Deep graph contrastive clustering has attracted widespread attentions due to its self-supervised representation learning paradigm and superior clustering performance.Although,two challenges emerge and result in high c...Deep graph contrastive clustering has attracted widespread attentions due to its self-supervised representation learning paradigm and superior clustering performance.Although,two challenges emerge and result in high computational costs.Most existing contrastive methods adopt the data augmentation and then representation learning strategy,where representation learning with trainable graph convolution is coupled with complex and fixed data augmentation,inevitably limiting the efficiency and flexibility.The similarity metric between positive-negative sample pairs is complex and contrastive objective is partial,limiting the discriminability of representation learning.To solve these challenges,a novel wide graph clustering network(WGCN)adhering to representation and then augmentation framework is proposed,which mainly consists of multiorder filter fusion(MFF)and double-level contrastive learning(DCL)modules.Specifically,the MFF module integrates multiorder low-pass filters to extract smooth and multi-scale topological features,utilizing self-attention fusion to reduce redundancy and obtain comprehensive embedding representation.Further,the DCL module constructs two augmented views by the parallel parameter-unshared Siamese encoders rather than complex augmentations on graph.To achieve simple yet effective self-supervised learning,representation self-supervision and structural consistency oriented double-level contrastive loss is designed,where representation self-supervision maximizes the agreement between pairwise augmented embedding representations and structural consistency promotes the mutual information correlation between appending neighborhoods with similar semantics.Extensive experiments on six benchmark datasets demonstrate the superiority of the proposed WGCN,especially highlighting its time-saving characteristic.The code could be available in the https://github.com/Tianxiang Zhao0474/WGCN.展开更多
Existing multi-view deep subspace clustering methods aim to learn a unified representation from multi-view data,while the learned representation is difficult to maintain the underlying structure hidden in the origin s...Existing multi-view deep subspace clustering methods aim to learn a unified representation from multi-view data,while the learned representation is difficult to maintain the underlying structure hidden in the origin samples,especially the high-order neighbor relationship between samples.To overcome the above challenges,this paper proposes a novel multi-order neighborhood fusion based multi-view deep subspace clustering model.We creatively integrate the multi-order proximity graph structures of different views into the self-expressive layer by a multi-order neighborhood fusion module.By this design,the multi-order Laplacian matrix supervises the learning of the view-consistent self-representation affinity matrix;then,we can obtain an optimal global affinity matrix where each connected node belongs to one cluster.In addition,the discriminative constraint between views is designed to further improve the clustering performance.A range of experiments on six public datasets demonstrates that the method performs better than other advanced multi-view clustering methods.The code is available at https://github.com/songzuolong/MNF-MDSC(accessed on 25 December 2024).展开更多
In this paper, we apply the Legendre spectral-collocation method to obtain approximate solutions of nonlinear multi-order fractional differential equations (M-FDEs). The fractional derivative is described in the Caput...In this paper, we apply the Legendre spectral-collocation method to obtain approximate solutions of nonlinear multi-order fractional differential equations (M-FDEs). The fractional derivative is described in the Caputo sense. The study is conducted through illustrative example to demonstrate the validity and applicability of the presented method. The results reveal that the proposed method is very effective and simple. Moreover, only a small number of shifted Legendre polynomials are needed to obtain a satisfactory result.展开更多
"Beauty is truth, truth beauty"-the famous line in English romantic poet John Keats'Ode on a Grecian Urn-has triggered wide discussion and numerous interpretations. From the point of"negative capabi..."Beauty is truth, truth beauty"-the famous line in English romantic poet John Keats'Ode on a Grecian Urn-has triggered wide discussion and numerous interpretations. From the point of"negative capability", a phrase first coined by Keats himself, this paper is attempting to display the consistency between that poetic line and the poet's creation and life attitude on the whole. For this purpose, this paper will mainly introduce and interpret five of Keats'famous odes in the order of their display of his"rising acceptance of life": Ode to a Nightingale, Ode on a Grecian Urn, Ode to Autumn, Ode on Melancholy and Ode on Indolence. This paper would like to show in the first three Keats's positive quest in different aspects and on certain levels, the fourth the underlying tone of life's polyphonous song, and the final the"negative capability"that constitutes his healthy attitude toward creation and life. Finally, this paper hopes to demonstrate that it is such capability that enables the poet to growingly accept life, and it is also essential to him as a philosophical poet.展开更多
In this paper, we will present a new method for making first-order systems of nonlinear autonomous ODEs that exhibit limit cycles with a specific geometric shape in two and three dimensions, or systems of ODEs where s...In this paper, we will present a new method for making first-order systems of nonlinear autonomous ODEs that exhibit limit cycles with a specific geometric shape in two and three dimensions, or systems of ODEs where surfaces in three dimensions have attractor behavior. The method is to make the general solutions first by using the exponential function, sine and cosine. We are building up the general solutions bit for bit according to the constant terms that contain the formula of the desired limit cycle, and differentiating them. We will obtain a system of ODEs with the desired behavior. We design the general solutions for a distinct purpose. Using the methods described in this paper, it is possible to make some systems of nonlinear ODEs that are exhibiting limit cycles with a distinct geometric shape in two or three dimensions, and some surfaces having attractor behavior. The pictures show the result.展开更多
基金supported by the National Natural Science Foundation of China(62225303,62403043,62433004)the Beijing Natural Science Foundation(4244085)+1 种基金the Postdoctoral Fellowship Program of China Postdoctoral Science Foundation(GZC20230203)the China Postdoctoral Science Foundation(2023M740201)。
文摘Deep graph contrastive clustering has attracted widespread attentions due to its self-supervised representation learning paradigm and superior clustering performance.Although,two challenges emerge and result in high computational costs.Most existing contrastive methods adopt the data augmentation and then representation learning strategy,where representation learning with trainable graph convolution is coupled with complex and fixed data augmentation,inevitably limiting the efficiency and flexibility.The similarity metric between positive-negative sample pairs is complex and contrastive objective is partial,limiting the discriminability of representation learning.To solve these challenges,a novel wide graph clustering network(WGCN)adhering to representation and then augmentation framework is proposed,which mainly consists of multiorder filter fusion(MFF)and double-level contrastive learning(DCL)modules.Specifically,the MFF module integrates multiorder low-pass filters to extract smooth and multi-scale topological features,utilizing self-attention fusion to reduce redundancy and obtain comprehensive embedding representation.Further,the DCL module constructs two augmented views by the parallel parameter-unshared Siamese encoders rather than complex augmentations on graph.To achieve simple yet effective self-supervised learning,representation self-supervision and structural consistency oriented double-level contrastive loss is designed,where representation self-supervision maximizes the agreement between pairwise augmented embedding representations and structural consistency promotes the mutual information correlation between appending neighborhoods with similar semantics.Extensive experiments on six benchmark datasets demonstrate the superiority of the proposed WGCN,especially highlighting its time-saving characteristic.The code could be available in the https://github.com/Tianxiang Zhao0474/WGCN.
基金supported by the National Key R&D Program of China(2023YFC3304600).
文摘Existing multi-view deep subspace clustering methods aim to learn a unified representation from multi-view data,while the learned representation is difficult to maintain the underlying structure hidden in the origin samples,especially the high-order neighbor relationship between samples.To overcome the above challenges,this paper proposes a novel multi-order neighborhood fusion based multi-view deep subspace clustering model.We creatively integrate the multi-order proximity graph structures of different views into the self-expressive layer by a multi-order neighborhood fusion module.By this design,the multi-order Laplacian matrix supervises the learning of the view-consistent self-representation affinity matrix;then,we can obtain an optimal global affinity matrix where each connected node belongs to one cluster.In addition,the discriminative constraint between views is designed to further improve the clustering performance.A range of experiments on six public datasets demonstrates that the method performs better than other advanced multi-view clustering methods.The code is available at https://github.com/songzuolong/MNF-MDSC(accessed on 25 December 2024).
文摘In this paper, we apply the Legendre spectral-collocation method to obtain approximate solutions of nonlinear multi-order fractional differential equations (M-FDEs). The fractional derivative is described in the Caputo sense. The study is conducted through illustrative example to demonstrate the validity and applicability of the presented method. The results reveal that the proposed method is very effective and simple. Moreover, only a small number of shifted Legendre polynomials are needed to obtain a satisfactory result.
文摘"Beauty is truth, truth beauty"-the famous line in English romantic poet John Keats'Ode on a Grecian Urn-has triggered wide discussion and numerous interpretations. From the point of"negative capability", a phrase first coined by Keats himself, this paper is attempting to display the consistency between that poetic line and the poet's creation and life attitude on the whole. For this purpose, this paper will mainly introduce and interpret five of Keats'famous odes in the order of their display of his"rising acceptance of life": Ode to a Nightingale, Ode on a Grecian Urn, Ode to Autumn, Ode on Melancholy and Ode on Indolence. This paper would like to show in the first three Keats's positive quest in different aspects and on certain levels, the fourth the underlying tone of life's polyphonous song, and the final the"negative capability"that constitutes his healthy attitude toward creation and life. Finally, this paper hopes to demonstrate that it is such capability that enables the poet to growingly accept life, and it is also essential to him as a philosophical poet.
文摘In this paper, we will present a new method for making first-order systems of nonlinear autonomous ODEs that exhibit limit cycles with a specific geometric shape in two and three dimensions, or systems of ODEs where surfaces in three dimensions have attractor behavior. The method is to make the general solutions first by using the exponential function, sine and cosine. We are building up the general solutions bit for bit according to the constant terms that contain the formula of the desired limit cycle, and differentiating them. We will obtain a system of ODEs with the desired behavior. We design the general solutions for a distinct purpose. Using the methods described in this paper, it is possible to make some systems of nonlinear ODEs that are exhibiting limit cycles with a distinct geometric shape in two or three dimensions, and some surfaces having attractor behavior. The pictures show the result.
