In the intricate network environment,the secure transmission of medical images faces challenges such as information leakage and malicious tampering,significantly impacting the accuracy of disease diagnoses by medical ...In the intricate network environment,the secure transmission of medical images faces challenges such as information leakage and malicious tampering,significantly impacting the accuracy of disease diagnoses by medical professionals.To address this problem,the authors propose a robust feature watermarking algorithm for encrypted medical images based on multi-stage discrete wavelet transform(DWT),Daisy descriptor,and discrete cosine transform(DCT).The algorithm initially encrypts the original medical image through DWT-DCT and Logistic mapping.Subsequently,a 3-stage DWT transformation is applied to the encrypted medical image,with the centre point of the LL3 sub-band within its low-frequency component serving as the sampling point.The Daisy descriptor matrix for this point is then computed.Finally,a DCT transformation is performed on the Daisy descriptor matrix,and the low-frequency portion is processed using the perceptual hashing algorithm to generate a 32-bit binary feature vector for the medical image.This scheme utilises cryptographic knowledge and zero-watermarking technique to embed watermarks without modifying medical images and can extract the watermark from test images without the original image,which meets the basic re-quirements of medical image watermarking.The embedding and extraction of water-marks are accomplished in a mere 0.160 and 0.411s,respectively,with minimal computational overhead.Simulation results demonstrate the robustness of the algorithm against both conventional attacks and geometric attacks,with a notable performance in resisting rotation attacks.展开更多
To address the current issues of inaccurate segmentation and the limited applicability of segmentation methods for building facades in point clouds, we propose a facade segmentation algorithm based on optimal dual-sca...To address the current issues of inaccurate segmentation and the limited applicability of segmentation methods for building facades in point clouds, we propose a facade segmentation algorithm based on optimal dual-scale feature descriptors. First, we select the optimal dual-scale descriptors from a range of feature descriptors. Next, we segment the facade according to the threshold value of the chosen optimal dual-scale descriptors. Finally, we use RANSAC (Random Sample Consensus) to fit the segmented surface and optimize the fitting result. Experimental results show that, compared to commonly used facade segmentation algorithms, the proposed method yields more accurate segmentation results, providing a robust data foundation for subsequent 3D model reconstruction of buildings.展开更多
Fourier Descriptors(FD) has been widely used in image analysis and computer vision for shape recognition as they can be made independent of translation,rotation,as well as scaling.They have also been used for develo...Fourier Descriptors(FD) has been widely used in image analysis and computer vision for shape recognition as they can be made independent of translation,rotation,as well as scaling.They have also been used for developing methods for the analysis and synthesis of four-bar linkages for path generation.This paper focuses on a comparative study of Fourier descriptors derived from various shape signatures of planar closed curves.This includes representations based on Cartesian coordinates,centroid distance,cumulative angle,and curvature.The comparison is conducted not only using commonly used criteria for shape representation and identification but also in the context of shape based retrieval of kinematic constraints for task centered mechanism design.Examples are provided to seek to extract geometric constraints such as circle,circular arc,ellipse and line-segment from a given motion.展开更多
This study evaluated a fixed long-range corrected range-separated hybrid (RSH) density functional associated with the Def2TZVP basis set alongside the Solvation Model based on Density (SMD) for the computation of the ...This study evaluated a fixed long-range corrected range-separated hybrid (RSH) density functional associated with the Def2TZVP basis set alongside the Solvation Model based on Density (SMD) for the computation of the structure, molecular properties and chemical reactivity of the M8 intermediate melanoidin pigment. The preference of the active sites pertinent to radical, nucleophilic and electrophilic attacks is made through linking them with the electrophilic and nucleophilic Parr functions, Fukui function indices, and condensed Dual Descriptor. This study showed that the MN12SX density functional is the most suitable one for predicting the chemical reactivity of this system.展开更多
It is currently admitted that the intermolecular forces implicated in Gas Liquid Chromatography (GLC) can be expressed as a product of parameters (or descriptors) of solutes and of parameters of solvents. The present ...It is currently admitted that the intermolecular forces implicated in Gas Liquid Chromatography (GLC) can be expressed as a product of parameters (or descriptors) of solutes and of parameters of solvents. The present study is limited to those of solutes, and among them the three ones are involved in the Van der Waals forces, whereas the two ones involved in the hydrogen bonding are left aside at this stage. These three studied parameters, which we call δ, ω and ε, respectively reflect the three types of Van der Waals forces: dispersion, orientation or polarity strictly speaking, and induction-polarizability. These parameters have been experimentally obtained in previous studies for 121 Volatile Organic Compounds (VOC) via an original Multiplicative Matrix Analysis (MMA) applied to a superabundant and accurate GLC data set. Then, also in previous studies, attempts have been made to predict these parameters via a Simplified Molecular Topology procedure (SMT). Because these last published results have been somewhat disappointing, a promising new strategy of prediction is developed and detailed in the present article.展开更多
Molecular reconstruction is a rapid and reliable way to provide molecular detail of petroleum fractions,which is required in the kinetic modeling of petroleum conversation processes at the molecular level.In the typic...Molecular reconstruction is a rapid and reliable way to provide molecular detail of petroleum fractions,which is required in the kinetic modeling of petroleum conversation processes at the molecular level.In the typical stochastic reconstruction method,the estimation of properties of pseudo molecules that are generated by Monte Carlo sampling depends on the building of predefined molecular libraries,which is expensive and inaccessible for certain petroleum fractions.In this paper,a novel stochastic reconstruction strategy is proposed,which is based on a stratified library of structural descriptors.Properties of pseudo molecules generated in the novel strategy can be directly estimated by group contribution method in the condition of lacking predefined molecular libraries.In this strategy,the molecular building diagram comprises two steps.First,the ring structure is configured by determining the number of rings.Different from the length of chain adopted in the traditional stochastic reconstruction method,in the second step,number of structural descriptors(SDs)for binding site and chain were determined sequentially for the configuration of binding site and saturated acyclic hydrocarbon chain.These structural descriptors for binding site and chain were selected from group contribution methods.To count the number of partial overlapping sections between structural descriptors for chain,two supplementary structural descriptors were created.All possible saturated structures of hydrocarbon chains can be represented by structural descriptors at the scale of property estimation.This strategy separates the building of a predefined molecule library from the stochastic reconstruction process.The exact structures of pseudo molecules represented by structural descriptors in this work can be determined with sufficient chemical knowledge.Fifty naphtha samples are tested independently to demonstrate the performance of the proposed strategy and the results show that the estimated properties were close enough to the experimental values.This strategy will benefit the molecular management of petrochemical industries and therefore improve economic and environmental efficiencies.展开更多
The adsorption behavior of folic acid onto(5,0) zigzag and(5,5) armchair carbon nanotube(SWCNT) has been investigated using B3 LYP density functional at the 6-31G* level. The adsorption energies,molecular orbit...The adsorption behavior of folic acid onto(5,0) zigzag and(5,5) armchair carbon nanotube(SWCNT) has been investigated using B3 LYP density functional at the 6-31G* level. The adsorption energies,molecular orbital analysis and structural changes at the adsorption site are indicative of covalent adsorption on the zigzag SWCNT surface,while the adsorption is physical on the armchair SWCNT surface. The density of states(DOS) Plot and the quantum molecular descriptors(QMD) are witness to the significant changes in the electronic properties of SWCNT systems after the attachment of adsorbed species to the tube surface. According to the calculated results,the single-walled carbon nanotubes are expected to be a potential efficient adsorbent for the adsorption of folic acid drug and also can be used as a suitable drug delivery vehicle within biological systems.展开更多
Single-atom catalysts(SACs)have been a research hotspot due to their high catalytic activity,selectivity,and atomic utilization rates.However,the theoretical research of SACs is relatively fragmented,which restricts f...Single-atom catalysts(SACs)have been a research hotspot due to their high catalytic activity,selectivity,and atomic utilization rates.However,the theoretical research of SACs is relatively fragmented,which restricts further understanding of SAC stability and activity.To address this issue,we report our analysis of the geometric structures,electronic characteristics,stabilities,catalytic activities,and descriptors of 132 graphene-based singleatom catalysts(M/GS)obtained from density functional theory calculations.Based on the calculated formation and binding energies,a stability map of M/GS was established to guide catalyst synthesis.The effects of metal atoms and support on the charge of metal atoms are discussed.The catalytic activities of M/GS in both nitrogen and oxygen reduction reactions are predicted based on the calculated magnetic moment and the adsorption energy.Combined with the electronegativity and d-band center,a two-dimensional descriptor is proposed to predict the O adsorption energy on M/GS.More importantly,this theoretical study provides predictive guidance for the preparation and rational design of highly stable and active single-atom catalysts using nitrogen doping on graphene.展开更多
A lot of 3D shape descriptors for 3D shape retrieval have been presented so far. This paper proposes a new mechanism, which employs several existing global and local 3D shape descriptors as input. With the sparse theo...A lot of 3D shape descriptors for 3D shape retrieval have been presented so far. This paper proposes a new mechanism, which employs several existing global and local 3D shape descriptors as input. With the sparse theory, some descriptors which play the most important role in measuring similarity between query model and the model in the dataset are selected automatically and an affinity matrix is constructed. Spectral clustering method can be implemented to this affinity matrix. Spectral embedding of this affinity matrix can be applied to retrieval, which integrating almost all the advantages of selected descriptors. In order to verify the performance of our approach, we perform experimental comparisons on Princeton Shape Benchmark database. Test results show that our method is a pose-oblivious, efficient and robustness method for either complete or incomplete models.展开更多
Fourier descriptors are used as features for 3-D aircraft classification and pose determination from a 2-D image recorded at an arbitrary viewing angle. By the feature ranking of Fourier descriptors, a classification ...Fourier descriptors are used as features for 3-D aircraft classification and pose determination from a 2-D image recorded at an arbitrary viewing angle. By the feature ranking of Fourier descriptors, a classification procedure based on the fast nearest neighbour rule is proposed to save the matching time of an unknown aircraft with a partial library search. The testing results of some typical examples indicate this method is generally applicable and efficient in 3-D aircraft recognition.展开更多
The logarithms of retention factors normalized to a hypothetical pure water eluent(log k w) were determined on a reversed phase high performance liquid chromatography(RP HPLC) column (Li Chrosorb RP 18 column...The logarithms of retention factors normalized to a hypothetical pure water eluent(log k w) were determined on a reversed phase high performance liquid chromatography(RP HPLC) column (Li Chrosorb RP 18 column) for 20 new α\|branched phenylsulfonyl acetates. The atomic charge method was applied to develop quantitative structure retention relationships(QSRRs). Among the available geometric and electronic descriptors, surface area (S), ovality (O), and the charge of carboxyl group(Q OC ) are significant. In the model, the contribution of surface area (S) is the greatest. The molecular mechanism of retention was demonstrated through the model. With the correlation coefficient ( r 2 adj , adjusted for degrees of freedom) of 0.964, the standard error of 0.164 and the F value of 170.39, the model has good predictive capacity.展开更多
Experimental determination of BCFs is expensive and demanding if performed correctly. Because of this, measuring the BCFs of many thousands of chemical substances that are potential regulatory interest is simply not p...Experimental determination of BCFs is expensive and demanding if performed correctly. Because of this, measuring the BCFs of many thousands of chemical substances that are potential regulatory interest is simply not possible. Hence, prediction of BCFs of the PCBs based on QSAR were made time to time to increase the probability of success and reduce the time and cost in exploring the toxicological and ecological characteristics of molecules. DFT methods are, in general, capable of generating a variety of isolated molecular descriptors as well as local reactivity descriptors quite accurately. In this work, prediction of BCFs of the fifty seven PCBs based on quantum chemical descriptors derived from DFT method using the B88-PW91 GGA energy function with the DZVP basis set have been made. The study concluded that dipole moment and ionization potential are reliable descriptors for correlation of bioconcentration factors of polychlorinated biphenyls with their electronic structures. The resulted QSAR model (r2 = 0.9139, ?= 0.8986, k = 2, SE = 0.2668) can be useful for predicting the BCFs of compounds prior to their synthesis.展开更多
Mangifera indica (mango) is a typically tropical fruit with considerable economic value. Brazil features a wide variety of cultivars of this fruit, most of which are known under several different names. Indeed, the no...Mangifera indica (mango) is a typically tropical fruit with considerable economic value. Brazil features a wide variety of cultivars of this fruit, most of which are known under several different names. Indeed, the nomenclature of mango varieties is still quite confusing. Up to now there has been no well-defined scientific principle to differentiate them. The objective of the present work is to compare the different clustering methods in assessing genetic divergence among mango accessions, as well as identify the minimum efficient descriptors for that crop. A total of 20 mango accessions in Cáceres, Mato Grosso state, Brazil were evaluated. When building dissimilarity matrices, the descriptors were divided according to the following groups: leaf, flower/inflorescence, fruit, seed and growth habit/ripening period. With these divisions, combinations were performed among the groups of descriptors. The similarity index was used to obtain the dissimilarity matrices. Later, the accessions were clustered using the methods of Tocher, Ward and UPGMA. The study observed that it was possible to reduce the number of descriptors from 64 to 35, and that the clustering methods were compatible with the study of the genetic diversity of mango.展开更多
基金National Natural Science Foundation of China,Grant/Award Numbers:62063004,62350410483Key Research and Development Project of Hainan Province,Grant/Award Number:ZDYF2021SHFZ093Zhejiang Provincial Postdoctoral Science Foundation,Grant/Award Number:ZJ2021028。
文摘In the intricate network environment,the secure transmission of medical images faces challenges such as information leakage and malicious tampering,significantly impacting the accuracy of disease diagnoses by medical professionals.To address this problem,the authors propose a robust feature watermarking algorithm for encrypted medical images based on multi-stage discrete wavelet transform(DWT),Daisy descriptor,and discrete cosine transform(DCT).The algorithm initially encrypts the original medical image through DWT-DCT and Logistic mapping.Subsequently,a 3-stage DWT transformation is applied to the encrypted medical image,with the centre point of the LL3 sub-band within its low-frequency component serving as the sampling point.The Daisy descriptor matrix for this point is then computed.Finally,a DCT transformation is performed on the Daisy descriptor matrix,and the low-frequency portion is processed using the perceptual hashing algorithm to generate a 32-bit binary feature vector for the medical image.This scheme utilises cryptographic knowledge and zero-watermarking technique to embed watermarks without modifying medical images and can extract the watermark from test images without the original image,which meets the basic re-quirements of medical image watermarking.The embedding and extraction of water-marks are accomplished in a mere 0.160 and 0.411s,respectively,with minimal computational overhead.Simulation results demonstrate the robustness of the algorithm against both conventional attacks and geometric attacks,with a notable performance in resisting rotation attacks.
文摘To address the current issues of inaccurate segmentation and the limited applicability of segmentation methods for building facades in point clouds, we propose a facade segmentation algorithm based on optimal dual-scale feature descriptors. First, we select the optimal dual-scale descriptors from a range of feature descriptors. Next, we segment the facade according to the threshold value of the chosen optimal dual-scale descriptors. Finally, we use RANSAC (Random Sample Consensus) to fit the segmented surface and optimize the fitting result. Experimental results show that, compared to commonly used facade segmentation algorithms, the proposed method yields more accurate segmentation results, providing a robust data foundation for subsequent 3D model reconstruction of buildings.
基金supported by National Science Foundation under Collaborative Research grants to Stony Brook University (Grant No. CMMI-0856594)University of Maryland at Baltimore County (Grant No. CMMI-0900517)supported by National Natural Science Foundation of China under Oversea Scholar Research Collaboration to Shanghai Jiao Tong University (Grant No. 50728503)
文摘Fourier Descriptors(FD) has been widely used in image analysis and computer vision for shape recognition as they can be made independent of translation,rotation,as well as scaling.They have also been used for developing methods for the analysis and synthesis of four-bar linkages for path generation.This paper focuses on a comparative study of Fourier descriptors derived from various shape signatures of planar closed curves.This includes representations based on Cartesian coordinates,centroid distance,cumulative angle,and curvature.The comparison is conducted not only using commonly used criteria for shape representation and identification but also in the context of shape based retrieval of kinematic constraints for task centered mechanism design.Examples are provided to seek to extract geometric constraints such as circle,circular arc,ellipse and line-segment from a given motion.
文摘This study evaluated a fixed long-range corrected range-separated hybrid (RSH) density functional associated with the Def2TZVP basis set alongside the Solvation Model based on Density (SMD) for the computation of the structure, molecular properties and chemical reactivity of the M8 intermediate melanoidin pigment. The preference of the active sites pertinent to radical, nucleophilic and electrophilic attacks is made through linking them with the electrophilic and nucleophilic Parr functions, Fukui function indices, and condensed Dual Descriptor. This study showed that the MN12SX density functional is the most suitable one for predicting the chemical reactivity of this system.
文摘It is currently admitted that the intermolecular forces implicated in Gas Liquid Chromatography (GLC) can be expressed as a product of parameters (or descriptors) of solutes and of parameters of solvents. The present study is limited to those of solutes, and among them the three ones are involved in the Van der Waals forces, whereas the two ones involved in the hydrogen bonding are left aside at this stage. These three studied parameters, which we call δ, ω and ε, respectively reflect the three types of Van der Waals forces: dispersion, orientation or polarity strictly speaking, and induction-polarizability. These parameters have been experimentally obtained in previous studies for 121 Volatile Organic Compounds (VOC) via an original Multiplicative Matrix Analysis (MMA) applied to a superabundant and accurate GLC data set. Then, also in previous studies, attempts have been made to predict these parameters via a Simplified Molecular Topology procedure (SMT). Because these last published results have been somewhat disappointing, a promising new strategy of prediction is developed and detailed in the present article.
基金the support of International(Regional)Cooperation and Exchange Project(61720106008)National Natural Science Fund for Distinguished Young Scholars(61925305)National Natural Science Foundation of China(61873093)。
文摘Molecular reconstruction is a rapid and reliable way to provide molecular detail of petroleum fractions,which is required in the kinetic modeling of petroleum conversation processes at the molecular level.In the typical stochastic reconstruction method,the estimation of properties of pseudo molecules that are generated by Monte Carlo sampling depends on the building of predefined molecular libraries,which is expensive and inaccessible for certain petroleum fractions.In this paper,a novel stochastic reconstruction strategy is proposed,which is based on a stratified library of structural descriptors.Properties of pseudo molecules generated in the novel strategy can be directly estimated by group contribution method in the condition of lacking predefined molecular libraries.In this strategy,the molecular building diagram comprises two steps.First,the ring structure is configured by determining the number of rings.Different from the length of chain adopted in the traditional stochastic reconstruction method,in the second step,number of structural descriptors(SDs)for binding site and chain were determined sequentially for the configuration of binding site and saturated acyclic hydrocarbon chain.These structural descriptors for binding site and chain were selected from group contribution methods.To count the number of partial overlapping sections between structural descriptors for chain,two supplementary structural descriptors were created.All possible saturated structures of hydrocarbon chains can be represented by structural descriptors at the scale of property estimation.This strategy separates the building of a predefined molecule library from the stochastic reconstruction process.The exact structures of pseudo molecules represented by structural descriptors in this work can be determined with sufficient chemical knowledge.Fifty naphtha samples are tested independently to demonstrate the performance of the proposed strategy and the results show that the estimated properties were close enough to the experimental values.This strategy will benefit the molecular management of petrochemical industries and therefore improve economic and environmental efficiencies.
文摘The adsorption behavior of folic acid onto(5,0) zigzag and(5,5) armchair carbon nanotube(SWCNT) has been investigated using B3 LYP density functional at the 6-31G* level. The adsorption energies,molecular orbital analysis and structural changes at the adsorption site are indicative of covalent adsorption on the zigzag SWCNT surface,while the adsorption is physical on the armchair SWCNT surface. The density of states(DOS) Plot and the quantum molecular descriptors(QMD) are witness to the significant changes in the electronic properties of SWCNT systems after the attachment of adsorbed species to the tube surface. According to the calculated results,the single-walled carbon nanotubes are expected to be a potential efficient adsorbent for the adsorption of folic acid drug and also can be used as a suitable drug delivery vehicle within biological systems.
基金the National Natural Science Foundation of China(No.91545122)Beijing Natural Science Foundation(2182066)+1 种基金Natural Science Foundation of Hebei Province of China(B2018502067)the Fundamental Research Funds for the Central Universities(2017XS121).
文摘Single-atom catalysts(SACs)have been a research hotspot due to their high catalytic activity,selectivity,and atomic utilization rates.However,the theoretical research of SACs is relatively fragmented,which restricts further understanding of SAC stability and activity.To address this issue,we report our analysis of the geometric structures,electronic characteristics,stabilities,catalytic activities,and descriptors of 132 graphene-based singleatom catalysts(M/GS)obtained from density functional theory calculations.Based on the calculated formation and binding energies,a stability map of M/GS was established to guide catalyst synthesis.The effects of metal atoms and support on the charge of metal atoms are discussed.The catalytic activities of M/GS in both nitrogen and oxygen reduction reactions are predicted based on the calculated magnetic moment and the adsorption energy.Combined with the electronegativity and d-band center,a two-dimensional descriptor is proposed to predict the O adsorption energy on M/GS.More importantly,this theoretical study provides predictive guidance for the preparation and rational design of highly stable and active single-atom catalysts using nitrogen doping on graphene.
基金Supported by National Natural Science Foundation of China(61222206,61173102,U0935004)the One Hundred Talent Project of the Chinese Academy of Sciences
文摘A lot of 3D shape descriptors for 3D shape retrieval have been presented so far. This paper proposes a new mechanism, which employs several existing global and local 3D shape descriptors as input. With the sparse theory, some descriptors which play the most important role in measuring similarity between query model and the model in the dataset are selected automatically and an affinity matrix is constructed. Spectral clustering method can be implemented to this affinity matrix. Spectral embedding of this affinity matrix can be applied to retrieval, which integrating almost all the advantages of selected descriptors. In order to verify the performance of our approach, we perform experimental comparisons on Princeton Shape Benchmark database. Test results show that our method is a pose-oblivious, efficient and robustness method for either complete or incomplete models.
文摘Fourier descriptors are used as features for 3-D aircraft classification and pose determination from a 2-D image recorded at an arbitrary viewing angle. By the feature ranking of Fourier descriptors, a classification procedure based on the fast nearest neighbour rule is proposed to save the matching time of an unknown aircraft with a partial library search. The testing results of some typical examples indicate this method is generally applicable and efficient in 3-D aircraft recognition.
基金TheNationalNaturalScienceFoundationofChina (No .2 9837180 )
文摘The logarithms of retention factors normalized to a hypothetical pure water eluent(log k w) were determined on a reversed phase high performance liquid chromatography(RP HPLC) column (Li Chrosorb RP 18 column) for 20 new α\|branched phenylsulfonyl acetates. The atomic charge method was applied to develop quantitative structure retention relationships(QSRRs). Among the available geometric and electronic descriptors, surface area (S), ovality (O), and the charge of carboxyl group(Q OC ) are significant. In the model, the contribution of surface area (S) is the greatest. The molecular mechanism of retention was demonstrated through the model. With the correlation coefficient ( r 2 adj , adjusted for degrees of freedom) of 0.964, the standard error of 0.164 and the F value of 170.39, the model has good predictive capacity.
文摘Experimental determination of BCFs is expensive and demanding if performed correctly. Because of this, measuring the BCFs of many thousands of chemical substances that are potential regulatory interest is simply not possible. Hence, prediction of BCFs of the PCBs based on QSAR were made time to time to increase the probability of success and reduce the time and cost in exploring the toxicological and ecological characteristics of molecules. DFT methods are, in general, capable of generating a variety of isolated molecular descriptors as well as local reactivity descriptors quite accurately. In this work, prediction of BCFs of the fifty seven PCBs based on quantum chemical descriptors derived from DFT method using the B88-PW91 GGA energy function with the DZVP basis set have been made. The study concluded that dipole moment and ionization potential are reliable descriptors for correlation of bioconcentration factors of polychlorinated biphenyls with their electronic structures. The resulted QSAR model (r2 = 0.9139, ?= 0.8986, k = 2, SE = 0.2668) can be useful for predicting the BCFs of compounds prior to their synthesis.
文摘Mangifera indica (mango) is a typically tropical fruit with considerable economic value. Brazil features a wide variety of cultivars of this fruit, most of which are known under several different names. Indeed, the nomenclature of mango varieties is still quite confusing. Up to now there has been no well-defined scientific principle to differentiate them. The objective of the present work is to compare the different clustering methods in assessing genetic divergence among mango accessions, as well as identify the minimum efficient descriptors for that crop. A total of 20 mango accessions in Cáceres, Mato Grosso state, Brazil were evaluated. When building dissimilarity matrices, the descriptors were divided according to the following groups: leaf, flower/inflorescence, fruit, seed and growth habit/ripening period. With these divisions, combinations were performed among the groups of descriptors. The similarity index was used to obtain the dissimilarity matrices. Later, the accessions were clustered using the methods of Tocher, Ward and UPGMA. The study observed that it was possible to reduce the number of descriptors from 64 to 35, and that the clustering methods were compatible with the study of the genetic diversity of mango.