of Computer Science and Engineering and Center for Neural Computation The Hebrew University Jerusalem 91904 Israel

ISBN: (纸本)0262122413

We introduce a new, non-parametric and principled, distance based clustering method. This method combines a pairwise based approach with a vector-quantization method which provide a meaningful interpretation to the resulting clusters. The idea is based on turning the distance matrix into a Markov process and then examine the decay of mutual-information during the relaxation of this process. The clusters emerge as quasi-stable structures during this relaxation, and then are extracted using the information bottleneck method. These clusters capture the information about the initial point of the relaxation in the most effective way. The method can cluster data with no geometric or other bias and makes no assumption about the underlying distribution.

关键词： Markov chain zero point distance matrix Traffic Bottlenecks data clustering information quasi-steady states

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Universality and individuality in a neural code 00

Universality and individuality in a neural code

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Annual Conference on neural Information Processing Systems

作者： William Bialek Rob R. de Ruyter van Steveninck Naftali Tishby Naama Brenner Elad Schneidman School of Computer Science and Engineering Center for Neural Computation Hebrew University Jerusalem 91904 Israel

ISBN: (纸本)0262122413

关键词： personal identity ECCENTRIC Codes coding Visual System Information Theory Action Potentials Flies

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Temporally Dependent Plasticity: An Information Theoretic Account 00

Temporally Dependent Plasticity: An Information Theoretic Ac...

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Annual Conference on neural Information Processing Systems

作者： Naftali Tishby Gal Chechik School of Computer Science and Engineering and the Interdisciplinary Center for Neural Computation The Hebrew University Jerusalem Israel

ISBN: (纸本)0262122413

The paradigm of Hebbian learning has recently received a novel interpretation with the discovery of synaptic plasticity that depends on the relative timing of pre and post synaptic spikes. This paper derives a temporally dependent learning rule from the basic principle of mutual information maximization and studies its relation to the experimentally observed plasticity. We find that a supervised spike-dependent learning rule sharing similar structure with the experimentally observed plasticity increases mutual information to a stable near optimal level. Moreover, the analysis reveals how the temporal structure of time-dependent learning rules is determined by the temporal filter applied by neurons over their inputs. These results suggest experimental prediction as to the dependency of the learning rule on neuronal biophysical parameters.

关键词： Cognitive Hypothesis Testing temporal filter Hebbian principle temporal structure Synaptic plasticity information Relative time

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Document clustering using word clusters via the information bottleneck method 00

Document clustering using word clusters via the information ...

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Proceedings of the 23rd annual international ACM SIGIR conference on Research and development in information retrieval

作者： Noam Slonim Naftali Tishby School of Computer Science and Engineering and The Interdisciplinary Center for Neural Computation The Hebrew University Jerusalem 91904 Israel

ISBN: (纸本)9781581132267

We present a novel implementation of the recently introduced information bottleneck method for unsupervised document clustering. Given a joint empirical distribution of words and documents, p(x, y), we first cluster the words, Y, so that the obtained word clusters, Ytilde;, maximally preserve the information on the documents. The resulting joint distribution. p(X, Ytilde;), contains most of the original information about the documents, I(X; Ytilde;) ≈ I(X; Y), but it is much less sparse and noisy. Using the same procedure we then cluster the documents, X, so that the information about the word-clusters is preserved. Thus, we first find word-clusters that capture most of the mutual information about to set of documents, and then find document clusters, that preserve the information about the word clusters. We tested this procedure over several document collections based on subsets taken from the standard 20Newsgroups corpus. The results were assessed by calculating the correlation between the document clusters and the correct labels for these documents. Finding from our experiments show that this double clustering procedure, which uses the information bottleneck method, yields significantly superior performance compared to other common document distributional clustering algorithms. Moreover, the double clustering procedure improves all the distributional clustering methods examined here.

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Perceptual grouping and segmentation by stochastic clustering

Perceptual grouping and segmentation by stochastic clusterin...

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Conference on computer Vision and Pattern Recognition (CVPR)

作者： Y. Gdalyahu N. Shental D. Weinshall Center for Neural Computation Hebrew University of Jerusalem Jerusalem Israel Hebrew University of Jerusalem Jerusalem Jerusalem IL School of Computer Science and Engineering Hebrew University of Jerusalem Jerusalem Israel

We use cluster analysis as a unifying principle for problems from low, middle and high level vision. The clustering problem is viewed as graph partitioning, where nodes represent data elements and the weights of the edges represent pairwise similarities. Our algorithm generates samples of cuts in this graph, by using David Karger's contraction algorithm, and computes an "average" cut which provides the basis for our solution to the clustering problem. The stochastic nature of our method makes it robust against noise, including accidental edges and small spurious clusters. The complexity of our algorithm is very low: O(N log/sup 2/ N)for N objects and a fired accuracy level. Without additional computational cost, our algorithm provides a hierarchy of nested partitions. We demonstrate the superiority of our method for image segmentation on a few real color images. Our second application includes the concatenation of edges in a cluttered scene (perceptual grouping), where we show that the same clustering algorithm achieves as good a grouping, if not better as more specialized methods.

关键词： Stochastic processes Clustering algorithms Partitioning algorithms Image segmentation Layout Electrical capacitance tomography Image analysis Application software computer vision Image databases

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