k-Means Has Polynomial Smoothed Complexity

Arthur, David; Manthey, Bodo; Röglin, Heiko

doi:10.1109/focs.2009.14

Cited by 76 publications

(65 citation statements)

References 28 publications

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“…Then, the discriminant analysis is applied by leave-one-out cross-validation with k-means clustering. 37 In statistics and data mining, the k-means method is one of the most widely used clustering algorithms with nearest mean, drawing its popularity from its speed in practice. 37,38 Leave-one-out crossvalidation involves single observation from the original sample as the validation data, and the remaining observations as the training data.…”

Section: Data Analysesmentioning

confidence: 99%

Discriminant analysis of functional optical topography for schizophrenia diagnosis

Chuang

Nakagome

et al. 2013

J. Biomed. Opt

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Abstract. Abnormal prefrontal function plays a central role in the cognition deficits of schizophrenic patients; however, the character of the relationship between discriminant analysis and prefrontal activation remains undetermined. Recently, evidence of low prefrontal cortex (PFC) activation in individuals with schizophrenia has also been found during verbal fluency tests (VFT) and other cognitive tests with several neuroimaging methods. The purpose of this study is to assess the hemodynamic changes of the PFC and discriminant analysis between schizophrenia patients and healthy controls during VFT task by utilizing functional optical topography. A total of 99 subjects including 53 schizophrenic patients and 46 age-and gender-matched healthy controls were studied. The results showed that the healthy group had larger activation in the right and left PFC than in the middle PFC. Besides, the schizophrenic group showed weaker task performance and lower activation in the whole PFC than the healthy group. The result of the discriminant analysis showed a significant difference with P value <0.001 in six channels (CH 23,29,31,40,42, 52) between the schizophrenic and healthy groups. Finally, 68.69% and 71.72% of subjects are correctly classified as being schizophrenic or healthy with all 52 channels and six significantly different channels, respectively. Our findings suggest that the left PFC can be a feature region for discriminant analysis of schizophrenic diagnosis.

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Section: Data Analysesmentioning

confidence: 99%

Discriminant analysis of functional optical topography for schizophrenia diagnosis

Chuang

Nakagome

et al. 2013

J. Biomed. Opt

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“…Our work is also related to existing work on characterizing the stability of numerical methods [4,8] as well as the smoothed complexity of algorithms [1,20,21]. The key difference between our work and existing work in these areas is that we explore the smoothness of the value as well as the structure of our results.…”

Section: Related Workmentioning

confidence: 95%

A Framework for Evaluating the Smoothness of Data-Mining Results

Misra

Golshan

Terzi

2012

Machine Learning and Knowledge Discovery in Databases

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Abstract. The data-mining literature is rich in problems that are formalized as combinatorial-optimization problems. An indicative example is the entity-selection formulation that has been used to model the problem of selecting a subset of representative reviews from a review corpus [11,22] or important nodes in a social network [10]. Existing combinatorial algorithms for solving such entity-selection problems identify a set of entities (e.g., reviews or nodes) as important. Here, we consider the following question: how do small or large changes in the input dataset change the value or the structure of the such reported solutions?We answer this question by developing a general framework for evaluating the smoothness (i.e, consistency) of the data-mining results obtained for the input dataset X. We do so by comparing these results with the results obtained for datasets that are within a small or a large distance from X. The algorithms we design allow us to perform such comparisons effectively and thus, approximate the results' smoothness efficiently. Our experimental evaluation on real datasets demonstrates the efficacy and the practical utility of our framework in a wide range of applications.

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“…Smoothed analysis has originally been invented to explain the practical performance of the simplex method [34]. Since then, smoothed analysis has been applied successfully to a variety of algorithms and problems [2,31,36]. We refer to Spielman and Teng for a survey [35].…”

Section: Smoothed Analysismentioning

confidence: 99%

Stochastic Mean Payoff Games: Smoothed Analysis and Approximation Schemes

Boros

Elbassioni

Fouz

et al. 2011

Automata, Languages and Programming

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We consider two-player zero-sum stochastic mean payoff games with perfect information modeled by a digraph with black, white, and random vertices. These BWR-games games are polynomially equivalent with the classical Gillette games, which include many well-known subclasses, such as cyclic games, simple stochastic games, stochastic parity games, and Markov decision processes. They can also be used to model parlor games such as Chess or Backgammon.It is a long-standing open question if a polynomial algorithm exists that solves BWR-games. In fact, a pseudo-polynomial algorithm for these games with an arbitrary number of random nodes would already imply their polynomial solvability. Currently, only two classes are known to have such a pseudo-polynomial algorithm: BW-games (the case with no random nodes) and ergodic BWR-games (in which the game's value does not depend on the initial position) with constant number of random nodes.We show that the existence of a pseudo-polynomial algorithm for BWR-games with a constant number of random vertices implies smoothed polynomial complexity and the existence of absolute and relative polynomial-time approximation schemes. In particular, we obtain smoothed polynomial complexity and derive absolute and relative approximation schemes for BW-games and ergodic BWR-games (assuming a technical requirement about the probabilities at the random nodes).

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k-Means Has Polynomial Smoothed Complexity

Cited by 76 publications

References 28 publications

Discriminant analysis of functional optical topography for schizophrenia diagnosis

Discriminant analysis of functional optical topography for schizophrenia diagnosis

A Framework for Evaluating the Smoothness of Data-Mining Results

Stochastic Mean Payoff Games: Smoothed Analysis and Approximation Schemes

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