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

Tutoring Students with Adaptive Strategies

Adaptive learning is a crucial part in intelligent tutoring systems. It provides students with appropriate tutoring interventions, based on students’ characteristics, status, and other related features, in order to optimize their learning outcomes. It is required to determine students’ knowledge level or learning progress, based on which it then uses proper techniques to choose the optimal interventions. In this dissertation work, I focus on these aspects related to the process in adaptive learning: student modeling, k-armed bandits, and contextual bandits. Student modeling. The main objective of student modeling is to develop cognitive models of students, including modeling content skills and knowledge about learning. In this work, we investigate the effect of prerequisite skill in predicting students’ knowledge in post skills, and we make use of the prerequisite performance in different student models. As a result, this makes them superior to traditional models. K-armed bandits. We apply k-armed bandit algorithms to personalize interventions for students, to optimize their learning outcomes. Due to the lack of diverse interventions and small difference of intervention effectiveness in educational experiments, we also propose a simple selection strategy, and compare it with several k-armed bandit algorithms. Contextual bandits. In contextual bandit problem, additional side information, also called context, can be used to determine which action to select. First, we construct a feature evaluation mechanism, which determines which feature to be combined with bandits. Second, we propose a new decision tree algorithm, which is capable of detecting aptitude treatment effect for students. Third, with combined bandits with the decision tree, we apply the contextual bandits to make personalization in two different types of data, simulated data and real experimental data

Cosmological constraints from Radial Baryon Acoustic Oscillation measurements and Observational Hubble data

We use the Radial Baryon Acoustic Oscillation (RBAO) measurements, distant type Ia supernovae (SNe Ia), the observational $H(z)$ data (OHD) and the Cosmic Microwave Background (CMB) shift parameter data to constrain cosmological parameters of $\Lambda$CDM and XCDM cosmologies and further examine the role of OHD and SNe Ia data in cosmological constraints. We marginalize the likelihood function over $h$ by integrating the probability density $P\propto e^{-\chi^{2}/2}$ to obtain the best fitting results and the confidence regions in the $\Omega_{m}-\Omega_{\Lambda}$ plane.With the combination analysis for both of the {\rm $\Lambda$}CDM and XCDM models, we find that the confidence regions of 68.3%, 95.4% and 99.7% levels using OHD+RBAO+CMB data are in good agreement with that of SNe Ia+RBAO+CMB data which is consistent with the result of Lin et al's work. With more data of OHD, we can probably constrain the cosmological parameters using OHD data instead of SNe Ia data in the future.Comment: 8 pages, 6 figures, 2 tables, accepted for publication in Physics Letters

Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions

We study the anisotropic effect of the Coulomb interaction on a 1/3-filling fractional quantum Hall system by using an exact diagonalization method on small systems in torus geometry. For weak anisotropy the system remains to be an incompressible quantum liquid, although anisotropy manifests itself in density correlation functions and excitation spectra. When the strength of anisotropy increases, we find the system develops a Hall-smectic-like phase with a one-dimensional charge density wave order and is unstable towards the one-dimensional crystal in the strong anisotropy limit. In all three phases of the Laughlin liquid, Hall-smectic-like, and crystal phases the ground state of the anisotropic Coulomb system can be well described by a family of model wave functions generated by an anisotropic projection Hamiltonian. We discuss the relevance of the results to the geometrical description of fractional quantum Hall states proposed by Haldane [ Phys. Rev. Lett. 107 116801 (2011)].Comment: 8 pages, 8 figure

Clustering Assisted Fundamental Matrix Estimation

In computer vision, the estimation of the fundamental matrix is a basic problem that has been extensively studied. The accuracy of the estimation imposes a significant influence on subsequent tasks such as the camera trajectory determination and 3D reconstruction. In this paper we propose a new method for fundamental matrix estimation that makes use of clustering a group of 4D vectors. The key insight is the observation that among the 4D vectors constructed from matching pairs of points obtained from the SIFT algorithm, well-defined cluster points tend to be reliable inliers suitable for fundamental matrix estimation. Based on this, we utilizes a recently proposed efficient clustering method through density peaks seeking and propose a new clustering assisted method. Experimental results show that the proposed algorithm is faster and more accurate than currently commonly used methods.Comment: 12 pages, 8 figures, 3 tables, Second International Conference on Computer Science and Information Technology (COSIT 2015) March 21~22, 2015, Geneva, Switzerlan