Dual Information Enhanced Multiview Attributed Graph Clustering.

Multiview attributed graph clustering is an important approach to partition multiview data based on the attribute characteristics and adjacent matrices from different views. Some attempts have been made in using graph neural network (GNN), which have achieved promising clustering performance. Despite this, few of them pay attention to the inherent specific information embedded in multiple views. Meanwhile, they are incapable of recovering the latent high-level representation from the low-level ones, greatly limiting the downstream clustering performance. To fill these gaps, a novel dual information enhanced multiview attributed graph clustering (DIAGC) method is proposed in this article. Specifically, the proposed method introduces the specific information reconstruction (SIR) module to disentangle the explorations of the consensus and specific information from multiple views, which enables graph convolutional network (GCN) to capture the more essential low-level representations. Besides, the contrastive learning (CL) module maximizes the agreement between the latent high-level representation and low-level ones and enables the high-level representation to satisfy the desired clustering structure with the help of the self-supervised clustering (SC) module. Extensive experiments on several real-world benchmarks demonstrate the effectiveness of the proposed DIAGC method compared with the state-of-the-art baselines.

Contrastive Multiview Attribute Graph Clustering With Adaptive Encoders.

Multiview attribute graph clustering aims to cluster nodes into disjoint categories by taking advantage of the multiview topological structures and the node attribute values. However, the existing works fail to explicitly discover the inherent relationships in multiview topological graph matrices while considering different properties between the graphs. Besides, they cannot well handle the sparse structure of some graphs in the learning procedure of graph embeddings. Therefore, in this article, we propose a novel contrastive multiview attribute graph clustering (CMAGC) with adaptive encoders method. Within this framework, the adaptive encoders concerning different properties of distinct topological graphs are chosen to integrate multiview attribute graph information by checking whether there exists high-order neighbor information or not. Meanwhile, the number of layers of the GCN encoders is selected according to the prior knowledge related to the characteristics of different topological graphs. In particular, the feature-level and cluster-level contrastive learning are conducted on the multiview soft assignment representations, where the union of the first-order neighbors from the corresponding graph pairs is regarded as the positive pairs for data augmentation and the sparse neighbor information problem in some graphs can be well dealt with. To the best of our knowledge, it is the first time to explicitly deal with the inherent relationships from the interview and intraview perspectives. Extensive experiments are conducted on several datasets to verify the superiority of the proposed CMAGC method compared with the state-of-the-art methods.

Incomplete Data Meets Uncoupled Case: A Challenging Task of Multiview Clustering.

Incomplete multiview clustering (IMC) methods have achieved remarkable progress by exploring the complementary information and consensus representation of incomplete multiview data. However, to our best knowledge, none of the existing methods attempts to handle the uncoupled and incomplete data simultaneously, which affects their generalization ability in real-world scenarios. For uncoupled incomplete data, the unclear and partial cross-view correlation introduces the difficulty to explore the complementary information between views, which results in the unpromising clustering performance for the existing multiview clustering methods. Besides, the presence of hyperparameters limits their applications. To fill these gaps, a novel uncoupled IMC (UIMC) method is proposed in this article. Specifically, UIMC develops a joint framework for feature inferring and recoupling. The high-order correlations of all views are explored by performing a tensor singular value decomposition (t-SVD)-based tensor nuclear norm (TNN) on recoupled and inferred self-representation matrices. Moreover, all hyperparameters of the UIMC method are updated in an exploratory manner. Extensive experiments on six widely used real-world datasets have confirmed the superiority of the proposed method in handling the uncoupled incomplete multiview data compared with the state-of-the-art methods.

A Tensor Approach for Uncoupled Multiview Clustering.

Multiview clustering plays an important part in unsupervised learning. Although the existing methods have shown promising clustering performances, most of them assume that the data is completely coupled between different views, which is unfortunately not always ensured in real-world applications. The clustering performance of these methods drops dramatically when handling the uncoupled data. The main reason is that: 1) cross-view correlation of uncoupled data is unclear, which limits the existing multiview clustering methods to explore the complementary information between views and 2) features from different views are uncoupled with each other, which may mislead the multiview clustering methods to partition data into wrong clusters. To address these limitations, we propose a tensor approach for uncoupled multiview clustering (T-UMC) in this article. Instead of pairwise correlation, T-UMC chooses a most reliable view by view-specific silhouette coefficient (VSSC) at first, and then couples the self-representation matrix of each view with it by pairwise cross-view coupling learning. After that, by integrating recoupled self-representation matrices into a third-order tensor, the high-order correlations of all views are explored with tensor singular value decomposition (t-SVD)-based tensor nuclear norm (TNN). And the view-specific local structures of each individual view are also preserved with the local structure learning scheme with manifold learning. Besides, the physical meaning of view-specific coupling matrix is also discussed in this article. Extensive experiments on six commonly used benchmark datasets have demonstrated the superiority of the proposed method compared with the state-of-the-art multiview clustering methods.

Refining Graph Structure for Incomplete Multi-View Clustering.

As a challenging problem, incomplete multi-view clustering (MVC) has drawn much attention in recent years. Most of the existing methods contain the feature recovering step inevitably to obtain the clustering result of incomplete multi-view datasets. The extra target of recovering the missing feature in the original data space or common subspace is difficult for unsupervised clustering tasks and could accumulate mistakes during the optimization. Moreover, the biased error is not taken into consideration in the previous graph-based methods. The biased error represents the unexpected change of incomplete graph structure, such as the increase in the intra-class relation density and the missing local graph structure of boundary instances. It would mislead those graph-based methods and degrade their final performance. In order to overcome these drawbacks, we propose a new graph-based method named Graph Structure Refining for Incomplete MVC (GSRIMC). GSRIMC avoids recovering feature steps and just fully explores the existing subgraphs of each view to produce superior clustering results. To handle the biased error, the biased error separation is the core step of GSRIMC. In detail, GSRIMC first extracts basic information from the precomputed subgraph of each view and then separates refined graph structure from biased error with the help of tensor nuclear norm. Besides, cross-view graph learning is proposed to capture the missing local graph structure and complete the refined graph structure based on the complementary principle. Extensive experiments show that our method achieves better performance than other state-of-the-art baselines.

Multiview Subspace Clustering With Grouping Effect.

Multiview subspace clustering (MVSC) is a recently emerging technique that aims to discover the underlying subspace in multiview data and thereby cluster the data based on the learned subspace. Though quite a few MVSC methods have been proposed in recent years, most of them cannot explicitly preserve the locality in the learned subspaces and also neglect the subspacewise grouping effect, which restricts their ability of multiview subspace learning. To address this, in this article, we propose a novel MVSC with grouping effect (MvSCGE) approach. Particularly, our approach simultaneously learns the multiple subspace representations for multiple views with smooth regularization, and then exploits the subspacewise grouping effect in these learned subspaces by means of a unified optimization framework. Meanwhile, the proposed approach is able to ensure the cross-view consistency and learn a consistent cluster indicator matrix for the final clustering results. Extensive experiments on several benchmark datasets have been conducted to validate the superiority of the proposed approach.

Smoothness Regularized Multiview Subspace Clustering With Kernel Learning.

Multiview subspace clustering has attracted an increasing amount of attention in recent years. However, most of the existing multiview subspace clustering methods assume linear relations between multiview data points when learning the affinity representation by means of the self-expression or fail to preserve the locality property of the original feature space in the learned affinity representation. To address the above issues, in this article, we propose a new multiview subspace clustering method termed smoothness regularized multiview subspace clustering with kernel learning (SMSCK). To capture the nonlinear relations between multiview data points, the proposed model maps the concatenated multiview observations into a high-dimensional kernel space, in which the linear relations reflect the nonlinear relations between multiview data points in the original space. In addition, to explicitly preserve the locality property of the original feature space in the learned affinity representation, the smoothness regularization is deployed in the subspace learning in the kernel space. Theoretical analysis has been provided to ensure that the optimal solution of the proposed model meets the grouping effect. The unique optimal solution of the proposed model can be obtained by an optimization strategy and the theoretical convergence analysis is also conducted. Extensive experiments are conducted on both image and document data sets, and the comparison results with state-of-the-art methods demonstrate the effectiveness of our method.

Structure and magnetism of two chair-shaped hexanuclear dysprosium(iii) complexes exhibiting slow magnetic relaxation.

Two novel hexanuclear DyIII complexes with polyhydroxy Schiff-base ligands, [Dy6(L1)4(µ3-OH)4(MeOH)4]Cl2·2MeOH·2MeCN (1) and [Dy6(HL2)2(µ3-OH)2(µ3-OCH3)2(piv)10(MeOH)2] (2) (H3L1 = N,N'-bis(3-methoxysalicylidene)(propylene-2-ol)-1,3-diamine, H3L2 = 2,3-dihydroxypropylimino)methyl)-6-methoxyphenol, piv = pivalate), have been prepared under solvothermal conditions and structurally characterized by single-crystal X-ray diffraction, elemental analyses, thermal analyses, and IR spectroscopy. Each of the hexanuclear complexes is constructed with Dy3 triangular motifs as building blocks, and the six DyIII ions are arranged in a chair-shaped conformation. Variable-temperature magnetic susceptibility measurements in the temperature range of 2-300 K indicate dominant ferromagnetic exchange interactions between the DyIII ions in the complexes. Both complexes exhibit slow magnetic relaxation behavior.

An infinite two-dimensional hybrid water-chloride network in a 4'-(furan-2-yl)-2,2':6',2''-terpyridine nickel(II) matrix.

A new complex, namely bis-[4'-(furan-2-yl)-2,2':6',2''-terpyridine]-nickel(II) dichloride deca-hydrate, [Ni(C19H13N3O)2]Cl2·10H2O, has been crystallized by solvent evaporation and characterized by single-crystal X-ray diffraction. The coordination environment of the NiII cation is distorted octa-hedral with slight deviations from an idealized geometry. The most intriguing structural feature is an infinite two-dimensional hybrid water-chloride network parallel to (011) constructed by O-H⋯O and O-H⋯Cl hydrogen bonds involving two independent chloride ions and ten independent solvent water mol-ecules with an l-shaped pattern. One of the furyl rings is disordered with a refined occupancy ratio of 0.786 (13):0.214 (13).

Poly[diaqua[µ4-4-(isonicotinamido)phthalato]nickel(II)] displaying an sra topology.

In the title compound, [Ni(C14H8N2O5)(H2O)2]n, the Ni(II) cation is six-coordinate with a slightly distorted octahedral coordination geometry and the 4-(isonicotinamido)phthalate ligand links the Ni(II) centres into a three-dimensional structure with sra topology. The structure is also stabilized by N-H···O hydrogen bonding between the uncoordinated amide groups of the ligand and extensive O-H···O hydrogen bonding between the two coordinated water molecules. The magnetic and thermal stability properties of the title compound are also discussed.

Poly[[tetra-aqua-tetra-kis-[µ3-5-(pyridine-4-carboxamido)-isophthalato]nickel(II)diterbium(III)] tetra-hydrate].

In the title compound, {[NiTb2(C14H8N2O5)4(H2O)4]·4H2O} n , the Tb(III) ion is coordinated by one water mol-ecule and seven O atoms from four 5-(pyridine-4-carboxamido)-isophthalate (L) ligands in a distorted square-anti-prismatic arrangement, while the Ni(II) ion, lying on an inversion center, is six-coordinated in an octa-hedral geometry by two pyridine N atoms, two carboxyl-ate O atoms and two water mol-ecules. One L ligand bridges two Tb(III) ions and one Ni(II) ion through two carboxyl-ate groups and one pyridine N atom. The other L ligand bridges two Tb(III) ions and one Ni(II) ion through two carboxyl-ate groups, while the uncoordinating pyridine N atom is hydrogen bonded to an adjacent coordinating water mol-ecule. Extensive O-H⋯O, N-H⋯O and O-H⋯N hydrogen bonds play an important role in stabilizing the crystal structure.

(4,6-Dimethyl-2-sulfanylidenepyrimidin-1-ium) trichlorido(thiourea-κS)zinc(II).

The title compound, (C6H9N2S)[ZnCl3{SC(NH2)2}], exists as a zincate where the zinc(II) centre is coordinated by three chloride ligands and a thiourea ligand to form the anion. The organic cation adopts the protonated 4,6-dimethyl-2-sulfanylidenepyrimidin-1-ium (L) form of 4,6-dimethylpyrimidine-2(1H)-thione. Two short N-H···Cl hydrogen bonds involving the pyrimidine H atoms and the [ZnCl3L](-) anion form a crystallographically centrosymmetric dimeric unit consisting of two anions and two cations. The packing structure is completed by longer-range hydrogen bonds donated by the thiourea NH2 groups to chloride ligand hydrogen-bond acceptors.

Poly[[(µ2-4,4'-bipyridine)(µ3-5-isonicotinamidoisophthalato)cobalt(II)] trihydrate].

In the title compound, {[Co(C(14)H(8)N(2)O(5))(C(10)H(8)N(2))]·3H(2)O}(n), the Co(II) cation is five-coordinated with a slightly distorted trigonal-bipyramidal geometry, and the 5-isonicotinamidoisophthalate ligands link Co(II) atoms into a layered structure. These two-dimensional arrays are further pillared by rod-like 4,4'-bipyridine ligands to give a three-dimensional framework with pcu (primitive cubic) topology. The magnetic and adsorption properties of the title compound are also discussed.

Poly[[tetra-aquatetrakis-[µ(3)-5-(pyridine-4-carboxamido)-isophthalato]cobalt(II)digadolinium(III)] tetra-hydrate].

In the centrosymmetric polymeric title compound, {[CoGd(2)(C(14)H(8)N(2)O(5))(4)(H(2)O)(4)]·4H(2)O}(n), the Gd(III) cation is coordinated by one water mol-ecule and four pyridine-4-carboxamido-isophthalate (L) anions in a distorted square-anti-prismatic arrangement, while the Co(II) cation, located on an inversion center, is coordinated by two pyridyl-N atoms, two carboxyl-ate-O atoms and two water mol-ecules in a distorted octa-hedral geometry. The asymmetric unit contains two anionic L ligands: one bridges two Gd cations and one Co cation through two carboxyl groups and one pyridine-N atom; the other bridges two Gd cations and one Co cation through two carboxyl groups and the uncoordinated pyridine-N atom is hydrogen-bonded to the adjacent coordinated water mol-ecule. Extensive O-H⋯O and N-H⋯O hydrogen bonds are present in the crystal structure.

Single-crystal-to-single-crystal transformations and selective adsorption of porous copper(II) frameworks.

A unique 4-fold interpenetrated (10,3)-b copper(II) framework exhibits reversible dehydration and rehydration in a single-crystal-to-single-crystal (SC-SC) process, and the dehydrated material can encapsulate CH(3)OH molecules, again in a SC-SC fashion, and shows selective adsorption of H(2) and CO(2) over N(2).

Reversible single-crystal-to-single-crystal transformation and highly selective adsorption property of three-dimensional cobalt(II) frameworks.

A three-dimensional (3D) coordination polymer, [Co(3)(L)(2)(BTEC)(H(2)O)(2)]·2H(2)O [1, HL = 3,5-di(imidazol-1-yl)benzoic acid, H(4)BTEC = 1,2,4,5-benzenetetracarboxylic acid], with tfz-d topology has been hydrothermally synthesized. The framework of 1 has high thermal stability and exhibits single-crystal-to-single-crystal (SCSC) transformations upon removing and rebinding the noncoordinated and coordinated water molecules. X-ray crystallographic analyses revealed that the coordination geometry of Co(II) changes from octahedral to square pyramid upon dehydration, accompanying the appearance of one-dimensional (1D) open channels with dimensions of 2.0 × 2.8 Å. The dehydrated form [Co(3)(L)(2)(BTEC)] (2) exhibits highly selective adsorption of water molecules over N(2), CH(3)OH, and CH(3)CH(2)OH, which could be used as sensors for water molecules. Furthermore, the magnetic properties of 1 and 2 were investigated, showing the existence of ferromagnetic interaction between the Co(II) atoms within the trinuclear subunit.

Temperature dependent selective gas sorption of the microporous metal-imidazolate framework [Cu(L)] [H2L = 1,4-di(1H-imidazol-4-yl)benzene].

A highly stable copper(II) microporous framework with cylindrical channels constructed from 1,4-di(1H-imidazol-4-yl)benzene (H(2)L) and CuCl(2)·2H(2)O is composed of Cu(II)-imidazolate tubes interconnected by the 1,4-phenylene group of L(2-), and shows temperature dependent selective gas sorption properties.

Poly[[tetra-aqua-tetra-kis-[µ(3)-5-(pyridine-4-carboxamido)-isophthalato]cobalt(II)dierbium(III)] tetra-hydrate].

In the centrosymmetric polymeric title compound, {[CoEr(2)(C(14)H(8)N(2)O(5))(4)(H(2)O)(4)]·4H(2)O}(n), the Er(III) cation has a coordination number of eight and is surrounded by seven carboxyl-ate O atoms from four 5-(pyridine-4-carboxamido)-isophthalate (L) ligands and one water mol-ecule, forming a distorted square-anti-prismatic arrangement. The Co(II) cation is located on an inversion center and is coordinated by two pyridine N atoms, two carboxyl-ate O atoms and two water mol-ecules in a distorted octa-hedral geometry. The asymmetric unit contains two anionic L ligands. One bridges two Er(III) cations and one Co(II) cation through two carboxyl-ate groups and one pyridine N atom, while the other bridges two Er(III) cations and one Co(II) cation through two carboxyl-ate groups. Extensive O-H⋯O, O-H⋯N and N-H⋯O hydrogen-bonding inter-actions are present in the crystal, involving all uncoordinated water mol-ecules and the uncoordinated pyridine N atom of one of the ligands bonded to an adjacent coordinated water mol-ecule. The title compound is isotypic with the gadolinium analogue.

Poly[[tetra-aqua-tetra-kis-[µ(3)-5-(pyridine-4-carboxamido)-isophthalato]-cobalt(II)-diholmium(III)] tetra-hydrate].

In the centrosymmetric polymeric title compound, {[CoHo(2)(C(14)H(8)N(2)O(5))(4)(H(2)O)(4)]·4H(2)O}(n), the Ho(III) ion is coordinated by one water mol-ecule and four 5-(pyridine-4-carboxamido)-isophthalate (L) ligands in a distorted square-anti-prismatic arrangement. The Co(II) ion, located on an inversion center, is coordinated by two pyridine N atoms, two carboxyl-ate O atoms and two water mol-ecules in a distorted octa-hedral geometry. One L ligand bridges two Ho ions and one Co ion through two carboxyl-ate groups and one pyridine N atom. The other L ligand bridges two Ho ions and one Co ion through two carboxyl-ate groups, while the uncoordinated pyridine N atom accepts a hydrogen bond from an adjacent coordinated water mol-ecule. Extensive O-H⋯O, N-H⋯O and O-H⋯N hydrogen bonding is present in the crystal.

catena-Poly[[[diaqua-cadmium(II)]-bis-[µ-3,5-bis-(isonicotinamido)benzoato]] tetra-hydrate].

The title compound, {[Cd(C(19)H(13)N(4)O(4))(2)(H(2)O)(2)]·4H(2)O}(n) or {[Cd(BBA)(2)(H(2)O)(2)]·4H(2)O}(n), where BBA is 3,5-bis-(iso-nicotin-amido)-benzoate, is isotypic with its Mn isologue [Chen et al. (2009 ▶). J. Coord. Chem.62, 2421-2428]. The cation sits on a twofold axis and is six-coordinated in a slightly distorted octa-hedral geometry; the polyhedra are linked into zigzag chains, which are further connected by N-H⋯O, O-H⋯O and O-H⋯N hydrogen bonds as well as π-π inter-actions [centroid-centroid distance of 3.639 (2) Å], giving a three-dimensional supra-molecular framework.