Constrained Instance Clustering in Multi-Instance Multi-Label Learning

In multi-instance multi-label (MIML) learning, datasets are given in the form of bags, each of which contains multiple instances and is associated with multiple labels. This paper considers a novel instance clustering problem in MIML learning, where the bag labels are used as background knowledge to help group instances into clusters. The goal is to recover the class labels or to find the subclasses within each class. Prior work on constraint-based clustering focuses on pairwise constraints and can not fully utilize the bag-level label information. We propose to encode the bag-label knowledge into soft bag constraints that can be easily incorporated into any optimization based clustering algorithm. As a specific example, we demonstrate how the bag constraints can be incorporated into a popular spectral clustering algorithm. Empirical results on both synthetic and real-world datasets show that the proposed method achieves promising performance compared to state-of-the-art methods that use pairwise constraints.Keywords: MIML, Bag Constraints, Instance Clustering, Spectral Clustering, Constrained Clusterin

Angular Correlations of the X-Ray Background and Clustering of Extragalactic X-Ray Sources

The information content of the autocorrelation function (ACF) of intensity fluctuations of the X-ray background (XRB) is analyzed. The tight upper limits set by ROSAT deep survey data on the ACF at arcmin scales imply strong constraints on clustering properties of X-ray sources at cosmological distances and on their contribution to the soft XRB. If quasars have a clustering radius r_0=12-20 Mpc (H_0=50), and their two point correlation function, is constant in comoving coordinates as indicated by optical data, they cannot make up more 40-50% of the soft XRB (the maximum contribution may reach 80% in the case of stable clustering, epsilon=0). Active Star-forming (ASF) galaxies clustered like normal galaxies, with r_0=10-12 Mpc can yield up to 20% or up to 40% of the soft XRB for epsilon=-1.2 or epsilon=0, respectively. The ACF on degree scales essentially reflects the clustering properties of local sources and is proportional to their volume emissivity. The upper limits on scales of a few degrees imply that hard X-ray selected AGNs have r_0<25 Mpc if epsilon=0 or r_0<20 Mpc if epsilon=-1.2. No significant constraints are set on clustering of ASF galaxies, due to their low local volume emissivity. The possible signal on scales >6 deg, if real, may be due to AGNs with r_0=20 Mpc; the contribution from clusters of galaxies with r_0~50 Mpc is a factor 2 lower.Comment: ApJ, in press (20 July 1993); 28 pages, TeX, ASTRPD-93-2-0

Fronthaul-Constrained Cloud Radio Access Networks: Insights and Challenges

As a promising paradigm for fifth generation (5G) wireless communication systems, cloud radio access networks (C-RANs) have been shown to reduce both capital and operating expenditures, as well as to provide high spectral efficiency (SE) and energy efficiency (EE). The fronthaul in such networks, defined as the transmission link between a baseband unit (BBU) and a remote radio head (RRH), requires high capacity, but is often constrained. This article comprehensively surveys recent advances in fronthaul-constrained C-RANs, including system architectures and key techniques. In particular, key techniques for alleviating the impact of constrained fronthaul on SE/EE and quality of service for users, including compression and quantization, large-scale coordinated processing and clustering, and resource allocation optimization, are discussed. Open issues in terms of software-defined networking, network function virtualization, and partial centralization are also identified.Comment: 5 Figures, accepted by IEEE Wireless Communications. arXiv admin note: text overlap with arXiv:1407.3855 by other author

Soft clustering analysis of galaxy morphologies: A worked example with SDSS

Context: The huge and still rapidly growing amount of galaxies in modern sky surveys raises the need of an automated and objective classification method. Unsupervised learning algorithms are of particular interest, since they discover classes automatically. Aims: We briefly discuss the pitfalls of oversimplified classification methods and outline an alternative approach called "clustering analysis". Methods: We categorise different classification methods according to their capabilities. Based on this categorisation, we present a probabilistic classification algorithm that automatically detects the optimal classes preferred by the data. We explore the reliability of this algorithm in systematic tests. Using a small sample of bright galaxies from the SDSS, we demonstrate the performance of this algorithm in practice. We are able to disentangle the problems of classification and parametrisation of galaxy morphologies in this case. Results: We give physical arguments that a probabilistic classification scheme is necessary. The algorithm we present produces reasonable morphological classes and object-to-class assignments without any prior assumptions. Conclusions: There are sophisticated automated classification algorithms that meet all necessary requirements, but a lot of work is still needed on the interpretation of the results.Comment: 18 pages, 19 figures, 2 tables, submitted to A

Modularity functions maximization with nonnegative relaxation facilitates community detection in networks

We show here that the problem of maximizing a family of quantitative functions, encompassing both the modularity (Q-measure) and modularity density (D-measure), for community detection can be uniformly understood as a combinatoric optimization involving the trace of a matrix called modularity Laplacian. Instead of using traditional spectral relaxation, we apply additional nonnegative constraint into this graph clustering problem and design efficient algorithms to optimize the new objective. With the explicit nonnegative constraint, our solutions are very close to the ideal community indicator matrix and can directly assign nodes into communities. The near-orthogonal columns of the solution can be reformulated as the posterior probability of corresponding node belonging to each community. Therefore, the proposed method can be exploited to identify the fuzzy or overlapping communities and thus facilitates the understanding of the intrinsic structure of networks. Experimental results show that our new algorithm consistently, sometimes significantly, outperforms the traditional spectral relaxation approaches