In this paper, we present our research on building computing machines consciousness about intuitive geometry based on mathematics experiments and statistical inference. The investigation consists of the following five...In this paper, we present our research on building computing machines consciousness about intuitive geometry based on mathematics experiments and statistical inference. The investigation consists of the following five steps. At first, we select a set of geometric configurations and for each configuration we construct a large amount of geometric data as observation data using dynamic geometry programs together with the pseudo-random number generator. Secondly, we refer to the geometric predicates in the algebraic method of machine proof of geometric theorems to construct statistics suitable for measuring the approximate geometric relationships in the observation data. In the third step, we propose a geometric relationship detection method based on the similarity of data distribution, where the search space has been reduced into small batches of data by pre-searching for efficiency, and the hypothetical test of the possible geometric relationships in the search results has be performed. In the fourth step, we explore the integer relation of the line segment lengths in the geometric configuration in addition. At the final step, we do numerical experiments for the pre-selected geometric configurations to verify the effectiveness of our method. The results show that computer equipped with the above procedures can find out the hidden geometric relations from the randomly generated data of related geometric configurations, and in this sense, computing machines can actually attain certain consciousness of intuitive geometry as early civilized humans in ancient Mesopotamia.展开更多
潜在狄利克雷分布(LDA)以词袋(bag of words,BOW)模型为基础,简化了建模的复杂度,但使得主题的语义连贯性较差,文档表征能力不强。为解决此问题,提出了一种基于语义分布相似度的主题模型。该模型在EM(expectation maximization)算法框架...潜在狄利克雷分布(LDA)以词袋(bag of words,BOW)模型为基础,简化了建模的复杂度,但使得主题的语义连贯性较差,文档表征能力不强。为解决此问题,提出了一种基于语义分布相似度的主题模型。该模型在EM(expectation maximization)算法框架下,使用GPU(generalized Pólya urn)模型加入单词-单词和文档-主题语义分布相似度来引导主题建模,从语义关联层面上削弱了词袋假设对主题产生的影响。在四个公开数据集上的实验表明,基于语义分布相似度的主题模型在主题语义连贯性、文本分类准确率方面相对于目前流行的主题建模算法表现得更加优越,同时该模型提高了收敛速度和模型精度。展开更多
文摘In this paper, we present our research on building computing machines consciousness about intuitive geometry based on mathematics experiments and statistical inference. The investigation consists of the following five steps. At first, we select a set of geometric configurations and for each configuration we construct a large amount of geometric data as observation data using dynamic geometry programs together with the pseudo-random number generator. Secondly, we refer to the geometric predicates in the algebraic method of machine proof of geometric theorems to construct statistics suitable for measuring the approximate geometric relationships in the observation data. In the third step, we propose a geometric relationship detection method based on the similarity of data distribution, where the search space has been reduced into small batches of data by pre-searching for efficiency, and the hypothetical test of the possible geometric relationships in the search results has be performed. In the fourth step, we explore the integer relation of the line segment lengths in the geometric configuration in addition. At the final step, we do numerical experiments for the pre-selected geometric configurations to verify the effectiveness of our method. The results show that computer equipped with the above procedures can find out the hidden geometric relations from the randomly generated data of related geometric configurations, and in this sense, computing machines can actually attain certain consciousness of intuitive geometry as early civilized humans in ancient Mesopotamia.
