The power of comparative reasoning

J. Yagnik, Dennis W. Strelow, David A. Ross, Ruei-Sung Lin
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引用次数: 129

Abstract

Rank correlation measures are known for their resilience to perturbations in numeric values and are widely used in many evaluation metrics. Such ordinal measures have rarely been applied in treatment of numeric features as a representational transformation. We emphasize the benefits of ordinal representations of input features both theoretically and empirically. We present a family of algorithms for computing ordinal embeddings based on partial order statistics. Apart from having the stability benefits of ordinal measures, these embeddings are highly nonlinear, giving rise to sparse feature spaces highly favored by several machine learning methods. These embeddings are deterministic, data independent and by virtue of being based on partial order statistics, add another degree of resilience to noise. These machine-learning-free methods when applied to the task of fast similarity search outperform state-of-the-art machine learning methods with complex optimization setups. For solving classification problems, the embeddings provide a nonlinear transformation resulting in sparse binary codes that are well-suited for a large class of machine learning algorithms. These methods show significant improvement on VOC 2010 using simple linear classifiers which can be trained quickly. Our method can be extended to the case of polynomial kernels, while permitting very efficient computation. Further, since the popular Min Hash algorithm is a special case of our method, we demonstrate an efficient scheme for computing Min Hash on conjunctions of binary features. The actual method can be implemented in about 10 lines of code in most languages (2 lines in MAT-LAB), and does not require any data-driven optimization.
比较推理的力量
等级相关度量以其对数值扰动的弹性而闻名,并广泛应用于许多评估度量中。这样的序数度量很少应用于作为表征变换的数值特征的处理。我们强调了输入特征的有序表示在理论上和经验上的好处。我们提出了一组基于偏序统计量的计算有序嵌入的算法。除了具有有序测度的稳定性优势外,这些嵌入是高度非线性的,产生了稀疏特征空间,这些特征空间受到几种机器学习方法的高度青睐。这些嵌入是确定性的,数据独立的,并且由于基于偏序统计,增加了对噪声的另一程度的弹性。当应用于快速相似性搜索任务时,这些不需要机器学习的方法优于具有复杂优化设置的最先进的机器学习方法。为了解决分类问题,嵌入提供了一种非线性转换,产生稀疏的二进制代码,非常适合于大量的机器学习算法。这些方法在使用简单线性分类器的VOC 2010上有了显著的改进,并且可以快速训练。我们的方法可以扩展到多项式核的情况,同时允许非常高效的计算。此外,由于流行的最小哈希算法是我们方法的一个特殊情况,我们展示了一个有效的方案来计算二元特征的连接最小哈希。在大多数语言中,实际的方法可以在大约10行代码中实现(MAT-LAB中为2行),并且不需要任何数据驱动的优化。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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