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Michael Lindenbaum

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6 papers

2 author rows

NeurIPS Conference 2014 Conference Paper

Approximating Hierarchical MV-sets for Hierarchical Clustering

Assaf Glazer
Omer Weissbrod
Michael Lindenbaum
Shaul Markovitch

The goal of hierarchical clustering is to construct a cluster tree, which can be viewed as the modal structure of a density. For this purpose, we use a convex optimization program that can efficiently estimate a family of hierarchical dense sets in high-dimensional distributions. We further extend existing graph-based methods to approximate the cluster tree of a distribution. By avoiding direct density estimation, our method is able to handle high-dimensional data more efficiently than existing density-based approaches. We present empirical results that demonstrate the superiority of our method over existing ones.

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NeurIPS Conference 2013 Conference Paper

q-OCSVM: A q-Quantile Estimator for High-Dimensional Distributions

Assaf Glazer
Michael Lindenbaum
Shaul Markovitch

In this paper we introduce a novel method that can efficiently estimate a family of hierarchical dense sets in high-dimensional distributions. Our method can be regarded as a natural extension of the one-class SVM (OCSVM) algorithm that finds multiple parallel separating hyperplanes in a reproducing kernel Hilbert space. We call our method q-OCSVM, as it can be used to estimate $q$ quantiles of a high-dimensional distribution. For this purpose, we introduce a new global convex optimization program that finds all estimated sets at once and show that it can be solved efficiently. We prove the correctness of our method and present empirical results that demonstrate its superiority over existing methods.

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NeurIPS Conference 2012 Conference Paper

Learning High-Density Regions for a Generalized Kolmogorov-Smirnov Test in High-Dimensional Data

Assaf Glazer
Michael Lindenbaum
Shaul Markovitch

We propose an efficient, generalized, nonparametric, statistical Kolmogorov-Smirnov test for detecting distributional change in high-dimensional data. To implement the test, we introduce a novel, hierarchical, minimum-volume sets estimator to represent the distributions to be tested. Our work is motivated by the need to detect changes in data streams, and the test is especially efficient in this context. We provide the theoretical foundations of our test and show its superiority over existing methods.

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AAAI Conference 1999 Conference Paper

Selective Sampling for Nearest Neighbor Classifiers

Michael Lindenbaum
Shaul Markovich
Dmitry Rusakov
Technion - Israel Institute of Technology

In the passive, traditional, approachto learning, the information available to the learner is a set of classified examples, whichare randomlydrawnfrom the instance space. In many applications, however, the initial classification of the training set is a costly process, andan intelligently selection of training examplesfromunlabeled data is doneby an active learner. This paper proposesa loolmheadalgorithm for example selection and addresses the problemof active learning in the context of nearest neighborclassifiers. Theproposedapproachrelies on using a random field modelfor the examplelabeling, whichimplies a dynamicchange of the label estimates during the samplingprocess. The proposedselective samplingalgorithm wasevaluated empirically on artificial andreal data sets. The experiments showthat the proposed method outperforms other methodsin most cases.

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AAAI Conference 1994 Conference Paper

Applying VC-Dimension Analysis to 3D Object Recognition from Perspective Projections

Michael Lindenbaum

We analyze the amount of information needed to carry out model-based recognition tasks, in the context of a probabilistic data collection model, and independently of the recognition method employed. We consider the very rich class of semi-algebraic 3D objects, and derive an upper bound on the number of data features that (provably) suffice for localizing the object with some pre-specified precision. Our bound is based on analysing the combinatorial complexity of the hypotheses class that one has to choose from, and quantifying it using a VC-dimension parameter. Once this parameter is found, the bounds are obtained by drawing relations between recognition and learning, and using well-known results from computational learning theory. It turns out that this bounds grow logarithmically in the algebraic complexity of the objects.

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ICRA Conference 1991 Conference Paper

Parallel strategies for geometric probing

Michael Lindenbaum
Alfred M. Bruckstein

The problem of recovering the shape of planar objects from line or finger probings arises in robotics. This problem is addressed under the assumption that composite probings are made. One composite probing comprises several (k) line or finger probings done simultaneously. An investigation is conducted of planar polygon reconstruction from sequences of composite k-probings. For every value of k, a lower bound on the number of k-probings required for reconstruction under any strategy is obtained. Specific strategies which are provably almost optimal are provided. >

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