LATTE: Application Oriented Social Network Embedding

In recent years, many research works propose to embed the network structured data into a low-dimensional feature space, where each node is represented as a feature vector. However, due to the detachment of embedding process with external tasks, the learned embedding results by most existing embedding models can be ineffective for application tasks with specific objectives, e.g., community detection or information diffusion. In this paper, we propose study the application oriented heterogeneous social network embedding problem. Significantly different from the existing works, besides the network structure preservation, the problem should also incorporate the objectives of external applications in the objective function. To resolve the problem, in this paper, we propose a novel network embedding framework, namely the "appLicAtion orienTed neTwork Embedding" (Latte) model. In Latte, the heterogeneous network structure can be applied to compute the node "diffusive proximity" scores, which capture both local and global network structures. Based on these computed scores, Latte learns the network representation feature vectors by extending the autoencoder model model to the heterogeneous network scenario, which can also effectively unite the objectives of network embedding and external application tasks. Extensive experiments have been done on real-world heterogeneous social network datasets, and the experimental results have demonstrated the outstanding performance of Latte in learning the representation vectors for specific application tasks.Comment: 11 Pages, 12 Figures, 1 Tabl

On Identity Tests for High Dimensional Data Using RMT

In this work, we redefined two important statistics, the CLRT test (Bai et.al., Ann. Stat. 37 (2009) 3822-3840) and the LW test (Ledoit and Wolf, Ann. Stat. 30 (2002) 1081-1102) on identity tests for high dimensional data using random matrix theories. Compared with existing CLRT and LW tests, the new tests can accommodate data which has unknown means and non-Gaussian distributions. Simulations demonstrate that the new tests have good properties in terms of size and power. What is more, even for Gaussian data, our new tests perform favorably in comparison to existing tests. Finally, we find the CLRT is more sensitive to eigenvalues less than 1 while the LW test has more advantages in relation to detecting eigenvalues larger than 1.Comment: 16 pages, 2 figures, 3 tables, To be published in the Journal of Multivariate Analysi

The Happer's puzzle degeneracies and Yangian

We find operators distinguishing the degenerate states for the Hamiltonian $H= x(K+{1/2})S_z +{\bf K}\cdot {\bf S}$ at $x=\pm 1$ that was given by Happer et al$^{[1,2]}$ to interpret the curious degeneracies of the Zeeman effect for condensed vapor of $^{87}$Rb. The operators obey Yangian commutation relations. We show that the curious degeneracies seem to verify the Yangian algebraic structure for quantum tensor space and are consistent with the representation theory of $Y(sl(2))$.Comment: 8 pages, Latex fil

Accessible Capacity of Secondary Users

A new problem formulation is presented for the Gaussian interference channels (GIFC) with two pairs of users, which are distinguished as primary users and secondary users, respectively. The primary users employ a pair of encoder and decoder that were originally designed to satisfy a given error performance requirement under the assumption that no interference exists from other users. In the scenario when the secondary users attempt to access the same medium, we are interested in the maximum transmission rate (defined as {\em accessible capacity}) at which secondary users can communicate reliably without affecting the error performance requirement by the primary users under the constraint that the primary encoder (not the decoder) is kept unchanged. By modeling the primary encoder as a generalized trellis code (GTC), we are then able to treat the secondary link and the cross link from the secondary transmitter to the primary receiver as finite state channels (FSCs). Based on this, upper and lower bounds on the accessible capacity are derived. The impact of the error performance requirement by the primary users on the accessible capacity is analyzed by using the concept of interference margin. In the case of non-trivial interference margin, the secondary message is split into common and private parts and then encoded by superposition coding, which delivers a lower bound on the accessible capacity. For some special cases, these bounds can be computed numerically by using the BCJR algorithm. Numerical results are also provided to gain insight into the impacts of the GTC and the error performance requirement on the accessible capacity.Comment: 42 pages, 12 figures, 2 tables; Submitted to IEEE Transactions on Information Theory on December, 2010, Revised on November, 201