The concise and informative representation of hyperspectral imagery is achieved via the introduced diffusion geometric coordinates derived from nonlinear dimension reduction maps - diffusion maps. The huge-volume high...The concise and informative representation of hyperspectral imagery is achieved via the introduced diffusion geometric coordinates derived from nonlinear dimension reduction maps - diffusion maps. The huge-volume high- dimensional spectral measurements are organized by the affinity graph where each node in this graph only connects to its local neighbors and each edge in this graph represents local similarity information. By normalizing the affinity graph appropriately, the diffusion operator of the underlying hyperspectral imagery is well-defined, which means that the Markov random walk can be simulated on the hyperspectral imagery. Therefore, the diffusion geometric coordinates, derived from the eigenfunctions and the associated eigenvalues of the diffusion operator, can capture the intrinsic geometric information of the hyperspectral imagery well, which gives more enhanced representation results than traditional linear methods, such as principal component analysis based methods. For large-scale full scene hyperspectral imagery, by exploiting the backbone approach, the computation complexity and the memory requirements are acceptable. Experiments also show that selecting suitable symmetrization normalization techniques while forming the diffusion operator is important to hyperspectral imagery representation.展开更多
In this paper, a novel method called fuzzy diffusion maps （FDM） is proposed to evaluate cartoon similarity, which is critical to the applications of cartoon recognition, cartoon clustering and cartoon reusing. We fi...In this paper, a novel method called fuzzy diffusion maps （FDM） is proposed to evaluate cartoon similarity, which is critical to the applications of cartoon recognition, cartoon clustering and cartoon reusing. We find that the features from heterogeneous sources have different influence on cartoon similarity estimation. In order to take all the features into consideration, a fuzzy consistent relation is presented to convert the preference order of the features into preference degree, from which the weights are calculated. Based on the features and weights, the sum of the squared differences （L2） can be calculated between any cartoon data. However, it has been demonstrated in some research work that the cartoon dataset lies in a low-dimensional manifold, in which the L2 distance cannot evaluate the similarity directly. Unlike the global geodesic distance preserved in Isomap, the local neighboring relationship preserved in Locally Linear Embedding, and the local similarities of neighboring points preserved in Laplacian Eigenmaps, the diffusion maps we adopt preserve diffusion distance summing over all paths of length connecting the two data. As a consequence, this diffusion distance is very robust to noise perturbation. Our experiment in cartoon classification using Receiver Operating Curves shows fuzzy consistent relation＇s excellent performance on weights assignment. The FDM＇s performance on cartoon similarity evaluation is tested on the experiments of cartoon recognition and clustering. The results show that FDM can evaluate the cartoon similarity more precisely and stably compared with other methods.展开更多
Classifying topological phases of matter with strong interactions is a notoriously challenging task and has attracted considerable attention in recent years.In this paper,we propose an unsupervised machine learning ap...Classifying topological phases of matter with strong interactions is a notoriously challenging task and has attracted considerable attention in recent years.In this paper,we propose an unsupervised machine learning approach that can classify a wide range of symmetry-protected interacting topological phases directly from the experimental observables and without a priori knowledge.We analytically show that Green’s functions,which can be derived from spectral functions that can be measured directly in an experiment,are suitable for serving as the input data for our learning proposal based on the diffusion map.As a concrete example,we consider a one-dimensional interacting topological insulators model and show that,through extensive numerical simulations,our diffusion map approach works as desired.In addition,we put forward a generic scheme to measure the spectral functions in ultracold atomic systems through momentum-resolved Raman spectroscopy.Our work circumvents the costly diagonalization of the system Hamiltonian,and provides a versatile protocol for the straightforward and autonomous identification of interacting topological phases from experimental observables in an unsupervised manner.展开更多
Molecular motion provides a way for biomolecules to mix and interact in living systems.Quantifying their motion is critical to the understanding of how biomolecules perform its function.However,it has been a challenge...Molecular motion provides a way for biomolecules to mix and interact in living systems.Quantifying their motion is critical to the understanding of how biomolecules perform its function.However,it has been a challenged task to spatially map the fast diffusion of unbound proteins in the heterogenous intracellular environment.Here we reported a new imaging technique named cumulative area based on single-molecule diffusivity mapping(CA-SMdM).The strategy is based on the comparison of singlemolecule images between a shorter and longer exposure time.With longer exposure time,molecules will travel further,thus giving more blurred single-molecule images,hence implying its local diffusion rates.We validated our technique through measuring the fast diffusion rates(10–40μm~2/s)of fluorescent dye in glycerol-water mixture,and found the values fit well with Stokes-Einstein equation.We further showed that the spatially mapping of diffusivity in live cells is plausible through CA-SMdM,and it faithfully reported the local diffusivity heterogeneity in cytosol and nucleus.CA-SMdM provides an efficient way to mapping the local molecular motion,and therefore will have profound applications in probing the biomolecular interactions for living systems.展开更多
基金The National Key Technologies R & D Program during the 11th Five-Year Plan Period (No.2006BAB15B01)
文摘The concise and informative representation of hyperspectral imagery is achieved via the introduced diffusion geometric coordinates derived from nonlinear dimension reduction maps - diffusion maps. The huge-volume high- dimensional spectral measurements are organized by the affinity graph where each node in this graph only connects to its local neighbors and each edge in this graph represents local similarity information. By normalizing the affinity graph appropriately, the diffusion operator of the underlying hyperspectral imagery is well-defined, which means that the Markov random walk can be simulated on the hyperspectral imagery. Therefore, the diffusion geometric coordinates, derived from the eigenfunctions and the associated eigenvalues of the diffusion operator, can capture the intrinsic geometric information of the hyperspectral imagery well, which gives more enhanced representation results than traditional linear methods, such as principal component analysis based methods. For large-scale full scene hyperspectral imagery, by exploiting the backbone approach, the computation complexity and the memory requirements are acceptable. Experiments also show that selecting suitable symmetrization normalization techniques while forming the diffusion operator is important to hyperspectral imagery representation.
基金supported by the National Research Foundation Grant,which is administered by the Media Development Authority Interactive Digital Media Programme Office,MDA (IDMPO)
文摘In this paper, a novel method called fuzzy diffusion maps （FDM） is proposed to evaluate cartoon similarity, which is critical to the applications of cartoon recognition, cartoon clustering and cartoon reusing. We find that the features from heterogeneous sources have different influence on cartoon similarity estimation. In order to take all the features into consideration, a fuzzy consistent relation is presented to convert the preference order of the features into preference degree, from which the weights are calculated. Based on the features and weights, the sum of the squared differences （L2） can be calculated between any cartoon data. However, it has been demonstrated in some research work that the cartoon dataset lies in a low-dimensional manifold, in which the L2 distance cannot evaluate the similarity directly. Unlike the global geodesic distance preserved in Isomap, the local neighboring relationship preserved in Locally Linear Embedding, and the local similarities of neighboring points preserved in Laplacian Eigenmaps, the diffusion maps we adopt preserve diffusion distance summing over all paths of length connecting the two data. As a consequence, this diffusion distance is very robust to noise perturbation. Our experiment in cartoon classification using Receiver Operating Curves shows fuzzy consistent relation＇s excellent performance on weights assignment. The FDM＇s performance on cartoon similarity evaluation is tested on the experiments of cartoon recognition and clustering. The results show that FDM can evaluate the cartoon similarity more precisely and stably compared with other methods.
基金supported by the National Natural Science Foundation of China(T2225008,12075128,11905108)support from the Shanghai Qi Zhi Institute.
文摘Classifying topological phases of matter with strong interactions is a notoriously challenging task and has attracted considerable attention in recent years.In this paper,we propose an unsupervised machine learning approach that can classify a wide range of symmetry-protected interacting topological phases directly from the experimental observables and without a priori knowledge.We analytically show that Green’s functions,which can be derived from spectral functions that can be measured directly in an experiment,are suitable for serving as the input data for our learning proposal based on the diffusion map.As a concrete example,we consider a one-dimensional interacting topological insulators model and show that,through extensive numerical simulations,our diffusion map approach works as desired.In addition,we put forward a generic scheme to measure the spectral functions in ultracold atomic systems through momentum-resolved Raman spectroscopy.Our work circumvents the costly diagonalization of the system Hamiltonian,and provides a versatile protocol for the straightforward and autonomous identification of interacting topological phases from experimental observables in an unsupervised manner.
基金supported by the National Key R&D Program of China(2022YFA1305400)the National Natural Science Foundation of China(22104113,22274122)。
文摘Molecular motion provides a way for biomolecules to mix and interact in living systems.Quantifying their motion is critical to the understanding of how biomolecules perform its function.However,it has been a challenged task to spatially map the fast diffusion of unbound proteins in the heterogenous intracellular environment.Here we reported a new imaging technique named cumulative area based on single-molecule diffusivity mapping(CA-SMdM).The strategy is based on the comparison of singlemolecule images between a shorter and longer exposure time.With longer exposure time,molecules will travel further,thus giving more blurred single-molecule images,hence implying its local diffusion rates.We validated our technique through measuring the fast diffusion rates(10–40μm~2/s)of fluorescent dye in glycerol-water mixture,and found the values fit well with Stokes-Einstein equation.We further showed that the spatially mapping of diffusivity in live cells is plausible through CA-SMdM,and it faithfully reported the local diffusivity heterogeneity in cytosol and nucleus.CA-SMdM provides an efficient way to mapping the local molecular motion,and therefore will have profound applications in probing the biomolecular interactions for living systems.
