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arXiv 1806.06124cs.LGstat.ML
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有监督模糊划分

Supervised Fuzzy Partitioning

Sharif University of Technology(谢里夫理工大学);Amirkabir University of Technology(阿米尔卡比尔理工大学)

Pooya Ashtari, Fateme Nateghi Haredasht, Hamid Beigy

摘要:

基于质心的聚类方法,包括k-均值和模糊c-均值,在许多应用中被认为是有效且易于实现的聚类方法。然而,这些算法不能直接应用于监督任务。因此,本文提出了一种生成模型,扩展了基于质心的聚类方法,适用于分类和回归任务。给定一个任意的损失函数,所提出的方法,被称为监督模糊划分(SFP),将标签信息纳入其目标函数通过一个替代项惩罚的经验风险。基于熵的正则化也被用来模糊化分区和加权特征,使该方法能够捕获更复杂的模式,识别重要特征,并在高维数据中产生更好的性能。为了有效地找到局部最优解,提出了一种基于块坐标下降法的迭代算法。在合成、真实世界和高维数据集上的广泛分类实验表明,SFP的预测性能与最先进的算法(如SVM和随机森林)具有竞争力。SFP具有优于此类方法的主要优点,因为它不仅导致灵活的非线性模型,而且可以在训练阶段利用任何凸损失函数而不损害计算效率。

英文摘要:

Centroid-based methods including k-means and fuzzy c-means are known as effective and easy-to-implement approaches to clustering purposes in many applications. However, these algorithms cannot be directly applied to supervised tasks. This paper thus presents a generative model extending the centroid-based clustering approach to be applicable to classification and regression tasks. Given an arbitrary loss function, the proposed approach, termed Supervised Fuzzy Partitioning (SFP), incorporates labels information into its objective function through a surrogate term penalizing the empirical risk. Entropy-based regularization is also employed to fuzzify the partition and to weight features, enabling the method to capture more complex patterns, identify significant features, and yield better performance facing high-dimensional data. An iterative algorithm based on block coordinate descent scheme is formulated to efficiently find a local optimum. Extensive classification experiments on synthetic, real-world, and high-dimensional datasets demonstrate that the predictive performance of SFP is competitive with state-of-the-art algorithms such as SVM and random forest. SFP has a major advantage over such methods, in that it not only leads to a flexible, nonlinear model but also can exploit any convex loss function in the training phase without compromising computational efficiency.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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