Invariant Graph Partition Comparison Measures

Symmetric graphs have non-trivial automorphism groups. This article starts with the proof that all partition comparison measures we have found in the literature fail on symmetric graphs, because they are not invariant with regard to the graph automorphisms. By the construction of a pseudometric space of equivalence classes of permutations and with Hausdorff’s and von Neumann’s methods of constructing invariant measures on the space of equivalence classes, we design three different families of invariant measures, and we present two types of invariance proofs. Last, but not least, we provide algorithms for computing invariant partition comparison measures as pseudometrics on the partition space. When combining an invariant partition comparison measure with its classical counterpart, the decomposition of the measure into a structural difference and a difference contributed by the group automorphism is derived.

Generating carbon schwarzites via zeolite-templating

Zeolite-templated carbons (ZTCs) comprise a relatively recent material class synthesized via the chemical vapor deposition of a carbon-containing precursor on a zeolite template, followed by the removal of the template. We have developed a theoretical framework to generate a ZTC model from any given zeolite structure, which we show can successfully predict the structure of known ZTCs. We use our method to generate a library of ZTCs from all known zeolites, to establish criteria for which zeolites can produce experimentally accessible ZTCs, and to identify over 10 ZTCs that have never before been synthesized. We show that ZTCs partition space into two disjoint labyrinths that can be described by a pair of interpenetrating nets. Since such a pair of nets also describes a triply periodic minimal surface (TPMS), our results establish the relationship between ZTCs and schwarzites—carbon materials with negative Gaussian curvature that resemble TPMSs—linking the research topics and demonstrating that schwarzites should no longer be thought of as purely hypothetical materials.

From Ensemble Clustering to Multi-View Clustering

Multi-View Clustering (MVC) aims to find the cluster structure shared by multiple views of a particular dataset. Existing MVC methods mainly integrate the raw data from different views, while ignoring the high-level information. Thus, their performance may degrade due to the conflict between heterogeneous features and the noises existing in each individual view. To overcome this problem, we propose a novel Multi-View Ensemble Clustering (MVEC) framework to solve MVC in an Ensemble Clustering (EC) way, which generates Basic Partitions (BPs) for each view individually and seeks for a consensus partition among all the BPs. By this means, we naturally leverage the complementary information of multi-view data in the same partition space. Instead of directly fusing BPs, we employ the low-rank and sparse decomposition to explicitly consider the connection between different views and detect the noises in each view. Moreover, the spectral ensemble clustering task is also involved by our framework with a carefully designed constraint, making MVEC a unified optimization framework to achieve the final consensus partition. Experimental results on six real-world datasets show the efficacy of our approach compared with both MVC and EC methods.

VIRTUAL DIMENSIONALITY ESTIMATION IN HYPERSPECTRAL IMAGERY BASED ON UNSUPERVISED FEATURE SELECTION

Virtual Dimensionality (VD) is a concept developed to estimate the number of distinct spectral signatures in hyperspectral imagery. Intuitively, detecting the number of spectrally distinct signatures depends on determining the number of distinct bands of the data. Considering this idea, the current paper aims at estimating the VD based on finding independent bands in the image partition space. Eventually, the number of independent selected bands is accepted as the VD estimate. The proposed method is automatic and distribution-free. In addition, no tuning parameters and noise estimation processes are needed. This method is compared with three well-known VD estimation methods using synthetic and real datasets. Experimental results show high speed and reliability in the performance of the proposed method.

VIRTUAL DIMENSIONALITY ESTIMATION IN HYPERSPECTRAL IMAGERY BASED ON UNSUPERVISED FEATURE SELECTION

Virtual Dimensionality (VD) is a concept developed to estimate the number of distinct spectral signatures in hyperspectral imagery. Intuitively, detecting the number of spectrally distinct signatures depends on determining the number of distinct bands of the data. Considering this idea, the current paper aims at estimating the VD based on finding independent bands in the image partition space. Eventually, the number of independent selected bands is accepted as the VD estimate. The proposed method is automatic and distribution-free. In addition, no tuning parameters and noise estimation processes are needed. This method is compared with three well-known VD estimation methods using synthetic and real datasets. Experimental results show high speed and reliability in the performance of the proposed method.

Reliability Analysis of Structured P2P System

Reliability is most important for structured p2p systems and how to exactly evaluate the metric-loss rate which is tightly related to reliability is a hot topic and challenge. Many research works of the loss rate only consider the situation that the loss rate is caused by next hop node failure (NF). Indeed, the lost of queuing message (QF) on the failure node also contribute to the loss rate. This paper presents an analytical model of loss rate caused by NF and NQ. In order to achieve the optimal performance of system through minimizing the NQ, we propose two methods: process power enhancing (PPE) and Space Partition (SP). In the heterogeneous systems, we can obtain the minimal loss rate via improving each nodes process power; in the homogeneous structured p2p systems, the partition space method can evenly partition the ID space so as to ensure the traffic load is uniformly distributed over all nodes.

GA-BASED TIME SERIES MODELS WITH THRESHOLD IN TWO DOMAINS

A new threshold time series model is proposed whose submodels are extended from AR to SARIMA and whose domains having thresholds are extended to two. By these two extensions, the newly proposed models offer more flexibility to piecewisely approximate nonstationary time series by a finite number of local stationary models. A genetic algorithm is applied to simultaneously search for appropriate model structures, estimate the optimal model coefficients, as well as partition space by finding appropriate thresholds. The resulting model is applied to a synthetic multi-frequency sine wave and two financial time series with improved modeling quality. The proposed model is also applied to seismogram analysis in order to recognize earthquake wave pattern related to locate arrival time of different waves.