Title | Probability-enhanced sufficient dimension reduction for binary classification. |

Publication Type | Journal Article |

Year of Publication | 2014 |

Authors | Shin, Seung Jun, Yichao Wu, Hao Helen Zhang, and Yufeng Liu |

Journal | Biometrics |

Volume | 70 |

Issue | 3 |

Pagination | 546-55 |

Date Published | 2014 Sep |

ISSN | 1541-0420 |

Keywords | Algorithms, Biometry, Computer Simulation, Data Interpretation, Statistical, Models, Statistical, Pattern Recognition, Automated, Regression Analysis |

Abstract | In high-dimensional data analysis, it is of primary interest to reduce the data dimensionality without loss of information. Sufficient dimension reduction (SDR) arises in this context, and many successful SDR methods have been developed since the introduction of sliced inverse regression (SIR) [Li (1991) Journal of the American Statistical Association 86, 316-327]. Despite their fast progress, though, most existing methods target on regression problems with a continuous response. For binary classification problems, SIR suffers the limitation of estimating at most one direction since only two slices are available. In this article, we develop a new and flexible probability-enhanced SDR method for binary classification problems by using the weighted support vector machine (WSVM). The key idea is to slice the data based on conditional class probabilities of observations rather than their binary responses. We first show that the central subspace based on the conditional class probability is the same as that based on the binary response. This important result justifies the proposed slicing scheme from a theoretical perspective and assures no information loss. In practice, the true conditional class probability is generally not available, and the problem of probability estimation can be challenging for data with large-dimensional inputs. We observe that, in order to implement the new slicing scheme, one does not need exact probability values and the only required information is the relative order of probability values. Motivated by this fact, our new SDR procedure bypasses the probability estimation step and employs the WSVM to directly estimate the order of probability values, based on which the slicing is performed. The performance of the proposed probability-enhanced SDR scheme is evaluated by both simulated and real data examples. |

DOI | 10.1111/biom.12174 |

Alternate Journal | Biometrics |

Original Publication | Probability-enhanced sufficient dimension reduction for binary classification. |

PubMed ID | 24779683 |

PubMed Central ID | PMC4670268 |

Grant List | R01 CA-085848 / CA / NCI NIH HHS / United States R01 CA085848 / CA / NCI NIH HHS / United States R01 CA149569 / CA / NCI NIH HHS / United States R01 CA-149569 / CA / NCI NIH HHS / United States P01 CA142538 / CA / NCI NIH HHS / United States |

# Probability-enhanced sufficient dimension reduction for binary classification.

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