Disclosure of Invention
In order to overcome the problems in the related art, the present disclosure provides a method and apparatus for identifying a risky user, a storage medium, and an electronic device.
In order to achieve the above object, according to a first aspect of the embodiments of the present disclosure, there is provided a method for identifying a risky user, including:
acquiring characteristic data of each user in a user set, wherein the user set comprises risk sample users and a plurality of users to be identified;
determining similarity among users in the user set by taking the minimized information entropy of the user set as a target, wherein the information entropy is used for representing the uncertainty of a clustering result obtained by clustering the user set, and the probability that each user in the information entropy belongs to one cluster is the proportion of the sum of the similarities between the user and other users in the user set to the sum of the similarities among the users in the user set;
based on a spectral clustering algorithm, clustering a user set according to the similarity between users in the user set so as to divide the user set into a plurality of clusters;
and determining the risk users from the plurality of users to be identified according to the distribution information of the risk sample users in the plurality of clusters.
Optionally, the information entropy is:
wherein H (X) is the information entropy; p (x)i) For user x in the user setiProbability of belonging to a cluster, n being the number of users in the set of users; wijFor user x in the user setiAnd user xjThe similarity between them.
Optionally, the clustering, based on a spectral clustering algorithm, the user set according to the similarity between users in the user set to divide the user set into a plurality of clusters includes:
respectively constructing a similarity matrix and a degree matrix according to the similarity between users in the user set, wherein elements in the similarity matrix are used for representing the similarity between two users in the user set, and elements in the degree matrix are used for representing the sum of the similarities between one user and other users in the user set;
constructing a target matrix according to at least the similarity matrix and the degree matrix, wherein each row vector of the target matrix represents a coordinate of one user in the user set in a feature space;
and clustering the row vectors subjected to dimensionality reduction on the target matrix to divide the user set into a plurality of clusters.
Optionally, the constructing a target matrix according to at least the similarity matrix and the degree matrix includes:
constructing a Laplace matrix according to the similarity matrix and the degree matrix;
performing feature mapping according to the Laplace matrix, and selecting feature values of the number of clusters;
constructing a characteristic vector matrix according to the characteristic vectors corresponding to the selected characteristic values;
and carrying out normalization processing on the row vectors of the characteristic vector matrix to obtain the target matrix.
Optionally, the feature data of each user in the user set includes features of the user in multiple dimensions;
constructing a target matrix according to at least the similarity matrix and the degree matrix, including:
constructing a Laplace matrix according to the similarity matrix and the degree matrix;
determining at least one candidate dimension from the multiple dimensions, and combining features of each user in the user set under each candidate dimension to obtain a feature combination;
constructing a diagonal matrix, a first intermediate matrix and a second intermediate matrix from the feature combinations and the Laplace matrix, respectively, based on the following formulas:
where U (j, j) is a diagonal matrix, PjIs the jth row of the projection matrix; alpha, beta and gamma are preset adjusting parameters; r is a correlation matrix for characterizing the degree of correlation between the features in the feature combination X, Rij=I(fi,fj),rij∈R,rijRepresenting mutual information between the features in the dimension i and the features in the dimension j in the feature combination X, and rij∈[0,1](ii) a A is the first intermediate matrix; h is the second intermediate matrix; d is the degree matrix; l is the Laplace matrix;
selecting the eigenvalue of the clustering number from all the eigenvalues of the second intermediate matrix;
respectively constructing a feature vector matrix and a projection matrix corresponding to the feature vector according to the feature vector, the first intermediate matrix and the feature combination corresponding to each selected feature value:
wherein T is the eigenvector matrix, and c is the number of clusters; v. of1,v2,…,vcSelecting characteristic vectors corresponding to the characteristic values; p is the projection matrix;
if the constructed projection matrix is not converged, repeating the step of determining at least one candidate dimension from the plurality of dimensions, and combining the features of each user in the user set under each candidate dimension to the constructed feature vector matrix and the projection matrix corresponding to the feature vector respectively until the constructed projection matrix is converged; and the number of the first and second groups,
and under the condition that the constructed projection matrix is converged, carrying out normalization processing on the row vector of the characteristic vector matrix corresponding to the projection matrix to obtain the target matrix.
According to a second aspect of the embodiments of the present disclosure, there is provided an apparatus for identifying a risky user, including:
the system comprises an acquisition module, a recognition module and a recognition module, wherein the acquisition module is used for acquiring characteristic data of each user in a user set, and the user set comprises risk sample users and a plurality of users to be recognized;
a first determining module, configured to determine similarity between users in the user set with a goal of minimizing an information entropy of the user set, where the information entropy is used to represent an uncertainty of a clustering result obtained by clustering the user set, and a probability that each user in the information entropy belongs to a cluster is a proportion of a sum of similarities between the user and other users in the user set to a sum of similarities between the users in the user set;
the clustering module is used for clustering the user set according to the similarity among the users in the user set based on a spectral clustering algorithm so as to divide the user set into a plurality of clusters;
and the second determining module is used for determining the risk users from the plurality of users to be identified according to the distribution information of the risk sample users in the plurality of clusters.
Optionally, the information entropy is:
wherein H (X) is the information entropy; p (x)i) For user x in the user setiProbability of belonging to a cluster, n being the number of users in the set of users; wijFor user x in the user setiAnd user xjThe similarity between them.
Optionally, the clustering module comprises:
a first construction submodule, configured to respectively construct a similarity matrix and a degree matrix according to a similarity between users in the user set, where an element in the similarity matrix is used to characterize a similarity between two users in the user set, and an element in the degree moment is used to characterize a sum of similarities between one user in the user set and other users;
a second constructing submodule, configured to construct a target matrix according to at least the similarity matrix and the degree matrix, where each row vector of the target matrix represents a coordinate of one user in the user set in a feature space;
and the clustering submodule is used for clustering the row vectors subjected to the dimensionality reduction on the target matrix so as to divide the user set into a plurality of clusters.
Optionally, the second constructing sub-module is configured to construct the target matrix according to the following:
constructing a Laplace matrix according to the similarity matrix and the degree matrix;
performing feature mapping according to the Laplace matrix, and selecting feature values of the number of clusters;
constructing a characteristic vector matrix according to the characteristic vectors corresponding to the selected characteristic values;
and carrying out normalization processing on the row vectors of the characteristic vector matrix to obtain the target matrix.
Optionally, the feature data of each user in the user set includes features of the user in multiple dimensions, and the second constructing sub-module is configured to construct the target matrix according to the following manner:
constructing a Laplace matrix according to the similarity matrix and the degree matrix;
determining at least one candidate dimension from the multiple dimensions, and combining features of each user in the user set under each candidate dimension to obtain a feature combination;
constructing a diagonal matrix, a first intermediate matrix and a second intermediate matrix from the feature combinations and the Laplace matrix, respectively, based on the following formulas:
where U (j, j) is a diagonal matrix, PjIs the jth row of the projection matrix; alpha, betaGamma is a preset adjusting parameter; r is a correlation matrix for characterizing the degree of correlation between the features in the feature combination X, Rij=I(fi,fj),rij∈R,rijRepresenting mutual information between the features in the dimension i and the features in the dimension j in the feature combination X, and rij∈[0,1](ii) a A is the first intermediate matrix; h is the second intermediate matrix; d is the degree matrix; l is the Laplace matrix;
selecting the eigenvalue of the clustering number from all the eigenvalues of the second intermediate matrix;
respectively constructing a feature vector matrix and a projection matrix corresponding to the feature vector according to the feature vector, the first intermediate matrix and the feature combination corresponding to each selected feature value:
wherein T is the eigenvector matrix, and c is the number of clusters; v. of1,v2,…,vcSelecting characteristic vectors corresponding to the characteristic values; p is the projection matrix;
if the constructed projection matrix is not converged, repeating the step of determining at least one candidate dimension from the plurality of dimensions, and combining the features of each user in the user set under each candidate dimension to the constructed feature vector matrix and the projection matrix corresponding to the feature vector respectively until the constructed projection matrix is converged; and the number of the first and second groups,
and under the condition that the constructed projection matrix is converged, carrying out normalization processing on the row vector of the characteristic vector matrix corresponding to the projection matrix to obtain the target matrix.
According to a third aspect of embodiments of the present disclosure, there is provided a computer readable storage medium having stored thereon a computer program which, when executed by a processor, performs the steps of the method of the first aspect.
According to a fourth aspect of the embodiments of the present disclosure, there is provided an electronic apparatus including: a memory having a computer program stored thereon; a processor for executing the computer program in the memory to implement the steps of the method of the first aspect.
Through the technical scheme, the following technical effects can be at least achieved: with the aim of minimizing the information entropy of the user set as a target, the similarity between the users in the user set can be automatically determined, and compared with the method for determining the similarity between the users in a manual mode, the method has the advantages of higher efficiency and accuracy and labor cost saving. Furthermore, the efficiency of the whole risk user identification process and the accuracy of the identification result can be improved, and the labor cost of the whole process is reduced.
Additional features and advantages of the disclosure will be set forth in the detailed description which follows.
Detailed Description
The following detailed description of specific embodiments of the present disclosure is provided in connection with the accompanying drawings. It should be understood that the detailed description and specific examples, while indicating the present disclosure, are given by way of illustration and explanation only, not limitation.
It is worth noting that the terms "first," "second," and the like in the description and claims of the present disclosure and in the above-described figures are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order.
In the related art, the risk user identification is mostly performed by manually determining the similarity between users based on the respective feature data of a plurality of users to be identified, and then performing the risk user identification according to the similarity between the users and the historical feature data of the risk users.
However, since the similarity between users depends on the experience and efficiency of the operator, the calculation efficiency and accuracy of the similarity between users are affected, and further, the efficiency of the identification process of the risk users and the accuracy of the identification result are affected. Moreover, the whole process requires manual work, so that the labor cost is high.
In view of this, the present disclosure provides a method and an apparatus for identifying a risky user, a storage medium, and an electronic device, so as to automatically identify the risky user based on respective feature data of a plurality of users to be identified, improve efficiency and accuracy of identifying the risky user, and reduce labor cost.
Fig. 1 is a flowchart illustrating a method of risk user identification according to an exemplary embodiment of the present disclosure. Referring to fig. 1, the method includes the steps of:
s101, acquiring characteristic data of each user in the user set.
The user set comprises risk sample users and a plurality of users to be identified.
Specifically, the feature data of each user can be customized according to the service scene of the specific application of the method. For example, in the case of credit service, the feature data of each user may include features of different dimensions of the user, such as age, academic calendar, income, credit information, and the like.
S102, with the aim of minimizing the information entropy of the user set as a target, determining the similarity between the users in the user set.
The information entropy of the user set is used for representing the uncertainty of a clustering result obtained by clustering the user set. The clustering result includes a plurality of clusters obtained by dividing the user set and user information included in each cluster, including but not limited to a young couple cluster, a parent-child cluster, a brother cluster, and the like.
The probability that each user belongs to one cluster in the information entropy is the proportion of the sum of the similarity between the user and other users to the sum of the similarity between the users in the user set.
For example, the information entropy of the feature data set may be the following formula (1).
Wherein, h (x) is the information entropy of the user set; p (x)
i) For user x in the user set
iProbability of belonging to a cluster, n being the number of users contained in the set of users; w
ijFor user x in the user set
iAnd user x
jSimilarity between them, W
ij∈R
n×nAnd is
d(x
i,x
j) For user x in the user set
iAnd user x
jThe euclidean distance between them, σ being the width parameter.
In a specific implementation, the width parameter σ may be calculated according to the above formula (1), and the similarity between users may be further calculated according to the width parameter σ.
S103, based on a spectral clustering algorithm, clustering is carried out on the user set according to the similarity among the users in the user set, so that the user set is divided into a plurality of clusters.
Specifically, the user relationship graph may be constructed according to the similarity between users in the user set, for example, the undirected weight graph G ═ V, E may be used to represent the user relationship graph, where V is the user set (including the risk sample user and the multiple users to be identified), and E is the edge set in the user relationship graph G, and the weight of each edge is used to characterize the similarity between two users connected by the edge.
Further, after the user relationship graph is constructed, the user relationship graph can be cut based on a spectral clustering algorithm, and then the users in the user set are divided into a plurality of clusters. In the specific implementation, as shown in fig. 2, the following steps can be performed:
s131, according to the similarity among the users in the user set, respectively constructing a similarity matrix and a degree matrix.
The elements in the similarity matrix are used for representing the similarity between two users in the user set, and the elements in the degree matrix are used for representing the sum of the similarities between one user in the user set and all other users.
S132, constructing a target matrix at least according to the similarity matrix and the degree matrix.
Wherein each row vector of the target matrix characterizes coordinates of one user in the set of users in the feature space.
In an alternative implementation, the laplacian matrix may be first constructed from the similarity matrix and the degree matrix. And then, performing feature mapping according to the Laplace matrix, calculating all the feature values of the Laplace matrix and the feature vector corresponding to each feature value, and selecting the feature values of the cluster number from all the feature values of the Laplace matrix. And finally, constructing a characteristic vector matrix according to the characteristic vectors corresponding to the selected characteristic values respectively, and carrying out normalization processing on the characteristic vector matrix to obtain a target matrix. For example, the laplacian matrix L may be first constructed according to formula (2), then k minimum eigenvalues are selected from all eigenvalues of the laplacian matrix L, and the eigenvectors v corresponding to the eigenvalues may be selected1,v2,…,vkConstructing a feature vector matrix V ═ V as column vectors1,v2,…,vk]∈Rn×kAnd carrying out normalization processing on the characteristic vector matrix according to a formula (3) to obtain a target matrix Y.
L=D-1/2WD-1/2 (2)
Wherein k is the number of clusters; l is a Laplace matrix; d is a degree matrix; w is a similarity matrix; y isijAre elements in the object matrix Y.
In another alternative implementation, the feature data of each user in the set of users includes features of the user in multiple dimensions. Accordingly, the laplacian matrix may be first constructed from the similarity matrix and the degree matrix. Then, at least one candidate dimension is determined from the multiple dimensions, and features of the users in the user set under each candidate dimension are combined to obtain a feature combination. Further, a diagonal matrix, a first intermediate matrix, and a second intermediate matrix are respectively constructed from the feature combinations and the laplacian matrix. Further, selecting the eigenvalue of the cluster number from all eigenvalues of the second intermediate matrix, and respectively constructing an eigenvector matrix and a projection matrix corresponding to the eigenvector according to the eigenvector, the first intermediate matrix and the combination of the characteristics corresponding to each selected eigenvalue. Further, whether the constructed projection matrix is converged is judged, if the projection matrix is not converged, it is indicated that the correlation of the features in the selected feature combination is low and redundant features exist, so that the step of determining at least one candidate dimension from the multiple dimensions, combining the features of each user in the user set in each candidate dimension to respectively construct a feature vector matrix and a projection matrix corresponding to the feature vector is repeatedly executed until the constructed projection matrix is converged, which indicates that the features in the selected feature combination are correlated and superior, and further under the condition, row vectors of the feature vectors corresponding to the projection matrix are subjected to normalization processing to obtain a target matrix.
In this implementation, the laplacian matrix may be constructed according to equation (2) above, the diagonal matrix, the first intermediate matrix, and the second intermediate matrix may be constructed according to equation (4) below, and the eigenvector matrix may be constructed, for exampleAnd the projection matrix corresponding to the eigenvector matrix may be constructed according to the following equation (5). In addition, for the selection of the eigenvalues of the second intermediate matrix, c minimum eigenvalues can be selected from all the eigenvalues of the second intermediate matrix, and the eigenvectors v corresponding to the eigenvalues respectively are selected1,v2,…,vcConstructing a feature vector matrix V ═ V as column vectors1,v2,…,vc]∈Rn×c
Where U (j, j) is a diagonal matrix, PjIs the jth row of the projection matrix; alpha, beta and gamma are preset adjusting parameters; r is a correlation matrix for characterizing the degree of correlation between the features in the feature combination X, Rij=I(fi,fj),rij∈R,rijRepresenting mutual information between the features in the dimension i and the features in the dimension j in the feature combination X, and rij∈[0,1](ii) a A is the first intermediate matrix; h is the second intermediate matrix; d is the degree matrix; l is the Laplace matrix; t is the eigenvector matrix, and c is the clustering number; v. of1,v2,…,vcSelecting characteristic vectors corresponding to the characteristic values; p is the projection matrix.
Through the implementation mode, automatic selection of the features of the users in the user set under different dimensions can be achieved, and dimension explosion caused by overhigh feature dimension is avoided. Secondly, as the correlation degree correlation matrix and the projection matrix used for representing the correlation degree between the features in the feature combination are used in the feature selection process, the correlation and the projection relation between the features are considered, so that the selected feature combination is better, the clustering result obtained by clustering all users according to the selected feature combination is more accurate, and the result of identifying the risk users based on the clustering result is more accurate.
S133, clustering the row vectors subjected to the dimensionality reduction on the target matrix so as to divide the user set into a plurality of clusters.
Specifically, the row vectors after the dimensionality reduction of the target matrix may be clustered based on a kmeans algorithm or other clustering algorithms known in the art, and if the ith row of the target matrix is classified as the a-th class, the user x in the corresponding user setiClassified as category a.
And S104, determining the risk user from the plurality of users to be identified according to the distribution information of the risk sample user in the plurality of clusters obtained by division.
The similarity of users in the same cluster is higher, while the similarity of users in different clusters is lower. Therefore, the risk user can be determined from the users to be identified according to the distribution information of the risk sample users in the plurality of clusters obtained by division.
In an alternative implementation manner, one risk sample user may be included in the user set, in which case, a cluster to which the risk sample user belongs may be used as a risk cluster, and a user to be identified in the risk cluster may be determined as a risk user.
In another alternative implementation manner, the user set may include a plurality of risk sample users, a proportion of the risk sample users in each cluster to total users in the cluster may be calculated according to a distribution situation of each risk sample user in a plurality of clusters, a cluster with a highest calculated proportion is used as a risk cluster, and a user to be identified in the cluster is determined as a risk user.
By adopting the risk user identification method, the similarity among the users in the user set can be automatically determined by taking the minimum information entropy of the user set as a target, and compared with the method for determining the similarity among the users in a manual mode, the efficiency and the accuracy are higher, and the labor cost is saved. Furthermore, the efficiency of the whole risk user identification process and the accuracy of the identification result can be improved, and the labor cost of the whole process is reduced.
Fig. 3 is a block diagram illustrating an apparatus for identifying an at risk user according to an exemplary embodiment of the present disclosure. Referring to fig. 3, the apparatus 300 includes:
an obtaining module 301, configured to obtain feature data of each user in a user set, where the user set includes a risk sample user and multiple users to be identified;
a first determining module 302, configured to determine similarity between users in the user set with a goal of minimizing an information entropy of the user set, where the information entropy is used to represent an uncertainty of a clustering result obtained by clustering the user set, and a probability that each user in the information entropy belongs to a cluster is a ratio of a sum of similarities between the user and other users in the user set to a sum of similarities between the users in the user set;
a clustering module 303, configured to perform clustering processing on a user set according to similarity between users in the user set based on a spectral clustering algorithm, so as to divide the user set into multiple clusters;
a second determining module 304, configured to determine a risk user from the multiple users to be identified according to distribution information of the risk sample user in the multiple clusters.
Optionally, the information entropy is:
wherein H (X) is the information entropy; p (x)i) For user x in the user setiProbability of belonging to a cluster, n being the number of users in the set of users; wijFor user x in the user setiAnd user xjThe similarity between them.
Optionally, as shown in fig. 4, the clustering module 303 includes:
the first constructing submodule 331, configured to respectively construct a similarity matrix and a degree matrix according to similarities between users in the user set, where an element in the similarity matrix is used to characterize the similarity between two users in the user set, and an element in the degree moment is used to characterize a sum of similarities between one user in the user set and other users;
a second constructing submodule 332, configured to construct a target matrix according to at least the similarity matrix and the degree matrix, where each row vector of the target matrix represents a coordinate of one user in the user set in a feature space;
the clustering sub-module 333 is configured to perform clustering processing on the reduced-dimension row vectors of the target matrix, so as to divide the user set into a plurality of clusters.
Optionally, the second construction sub-module 332 is configured to construct the target matrix according to the following manner:
constructing a Laplace matrix according to the similarity matrix and the degree matrix;
performing feature mapping according to the Laplace matrix, and selecting feature values of the number of clusters;
constructing a characteristic vector matrix according to the characteristic vectors corresponding to the selected characteristic values;
and carrying out normalization processing on the row vectors of the characteristic vector matrix to obtain the target matrix.
Optionally, the feature data of each user in the user set includes features of the user in multiple dimensions, and the second constructing sub-module 332 is configured to construct the target matrix according to the following manner:
constructing a Laplace matrix according to the similarity matrix and the degree matrix;
determining at least one candidate dimension from the multiple dimensions, and combining features of each user in the user set under each candidate dimension to obtain a feature combination;
constructing a diagonal matrix, a first intermediate matrix and a second intermediate matrix from the feature combinations and the Laplace matrix, respectively, based on the following formulas:
where U (j, j) is a diagonal matrix, PjIs the jth row of the projection matrix; alpha, beta and gamma are preset adjusting parameters; r is a correlation matrix for characterizing the degree of correlation between the features in the feature combination X, Rij=I(fi,fj),rij∈R,rijRepresenting mutual information between the features in the dimension i and the features in the dimension j in the feature combination X, and rij∈[0,1](ii) a A is the first intermediate matrix; h is the second intermediate matrix; d is the degree matrix; l is the Laplace matrix;
selecting the eigenvalue of the clustering number from all the eigenvalues of the second intermediate matrix;
respectively constructing a feature vector matrix and a projection matrix corresponding to the feature vector according to the feature vector, the first intermediate matrix and the feature combination corresponding to each selected feature value:
wherein T is the eigenvector matrix, and c is the number of clusters; v. of1,v2,…,vcSelecting characteristic vectors corresponding to the characteristic values; p is the projection matrix;
if the constructed projection matrix is not converged, repeating the step of determining at least one candidate dimension from the plurality of dimensions, and combining the features of each user in the user set under each candidate dimension to the constructed feature vector matrix and the projection matrix corresponding to the feature vector respectively until the constructed projection matrix is converged; and the number of the first and second groups,
and under the condition that the constructed projection matrix is converged, carrying out normalization processing on the row vector of the characteristic vector matrix corresponding to the projection matrix to obtain the target matrix.
It is obvious to those skilled in the art that, for convenience and simplicity of description, the foregoing division of the functional modules is merely used as an example, and in practical applications, the above function distribution may be performed by different functional modules according to needs, that is, the internal structure of the device is divided into different functional modules to perform all or part of the above described functions.
In addition, with regard to the apparatus in the above-described embodiment, the specific manner in which each module performs the operation has been described in detail in the embodiment related to the method, and will not be elaborated herein.
By adopting the device, the similarity among the users in the user set can be automatically determined by taking the minimum information entropy of the user set as a target, and compared with the method of determining the similarity among the users in a manual mode, the efficiency and the accuracy are higher, and the labor cost is saved. Furthermore, the efficiency of the whole risk user identification process and the accuracy of the identification result can be improved, and the labor cost of the whole process is reduced.
Fig. 5 is a block diagram illustrating an electronic device 500 according to an exemplary embodiment of the present disclosure. For example, the electronic device 500 may be provided as a server. Referring to fig. 5, the electronic device 500 comprises a processor 522, which may be one or more in number, and a memory 532 for storing computer programs executable by the processor 522. The computer programs stored in memory 532 may include one or more modules that each correspond to a set of instructions. Further, the processor 522 may be configured to execute the computer program to perform the above-described risky user identification method.
Additionally, the electronic device 500 may also include a power component 526 and a communication component 550, the power component 526 may be configured to perform power management of the electronic device 500, and the communication component 550 may be configured to enable communication, e.g., wired or wireless communication, of the electronic device 500. In addition, the electronic device 500 may also include input/output (I/O) interfaces 558. The electronic device 500 may operate based on an operating system stored in memory 532, such as Windows Server, Mac OS XTM, UnixTM, Linux, and the like.
In another exemplary embodiment, a computer readable storage medium comprising program instructions which, when executed by a processor, implement the steps of the above-described method of risk user identification is also provided. For example, the computer readable storage medium may be the memory 532 described above including program instructions that are executable by the processor 522 of the electronic device 500 to perform the method for at risk user identification described above.
The preferred embodiments of the present disclosure are described in detail with reference to the accompanying drawings, however, the present disclosure is not limited to the specific details of the above embodiments, and various simple modifications may be made to the technical solution of the present disclosure within the technical idea of the present disclosure, and these simple modifications all belong to the protection scope of the present disclosure.
It should be noted that the various features described in the above embodiments may be combined in any suitable manner without departing from the scope of the invention. In order to avoid unnecessary repetition, various possible combinations will not be separately described in this disclosure.
In addition, any combination of various embodiments of the present disclosure may be made, and the same should be considered as the disclosure of the present disclosure, as long as it does not depart from the spirit of the present disclosure.