Fast k-means based on KNN Graph

In the era of big data, k-means clustering has been widely adopted as a basic processing tool in various contexts. However, its computational cost could be prohibitively high as the data size and the cluster number are large. It is well known that the processing bottleneck of k-means lies in the operation of seeking closest centroid in each iteration. In this paper, a novel solution towards the scalability issue of k-means is presented. In the proposal, k-means is supported by an approximate k-nearest neighbors graph. In the k-means iteration, each data sample is only compared to clusters that its nearest neighbors reside. Since the number of nearest neighbors we consider is much less than k, the processing cost in this step becomes minor and irrelevant to k. The processing bottleneck is therefore overcome. The most interesting thing is that k-nearest neighbor graph is constructed by iteratively calling the fast $k$-means itself. Comparing with existing fast k-means variants, the proposed algorithm achieves hundreds to thousands times speed-up while maintaining high clustering quality. As it is tested on 10 million 512-dimensional data, it takes only 5.2 hours to produce 1 million clusters. In contrast, to fulfill the same scale of clustering, it would take 3 years for traditional k-means

On local stabilities of pp-K\"ahler structures

By use of a natural extension map and a power series method, we obtain a local stability theorem for p-K\"ahler structures with the $(p,p+1)$-th mild $\partial\bar\partial$-lemma under small differentiable deformations.Comment: Several typos have been fixed. Final version to appear in Compositio Mathematica. arXiv admin note: text overlap with arXiv:1609.0563

Globalization and Regional Income Inequality--Evidence from within China

China¡¯s recent accession to the WTO is expected to accelerate its integration into the world economy, which aggravates concerns over the impact of globalization on the already rising inter-region income inequality in China. This paper discusses China¡¯s globalization process and estimates an income generating function, incorporating trade and FDI variables. It then applies the newly developed Shapley value decomposition technique to quantify the contributions of globalization, along with other variables, to regional inequality. It is found that (a) globalization constitutes a positive and substantial share to regional inequality and the share rises over time; (b) capital is one of the largest and increasingly important contributor to regional inequality; (c) economic reform characterized by privatization exerts a significant impact on regional inequality; and (d) the relative contributions of education, location, urbanization and dependency ratio to regional inequality have been declining.

Globalization and Regional Income Inequality: Evidence from within China

globalization, inequality, decomposition, Shapley value, China