CN117173496A - High-dimensional data dimension reduction method and system for maintaining one-dimensional topological characteristics - Google Patents
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Abstract
The invention relates to the technical field of data dimension reduction, in particular to a high-dimension data dimension reduction method and a system for maintaining one-dimension topological characteristics, wherein the method comprises the following steps: constructing a reeb graph of high-dimensional data as a data skeleton; extracting one-dimensional topological features of the data skeleton to obtain one-dimensional topological features of the data skeleton; performing constraint graph layout aiming at skeleton nodes contained in the one-dimensional topological features to obtain the optimal constraint layout of the skeleton nodes; and projecting other nodes except the skeleton node by using an improved L-Isomap algorithm based on the optimal constraint layout, so as to realize dimension reduction of high-dimension data. The invention uses the circular ring as the visual coding of the one-dimensional topological feature, and uses the constraint graph layout algorithm to perform graph layout on the one-dimensional topological feature of the high-dimensional data in the two-dimensional space, thereby effectively avoiding the overlapping and distortion of the one-dimensional topological feature of the high-dimensional data in the visual space.
Description
Technical Field
The invention relates to the technical field of data dimension reduction, in particular to a high-dimension data dimension reduction method and system for maintaining one-dimension topological characteristics.
Background
Today, high-dimensional data frequently occurs in the fields of statistics, data science, life science, etc. Data that these fields require to process for complex transactions often have tens of dimensional features, such as satellite telemetry spectral data, pathology statistics, complex chemical components, and the like. While advances in information technology have enabled detailed features of things to be acquired and stored, the vast amount of information presents difficulties in data analysis and pattern mining. The data dimension reduction is particularly important because the human cannot directly observe the rule of data with more than three dimensions.
Most of the current dimension reduction technologies are aimed at preserving distance information of high-dimension data, and a small part of the current dimension reduction technologies are aimed at preserving topological structures of the data. However, none of them reprocess in the visual space for the one-dimensional topological feature of the data, so that the topological feature of the data has a phenomenon of deformation overlapping in the visual space, which affects the user's exploration of the data feature.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a high-dimensional data dimension reduction method and system for maintaining one-dimensional topological characteristics.
To achieve the above object, in a first aspect, the present invention provides a high-dimensional data dimension reduction method for maintaining one-dimensional topological features, the method comprising the steps of: constructing a reeb graph of high-dimensional data as a data skeleton; extracting one-dimensional topological features of the data skeleton to obtain one-dimensional topological features of the data skeleton; performing constraint graph layout aiming at skeleton nodes contained in the one-dimensional topological features to obtain the optimal constraint layout of the skeleton nodes; and projecting other nodes except the skeleton node by using an improved L-Isomap algorithm based on the optimal constraint layout, so as to realize dimension reduction of high-dimension data. The invention uses the circular ring as the visual coding of the one-dimensional topological feature, and uses the constraint graph layout algorithm to perform graph layout on the one-dimensional topological feature of the high-dimensional data in the two-dimensional space, thereby effectively avoiding the overlapping and distortion of the one-dimensional topological feature of the high-dimensional data in the visual space.
Optionally, the constructing the reeb graph of the high-dimensional data as the data skeleton includes the following steps:
converting the point cloud in the high-dimensional data into an available numerical value;
dividing the numerical range of the available numerical representation into a plurality of subintervals;
using the available numerical values as input, and dividing the point set covered by each subinterval into a plurality of cluster clusters by using a clustering algorithm;
and taking the mass center of each cluster as a landmark point, connecting the landmark points of the two intersected clusters to obtain the reeb graph, and taking the reeb graph as the data skeleton.
Further, the key features of the data can be effectively captured and the complexity of the data can be reduced by constructing a reeb graph of the high-dimensional data to obtain the data skeleton.
Optionally, the performing constraint graph layout on the skeleton node included in the one-dimensional topological feature to obtain an optimal constraint layout of the skeleton node includes the following steps:
using a visual code of a ring shape to visualize the one-dimensional topological feature into a two-dimensional space, and setting an iteration ending condition;
and carrying out iterative optimization constraint graph layout according to the iterative ending condition, and further obtaining the optimal constraint layout of the skeleton node.
Further, when the constraint map is used for layout of the data skeleton, three aspects of constraint are mainly included, namely reeb map constraint, annular shape constraint and annular non-overlapping constraint, so that overlapping and distortion of one-dimensional topological features of high-dimensional data in a visual space are avoided while the integral structure of the data skeleton is maintained.
Optionally, the performing the iterative optimization of the constraint graph layout according to the iteration end condition, so as to obtain the optimal constraint layout of the skeleton node includes the following steps:
calculating edge vectors of the point-to-point distances between the skeleton nodes to obtain an edge vector matrix;
acquiring ideal layout coordinates of the skeleton nodes, and further acquiring a first target edge vector of an ideal ring;
acquiring a second target edge vector based on the overlapping relation of the one-dimensional topological features;
calculating constraint layout loss by using the edge vector, the first target edge vector and the second target edge vector, so as to obtain the current constraint layout of the skeleton node, and updating the constraint layout of the last time, wherein the constraint layout loss comprises a first part, a second part and a third part;
calculating a current edge vector matrix according to the current constraint layout, and using the current edge vector matrix as the edge vector matrix in the next iteration, so as to calculate the constraint layout of the skeleton node in the next iteration;
Repeating the steps until the iteration ending condition is met, and taking the finally obtained constraint layout as the optimal constraint layout to output.
Further, the data skeleton is continuously and iteratively optimized based on the constraint graph layout, overlapping and distortion of one-dimensional topological features of the high-dimensional data in a visual space are avoided, and finally the optimal constraint layout of the data skeleton is obtained. Wherein the edge vectors are used for reeb graph constraints, the first target edge vector is used for circular shape constraints, and the second target edge vector is used for circular non-overlapping constraints.
Optionally, the obtaining the ideal layout coordinates of the skeleton node, and further obtaining the first target edge vector of the ideal ring includes the following steps:
calculating the ideal layout coordinates according to the current layout coordinates of the skeleton nodes;
matching the current layout coordinates and skeleton nodes represented by the ideal layout coordinates one by using an ICP nearest point matching algorithm, and carrying out affine transformation on the ideal layout coordinates to obtain affine transformation ideal layout coordinates of the skeleton nodes;
calculating the first target edge vector according to the affine transformation ideal layout coordinates, wherein the first target edge vector meets the following relation:
d_shape ij ＝M(x_ideal i -x_ideal j )
Wherein d_shape ij For the first target edge vector between the skeleton node i and the skeleton node j, M is an affine matrix, x_ideal i X_ideal is the ideal layout coordinate of the skeleton node i j Ideal layout coordinates for the skeleton node j.
Optionally, the acquiring the second target edge vector based on the overlapping relation of the one-dimensional topological feature includes the following steps:
judging whether the overlapped one-dimensional topological features exist in the current constraint layout or not;
calculating the minimum permeability of the two overlapped one-dimensional topological features;
setting a second target edge vector based on the minimum permeability and the current layout coordinates of the two one-dimensional topological features with overlap, wherein the second target edge vector meets the following relation:
d_pverlap ij ＝(x 2i -x 2j )+mdp
wherein d_pverlap ij For a second target edge vector, x, between a skeleton node i in a first one of the two one-dimensional topological features and a skeleton node j in a second one of the two one-dimensional topological features that are overlapped 2i For the current layout coordinates of skeleton node i in the first one of the two one-dimensional topological features with overlap, x 2j And (3) for the current layout coordinates of the skeleton node j in the second one-dimensional topological feature in the two overlapped one-dimensional topological features, mdp is the minimum permeability.
Optionally, the first portion is determined by a first loss function, the first loss function satisfying the following relation:
wherein, loss reed Representing the first loss function, ω ij Is equal to d ij Related parameters, x i X is the current layout coordinate of the skeleton node i j D is the current layout coordinate of the skeleton node j ij Is an edge vector between the skeleton node i and the skeleton node j.
Furthermore, the first loss function performs reeb graph constraint on the one-dimensional topological feature based on the edge vector, so that the overall structure of the data skeleton is maintained.
Optionally, the second portion is determined by a second loss function, the second loss function satisfying the following relation:
wherein, loss shape Representing the second loss function, E circle For the edge set of all rings in two-dimensional space, ω 1ij Is d_shape ij Related parameters, x i X is the current layout coordinate of the ith skeleton node j The current layout coordinate of the j-th skeleton node is M is an affine matrix, x_ideal i X_ideal is the ideal layout coordinate of the skeleton node i j For the ideal layout coordinates of the skeleton node j, x_shape ij Is a first target edge vector between the skeleton node i and the skeleton node j.
Further, the second loss function performs annular shape constraint on the one-dimensional topological feature based on the first target edge vector, so that overlapping and distortion of the one-dimensional topological feature of the high-dimensional data in a visual space can be avoided.
Optionally, the third portion is determined by a third loss function, the third loss function satisfying the following relationship:
wherein, loss overlap Representing the third loss function, ω 2ij Is x_overlap with ij Related parameters, x 1i For the current layout coordinates of skeleton node i in the first one of the two one-dimensional topological features with overlap, x 2j For the current layout coordinates of skeleton node j in the second one of the two one-dimensional topological features with overlap, x_overlap ij Skeleton segments in first one of two one-dimensional topological features with overlapA second target edge vector between the point i and the skeleton node j in the second one-dimensional topological feature a For the first of two said one-dimensional topological features with overlap, circle b For a second of the two one-dimensional topological features where there is overlap.
Further, the third loss function performs annular non-overlapping constraint on the one-dimensional topological feature based on the second target edge vector, so that overlapping and distortion of the one-dimensional topological feature of the high-dimensional data in a visual space can be avoided.
In a second aspect, the present invention also provides a high-dimensional data dimension reduction system for maintaining one-dimensional topological features, where the system uses a high-dimensional data dimension reduction method for maintaining one-dimensional topological features provided by the present invention, and the system includes: the framework extraction module is used for constructing a reeb graph of the high-dimensional data as a data framework; the feature extraction module is used for extracting one-dimensional topological features of the data skeleton to obtain one-dimensional topological features of the data skeleton; the constraint layout module is used for carrying out constraint graph layout aiming at skeleton nodes contained in the one-dimensional topological features to obtain the optimal constraint layout of the skeleton nodes; and the mapping dimension reduction module is used for projecting other nodes except the skeleton node by using an improved L-Isomap algorithm based on the optimal constraint layout, so as to realize dimension reduction of high-dimension data.
Furthermore, the system provided by the application can improve the efficiency of reducing the dimension of the high-dimension data while avoiding the overlapping and distortion of the one-dimensional topological feature of the high-dimension data in the visual space based on the method provided by the application.
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In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are needed in the embodiments will be briefly described below, it being understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered as limiting the scope, and other related drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic flow chart of a method for dimension reduction of high-dimensional data for maintaining one-dimensional topological features according to an embodiment of the application;
FIG. 2 is a schematic diagram of obtaining a reeb map using high-dimensional data in accordance with an embodiment of the present application;
FIG. 3 is a schematic diagram of a process for performing annular shape constraint on one-dimensional topological features according to an embodiment of the present application;
FIG. 4 is a schematic diagram of a process for performing annular non-overlapping constraints on one-dimensional topological features according to an embodiment of the present application;
FIG. 5 is a three-dimensional spatial data schematic with three overlapping rings according to an embodiment of the present application;
FIG. 6 is a schematic diagram of a data skeleton of three-dimensional spatial data with three overlapping rings extracted using the method provided by the present invention;
FIG. 7 is a projection result of three-dimensional spatial data having three overlapping loops onto a two-dimensional space using an MDS algorithm in accordance with an embodiment of the present invention;
FIG. 8 is a projection result of three-dimensional space data having three overlapping rings onto a two-dimensional space using UMAP algorithm in accordance with an embodiment of the present invention;
FIG. 9 is a projection result of three-dimensional space data having three overlapping rings projected into a two-dimensional space using the method provided by the present invention;
FIG. 10 is a persistence view of three dimensional spatial data having three overlapping loops in accordance with an embodiment of the invention;
FIG. 11 is a persistence plot of projection results of three-dimensional spatial data having three overlapping loops projected into a two-dimensional space using an MDS algorithm in accordance with an embodiment of the present invention;
FIG. 12 is a persistence plot of projection results after three-dimensional spatial data having three overlapping loops is projected into two-dimensional space using UMAP algorithm in accordance with an embodiment of the present invention;
FIG. 13 is a persistence view of a projection result of three-dimensional spatial data having three overlapping rings projected into a two-dimensional space using the method provided by the present invention in accordance with an embodiment of the present invention;
FIG. 14 is a schematic diagram of a high-dimensional data-reduction system framework for maintaining one-dimensional topological features according to an embodiment of the present invention.
Detailed Description
Specific embodiments of the invention will be described in detail below, it being noted that the embodiments described herein are for illustration only and are not intended to limit the invention. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. However, it will be apparent to one of ordinary skill in the art that: no such specific details are necessary to practice the invention. In other instances, well-known circuits, software, or methods have not been described in detail in order not to obscure the invention.
Throughout the specification, references to "one embodiment," "an embodiment," "one example," or "an example" mean: a particular feature, structure, or characteristic described in connection with the embodiment or example is included within at least one embodiment of the invention. Thus, the appearances of the phrases "in one embodiment," "in an embodiment," "one example," or "an example" in various places throughout this specification are not necessarily all referring to the same embodiment or example. Furthermore, the particular features, structures, or characteristics may be combined in any suitable combination and/or sub-combination in one or more embodiments or examples. Moreover, those of ordinary skill in the art will appreciate that the illustrations provided herein are for illustrative purposes and that the illustrations are not necessarily drawn to scale.
It should be noted in advance that in an alternative embodiment, the same symbols or alphabet meaning and number are the same as those present in all formulas, except where separate descriptions are made.
In an alternative embodiment, referring to fig. 1, the present invention provides a high-dimensional data dimension reduction method for maintaining one-dimensional topological features, the method comprising the steps of:
s1, constructing a reeb graph of high-dimensional data as a data skeleton.
The Reeb graph is a data-based topology construction method, and key features of data can be effectively captured and complexity of the data can be reduced by constructing the Reeb graph of high-dimensional data to acquire a data skeleton. Referring to fig. 2, S1 specifically includes the following steps:
s11, converting the point cloud in the high-dimensional data into an available numerical value.
Specifically, in this embodiment, one source point is selected from the point clouds in the high-dimensional data, then the distances from other point clouds to the source point are calculated, and the calculated distances are used as available values of the point clouds. This transformation of the point cloud into usable values is the process of coloring the point cloud with a height function as a filtered value function, as shown in fig. 2 (a), and will not be described in detail herein because this is the prior art.
S12, dividing the numerical range which can be represented by the numerical value into a plurality of subintervals.
Specifically, in the present embodiment, the numerical range shown in fig. 2 (a) is [0-4.2], and the closer the height position of the point cloud is to 4.2, the darker the color of the point cloud is. According to the numerical range, please refer to (b) in fig. 2, the interval length is set to be 1, the repetition rate is set to be 0.2, and the numerical range is further divided into 5 subintervals, wherein the 5 subintervals are sequentially [0-1], [0.8-1.8], [1.6-2.6], [2.4-3.4], [3.2-4.2] from bottom to top, wherein the darker area represents the overlapping area between subintervals, the interval length is the length of the subintervals, and the repetition rate is the length of the overlapping area between subintervals.
S13, taking the available numerical values as input, and dividing the point set covered by each subinterval into a plurality of cluster clusters by using a clustering algorithm.
Specifically, in this embodiment, based on step S12, please refer to (c) in fig. 2, available numerical values of each subinterval are used as input, and a DBSCAN density clustering algorithm is selected to cluster corresponding point sets of each subinterval, so as to obtain 8 clusters.
S14, taking the mass center of each cluster as a landmark point, connecting the landmark points of the two intersected clusters to obtain the reeb graph, and taking the reeb graph as the data skeleton.
Specifically, in this embodiment, two clusters that intersect are two clusters obtained from two subintervals where there is an overlap region. Please refer to (d) in fig. 2, the diagram is a reeb diagram obtained based on step S13, wherein each landmark point is a skeleton node of the data skeleton, and a connection line between two landmark points is an edge between two skeleton nodes.
S2, extracting one-dimensional topological features of the data skeleton to obtain one-dimensional topological features of the data skeleton.
Specifically, in this embodiment, a persistent coherent method is used to extract one-dimensional topological features in the data skeleton, where persistent coherent is a core tool for calculating topology and analyzing topological data, and has a certain robustness to noise and transformation of data, and through flexible parameter setting, it can adapt to requirements of different types of data sets and analysis, which is the prior art, and will not be described in detail herein.
And S3, carrying out constraint graph layout aiming at skeleton nodes contained in the one-dimensional topological features to obtain the optimal constraint layout of the skeleton nodes.
When the constraint map is used for laying out the data skeleton, three aspects of constraint are mainly included, namely reeb map constraint, annular shape constraint and annular non-overlapping constraint, so that overlapping and distortion of one-dimensional topological features of high-dimensional data in a visual space are avoided while the integral structure of the data skeleton is maintained, and S3 specifically comprises the following steps:
S31, using the visual coding of the circular ring shape to visualize the one-dimensional topological feature into a two-dimensional space, and setting an iteration ending condition.
Specifically, in this embodiment, the use of the ring-shaped visualization code to visualize the one-dimensional topological feature to the two-dimensional space is the prior art, and the iteration end condition is that the maximum iteration number is reached.
S32, carrying out iterative optimization constraint graph layout according to the iterative ending condition, and further obtaining the optimal constraint layout of the skeleton node.
Wherein, S32 specifically further comprises the following steps:
s321, calculating edge vectors of the point-to-point distances among the skeleton nodes to obtain an edge vector matrix. Specifically, in the present embodiment, the edge vectors satisfy the following relationship:
d ij ＝x i -x j
wherein d ij Is the edge vector between the skeleton node i and the skeleton node j, x i As the current layout coordinate of the skeleton node i, x j Is the current layout coordinates of skeleton node j.
Further, the purpose of computing the edge vector is to provide a data basis for the computation of the first loss function for the purpose of reeb graph constraints.
S322, obtaining ideal layout coordinates of the skeleton nodes, and further obtaining a first target edge vector of an ideal ring.
Referring to fig. 3, S322 specifically further includes the following steps:
S3221, calculating the ideal layout coordinates according to the current layout coordinates of the skeleton nodes.
Specifically, in this embodiment, the one-dimensional topological feature is visualized to the two-dimensional space by using the visualization coding of the ring shape, so that the current layout of the skeleton node is shown in fig. 3 (a), and the layout of the skeleton node corresponds to the original layout of the one-dimensional topological feature. In order to maintain the shape of the ring in two dimensions, it is necessary to constrain the shape of the ring in two dimensions, i.e. to constrain the shape of the one-dimensional topological feature in two dimensions.
Firstly, calculating an ideal shape of a circular ring in a two-dimensional space, wherein the ideal shape is determined by the circle center and the radius of the circular ring and the number of skeleton nodes on the circular ring. The circle center is the average value of the current layout coordinates of all framework nodes on the circular ring, the radius is the average value of the distances from all framework nodes to the circle center on the circular ring, and the circle center and the radius of one circular ring in the two-dimensional space respectively meet the following relations:
wherein x is center Is the center of an ideal shape, r ideal Is the radius of the ideal shape, and n is the number of skeleton nodes on the ring.
Further, the ideal layout coordinates of the skeleton nodes on the ring can be obtained by using the circle center and the radius of the ideal shape of the ring in the two-dimensional space, so that the ideal layout coordinates of the ideal shape of the ring in the two-dimensional space can be obtained as shown in (b) of fig. 3, and the ideal layout coordinates satisfy the following relationship:
x_ideal i ＝x center +[r ideal ×cos(i×θ)，r ideal ×sin(i×θ)]
Wherein x_ideal i θ=2pi/n, which is the ideal layout coordinate of skeleton node i.
S3222, matching skeleton nodes represented by the current layout coordinates and the ideal layout coordinates one by using an ICP nearest point matching algorithm, and carrying out affine transformation on the ideal layout coordinates to obtain affine transformation ideal layout coordinates of the skeleton nodes.
Specifically, in this embodiment, please refer to (c) in fig. 3, the ideal layout coordinates of the skeleton node obtained in S3221 and the current layout coordinates thereof are not in the same position, which is specifically represented by translation of the position of the skeleton node on the ring, and this step is to match the ring and the skeleton node on the ideal shape thereof one by one, that is to match the black dots in (c) in 3 with the gray dots one by one, and affine transform the ideal layout coordinates of the skeleton node on the ring, so as to obtain affine transformed ideal layout coordinates of the skeleton node, and provide a data base for subsequent computation.
S3223, calculating the first target edge vector according to the affine transformation ideal layout coordinates, wherein the first target edge vector meets the following relation:
d_shape ij ＝M(x_ideal i -x_ideal j )
wherein d_shape ij For the skeletal node i and the bone First target edge vector between frame nodes j, M is affine matrix, x_ideal i X_ideal is the ideal layout coordinate of the skeleton node i j Ideal layout coordinates for the skeleton node j.
Specifically, in the present embodiment, M (x_ideal) i -x_ideal j )＝MX_ideal i -MX_ideal j ，MX_ideal i Ideal layout coordinates for affine transformation of skeleton node i, mx_ideal j Ideal layout coordinates for affine transformation of skeleton node j, mx_ideal i And MX_ideal j Referring to fig. 3 (c) and (d), the affine matrix can be obtained by the following function:
furthermore, the first target edge vector provides a data basis for the calculation of the second loss function, is used for annular shape constraint when the data is subjected to dimension reduction, and is beneficial to avoiding the overlapping and distortion of one-dimensional topological features of high-dimensional data in a visual space.
S323, acquiring a second target edge vector based on the overlapping relation of the one-dimensional topological features.
Referring to fig. 4, S323 specifically further includes the following steps:
s3231, judging whether the overlapped one-dimensional topological feature exists in the current constraint layout.
Specifically, in this embodiment, please refer to (a) and (b) in fig. 4, in the process of searching the optimal constraint layout according to the iteration end condition, a constraint layout of a skeleton node is output in each iteration, and in the first iteration, the current constraint layout is the original layout of the skeleton node, that is, the current layout of the skeleton node in the first iteration; in each iteration thereafter, the current constraint layout is the constraint layout output by the last iteration. For two arbitrary one-dimensional topological features, if the distance between any one skeleton node in the first one-dimensional topological feature and the circle center of the second one-dimensional topological feature is larger than the radius of the second one-dimensional topological feature, the two one-dimensional topological features are overlapped. It will be readily seen that the current layout of the two one-dimensional topological features in fig. 4 (a) is overlapping.
S3232, for two one-dimensional topological features with overlapping, calculating the minimum permeability of the two one-dimensional topological features.
Specifically, in this embodiment, please refer to (c) in fig. 4, the minimum permeability mpd is the shortest vector that moves one ring out of the other.
Further, for two overlapped one-dimensional topological features, respectively ordering skeleton nodes of the first one-dimensional topological feature and skeleton nodes of the second one-dimensional topological feature according to polar angles, and then calculating a convex hull polygon formed by the skeleton nodes of the first one-dimensional topological feature and a Minkowski Sum of the convex hull polygon formed by the skeleton nodes of the second one-dimensional topological feature, so as to obtain the minimum Minkowski as mpd. This is prior art and is therefore only described generally herein without specific explanation.
S3233, setting a second target edge vector based on the minimum permeability and the current layout coordinates of the two overlapped one-dimensional topological features, wherein the second target edge vector meets the following relation:
d_overlap ij ＝(x 1i -x 2j )+mdp
wherein d_overlap ij For a second target edge vector, x, between a skeleton node i in a first one of the two one-dimensional topological features and a skeleton node j in a second one of the two one-dimensional topological features that are overlapped 1i For the current layout coordinates of skeleton node i in the first one of the two one-dimensional topological features with overlap, x 2j And (3) for the current layout coordinates of the skeleton node j in the second one-dimensional topological feature in the two overlapped one-dimensional topological features, mdp is the minimum permeability.
Specifically, in this embodiment, the second target edge vector is used for the annular non-overlapping constraint when the data is reduced in dimension. Referring to fig. 4 (d), the current layout of the two one-dimensional topological features is overlapped initially, and after the annular non-overlapping constraint, the two one-dimensional topological features with the overlapping are separated, and the layout manner between them is changed from the current layout with the overlapping initially to the non-overlapping ideal layout, so that the overlapping and distortion of the one-dimensional topological features of the high-dimensional data in the visual space can be avoided.
S324, calculating constraint layout loss by using the edge vector, the first target edge vector and the second target edge vector, further obtaining the current constraint layout of the skeleton node, and updating the constraint layout of the last time, wherein the constraint layout loss comprises a first part, a second part and a third part.
Specifically, in the present embodiment, the first loss function, the second loss function, and the third loss function satisfy the following relationships, respectively:
wherein, loss reed Representing a first loss function omega ij Is equal to d ij The parameter of the correlation is set to be,d ij is d ij Is a mold of (2); loss (Low Density) shape Representing a second loss function, E circle For the edge set of all rings in two-dimensional space, ω 1ij Is d_shape ij Related parameters->d_shape ij For d_shape ij Is a mold of (2); loss (Low Density) overlap Represents a third loss function omega 2ij Is d_overlap with ij Related parameters, d_overlap ij For the second target edge vector between the skeleton node i in the first one-dimensional topological feature and the skeleton node j in the second one-dimensional topological feature in the two overlapped one-dimensional topological features, circle a For the first one of two overlapping one-dimensional topological features, circle b For the second of the two one-dimensional topological features with overlap +.>d_overlap ij For d_overlap ij Is a mold of (a).
And further, constraint layout loss can be obtained to meet the following relationship:
wherein Loss is constraint layout Loss, circle k Is the kth one-dimensional topological feature.
Writing constraint layout loss into a matrix form, then:
Stress(X)＝Tr(X T L 1 X)-2Tr(X T J 1 D)+Tr(X T L 2 X)-2Tr(X T J 2 D 1 )+Tr(X T L 3 X)-2Tr(X T J 3 D 2 )+C
wherein Stress (X) represents a matrix form of constraint layout loss about X, X is the current constraint layout of skeleton nodes in one-dimensional topological features, T represents transposition operation, and L 1 Is with omega ij Related n-dimensional weighted Laplace matrix, L 2 Is with omega 1ij Related n-dimensional weighted Laplace matrix, L 3 Is with omega 2ij Related n-dimensional weighted Laplace matrix, J 1 To store a matrix of all edge vector weights, J 2 To store a matrix of all first target edge vector weights, J 3 To store the matrix of all second target edge vector weightsD is an edge vector matrix, D 1 D is a matrix formed by all first target edge vectors 2 For a matrix made up of all second target edge vectors, C is a constant, C is determined by the possible constants within the relation of the calculated Loss, tr represents the trace of the acquisition matrix.
Further, L 1 And J 1 Obtained by the following relations:
wherein omega ik Method for calculating and omega ij The calculation method of (1) is the same as that of L 2 And L 3 Can be obtained by and L 1 Obtained in the same way, J 2 And J 3 Can be obtained by and L 1 Acquired in the same way, all that is needed is to calculate ω as required ij Replaced by omega 1ij Or omega 2ij And (3) obtaining the product.
Deriving Stress (X) for X and setting the derivative to 0 yields the following relationship:
further, the calculated edge vector, the first target edge vector and the second target edge vector are brought into the relational expression, so that the current constraint layout of the skeleton node can be obtained, and the previous constraint layout is updated by using the current constraint layout.
S325, calculating a current edge vector matrix according to the current constraint layout, and using the current edge vector matrix as the edge vector matrix in the next iteration, so as to calculate the constraint layout of the skeleton node in the next iteration.
Specifically, in this embodiment, according to the constraint layout of the skeleton node at the current position, the current edge vector is calculated by using the calculation method in step S321, so as to obtain a current edge vector matrix, and the current edge vector matrix is used as the edge vector matrix in the next iteration, where this step is actually updating the edge vector, and the calculation of the edge vector can be skipped in the next iteration to calculate the constraint layout of the skeleton node in the next iteration.
S326, repeating the steps until the iteration ending condition is met, and outputting the finally obtained constraint layout as the optimal constraint layout.
Specifically, in this embodiment, steps S321 to S325 are repeated until the number of iterations reaches the maximum number of iterations, and the constraint layout obtained finally is output as the optimal constraint layout.
And S4, projecting other nodes except the skeleton node by using an improved L-Isomap algorithm based on the optimal constraint layout, so as to realize dimension reduction of high-dimension data.
Specifically, in this embodiment, the landmark points obtained in step S14 are used to replace the landmark points randomly selected in the conventional L-Isomap algorithm, and the MDS algorithm in the conventional L-Isomap algorithm is replaced by the calculation method of step S3 in this embodiment, so as to further improve the L-Isomap algorithm. And finally, taking the optimal constraint layout as the input of the improved L-Isomap algorithm, and projecting out other nodes except skeleton nodes in the high-dimensional data, so that the dimension reduction of the high-dimensional data is realized.
The advantages of the present invention over the prior art will be described below by means of specific projection results and persistence figures.
Specifically, in this embodiment, please refer to fig. 5, three-dimensional space data with three overlapping rings is selected, and then the data skeleton of the three-dimensional space data is extracted by using the method provided by the invention, and the extraction result is shown in fig. 6. It is not difficult to see from fig. 5 and 6 that the three-dimensional space data has three important one-dimensional topological features, and that the prior art projects the three-dimensional space data into the two-dimensional space to produce a poor visual effect due to the overlapping of the data in the three-dimensional space data.
Further, referring to fig. 7, when the MDS algorithm is used to project the three-dimensional space data into the two-dimensional space, the projection result shows that three rings are nested with each other, and if the colors of the nodes in the projection result are not different, it is difficult for the related personnel to identify three one-dimensional topological features from the three one-dimensional topological features; referring to fig. 8, when the three-dimensional space data is projected into the two-dimensional space by using the UMAP algorithm, the projection result can better separate the three rings, but the overall structure of the rings cannot be maintained, which is not beneficial to understanding of related personnel; referring to fig. 9, it can be seen that the projection result of the method provided by the invention not only can well separate three rings in the three-dimensional space data in the two-dimensional space, but also can well maintain the overall structure of each ring.
Still further, three important one-dimensional topological features in the persistence map are represented by three larger black dots, please refer to fig. 10, three important one-dimensional topological features exist in the persistence map of the three-dimensional spatial data, the three one-dimensional topological features start to appear when the abscissa is 0.462, death occurs when the ordinate is 4.33, and some denser gray dots exist near the dotted line in the map, and the gray dots are topological noise. Referring to fig. 11, after the three-dimensional space data is projected into the two-dimensional space by using the MDS algorithm, three important one-dimensional topological features in the three-dimensional space data can be represented in a persistence graph of the projection result, the three important one-dimensional topological features begin to appear when the abscissa is 1, death occurs when the ordinate is 2.24, and two small black points far from the dotted line exist in the graph, and the two small black points represent two secondary one-dimensional topological features in the three-dimensional space data, but compared with fig. 5 and fig. 7, it is not difficult to obtain that the MDS algorithm hardly presents the real relative positions of the one-dimensional topological features. Referring to fig. 12, it can be seen from the persistence graph that after the three-dimensional space data is projected into the two-dimensional space by using the UMAP algorithm, the projection result only retains two important one-dimensional topological features in the three-dimensional space data, and the two one-dimensional topological features begin to appear when the abscissa is 2.7 and die when the ordinate is 5.79; referring to fig. 13, it can be seen from the persistence graph that, after the three-dimensional space data is projected into the two-dimensional space by the method provided by the invention, the projection result can show three important one-dimensional topological features in the three-dimensional space data, the three one-dimensional topological features begin to appear when the abscissa is 0.962 and die when the ordinate is 12, and compared with fig. 10, the topology noise is reduced to a certain extent by the method provided by the invention, and compared with fig. 9 and 5, the real relative position of the important one-dimensional topological features in the high-dimensional data can be accurately shown by the method provided by the invention.
It should be noted that, in some cases, the actions described in the specification may be performed in a different order and still achieve desirable results, and in this embodiment, the order of steps is merely provided to make the embodiment more clear, and it is convenient to describe the embodiment without limiting it.
In an alternative embodiment, please refer to fig. 14, the present invention further provides a high-dimensional dimension-reduction system for maintaining one-dimensional topological features, which uses a high-dimensional dimension-reduction method for maintaining one-dimensional topological features provided by the present invention, and the system includes a skeleton extraction module A1, a feature extraction module A2, a constraint layout module A3, and a mapping dimension-reduction module A4.
The skeleton extraction module A1 is used for constructing a reeb graph of high-dimensional data as a data skeleton.
Specifically, in this embodiment, the high-dimensional data is first input into the skeleton extraction module A1, and then the skeleton extraction module A1 executes the content of step S1 to obtain a data skeleton of the high-dimensional data, and the data skeleton is transmitted to the feature extraction module A2.
The feature extraction module A2 is used for extracting one-dimensional topological features of the data skeleton to obtain one-dimensional topological features of the data skeleton.
Specifically, in this embodiment, the feature extraction module A2 is connected to the skeleton extraction module A1 through a data line, the feature extraction module A2 first receives the data skeleton transmitted from the skeleton extraction module A1, and then the feature extraction module A2 executes the content described in step S2 to obtain one-dimensional topological features of the data skeleton, and transmits the one-dimensional topological features to the constraint layout module A3.
And the constraint layout module A3 is used for carrying out constraint graph layout aiming at skeleton nodes contained in the one-dimensional topological feature to obtain the optimal constraint layout of the skeleton nodes.
Specifically, in this embodiment, the constraint layout module A3 is connected to the feature extraction module A2 through a data line, the constraint layout module A3 first receives the one-dimensional topological feature transmitted by the feature extraction module A2, and then the constraint layout module A3 executes the content described in step S3 to obtain an optimal constraint layout of the skeleton node, and transmits the optimal constraint layout to the mapping dimension reduction module A4.
The mapping dimension reduction module A4 is used for projecting other nodes except the skeleton node by using an improved L-Isomap algorithm based on the optimal constraint layout, so as to realize dimension reduction of high-dimension data.
Specifically, in this embodiment, the mapping dimension reduction module A4 is connected to the constraint layout module A3 through a data line, the mapping dimension reduction module A4 first receives the optimal constraint layout transmitted by the constraint layout module A3, and then the mapping dimension reduction module A4 executes the content described in step S4, so as to further implement dimension reduction on high dimension.
In summary, the method uses the circular ring as the visual coding of the one-dimensional topological feature, and uses the constraint graph layout algorithm, including graph layout of the one-dimensional topological feature of the high-dimensional data in the two-dimensional space by using reeb constraint, annular shape constraint and annular non-overlapping constraint, so that the overlapping and distortion of the one-dimensional topological feature of the high-dimensional data in the visual space are effectively avoided, and the method provided by the invention can reduce the topological noise in the high-dimensional data, and shows higher accuracy and reliability when the dimension of the high-dimensional data is reduced.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention, and are intended to be included within the scope of the appended claims and description.
Claims (10)
1. The high-dimensional data dimension reduction method for maintaining one-dimensional topological characteristics is characterized by comprising the following steps of:
constructing a reeb graph of high-dimensional data as a data skeleton;
extracting one-dimensional topological features of the data skeleton to obtain one-dimensional topological features of the data skeleton;
performing constraint graph layout aiming at skeleton nodes contained in the one-dimensional topological features to obtain the optimal constraint layout of the skeleton nodes;
and projecting other nodes except the skeleton node by using an improved L-Isomap algorithm based on the optimal constraint layout, so as to realize dimension reduction of high-dimension data.
2. The method for dimension reduction of high-dimensional data with one-dimensional topological feature maintained according to claim 1, wherein the constructing the reeb graph of the high-dimensional data as a data skeleton comprises the following steps:
converting the point cloud in the high-dimensional data into an available numerical value;
dividing the numerical range of the available numerical representation into a plurality of subintervals;
using the available numerical values as input, and dividing the point set covered by each subinterval into a plurality of cluster clusters by using a clustering algorithm;
and taking the mass center of each cluster as a landmark point, connecting the landmark points of the two intersected clusters to obtain the reeb graph, and taking the reeb graph as the data skeleton.
3. The method for dimension reduction of high-dimensional data for maintaining one-dimensional topological features according to claim 1, wherein the step of performing constraint graph layout on skeleton nodes contained in the one-dimensional topological features to obtain an optimal constraint layout of the skeleton nodes comprises the following steps:
using a visual code of a ring shape to visualize the one-dimensional topological feature into a two-dimensional space, and setting an iteration ending condition;
and carrying out iterative optimization constraint graph layout according to the iterative ending condition, and further obtaining the optimal constraint layout of the skeleton node.
4. A method for dimension reduction of high-dimensional data with one-dimensional topological feature maintained according to claim 3, wherein the constraint graph layout which is iteratively optimized according to the iteration end condition, and further obtaining the optimal constraint layout of the skeleton node, comprises the following steps:
calculating edge vectors of the point-to-point distances between the skeleton nodes to obtain an edge vector matrix;
acquiring ideal layout coordinates of the skeleton nodes, and further acquiring a first target edge vector of an ideal ring;
acquiring a second target edge vector based on the overlapping relation of the one-dimensional topological features;
calculating constraint layout loss by using the edge vector, the first target edge vector and the second target edge vector, so as to obtain the current constraint layout of the skeleton node, and updating the constraint layout of the last time, wherein the constraint layout loss comprises a first part, a second part and a third part;
Calculating a current edge vector matrix according to the current constraint layout, and using the current edge vector matrix as the edge vector matrix in the next iteration, so as to calculate the constraint layout of the skeleton node in the next iteration;
repeating the steps until the iteration ending condition is met, and taking the finally obtained constraint layout as the optimal constraint layout to output.
5. The method for dimension reduction of high-dimensional data with one-dimensional topological feature maintained according to claim 4, wherein the step of obtaining the ideal layout coordinates of the skeleton node, and further obtaining the first target edge vector of the ideal ring comprises the following steps:
calculating the ideal layout coordinates according to the current layout coordinates of the skeleton nodes;
matching the current layout coordinates and skeleton nodes represented by the ideal layout coordinates one by using an ICP nearest point matching algorithm, and carrying out affine transformation on the ideal layout coordinates to obtain affine transformation ideal layout coordinates of the skeleton nodes;
calculating the first target edge vector according to the affine transformation ideal layout coordinates, wherein the first target edge vector meets the following relation:
d_shape ij ＝M(x_ideal i -x_ideal j )
wherein d_shape ij For the first target edge vector between the skeleton node i and the skeleton node j, M is an affine matrix, x_ideal i X_ideal is the ideal layout coordinate of the skeleton node i j Ideal layout coordinates for the skeleton node j.
6. The method for dimension reduction of high-dimensional data maintaining one-dimensional topological features according to claim 5, wherein the step of obtaining a second target edge vector based on the overlapping relation of the one-dimensional topological features comprises the steps of:
judging whether the overlapped one-dimensional topological features exist in the current constraint layout or not;
calculating the minimum permeability of the two overlapped one-dimensional topological features;
setting a second target edge vector based on the minimum permeability and the current layout coordinates of the two one-dimensional topological features with overlap, wherein the second target edge vector meets the following relation:
d_overlap ij ＝(x 2i -x 2j )+mdp
wherein d_overlap ij For skeleton node i in first one of the one-dimensional topological features and second one of the one-dimensional topological features in which overlapping two one-dimensional topological features existSecond target edge vector, x, between skeleton nodes j 2i For the current layout coordinates of skeleton node i in the first one of the two one-dimensional topological features with overlap, x 2j And (3) for the current layout coordinates of the skeleton node j in the second one-dimensional topological feature in the two overlapped one-dimensional topological features, mdp is the minimum permeability.
7. The method of dimension reduction of high-dimensional data maintaining one-dimensional topological features according to claim 5, wherein the first part is determined by a first loss function, and wherein the first loss function satisfies the following relationship:
wherein, loss reed Representing the first loss function, ω ij Is equal to d ij Related parameters, x i X is the current layout coordinate of the skeleton node i j D is the current layout coordinate of the skeleton node j ij Is an edge vector between the skeleton node i and the skeleton node j.
8. The method of dimension reduction of high-dimensional data maintaining one-dimensional topological features according to claim 5, wherein the second part is determined by a second loss function, the second loss function satisfying the following relationship:
wherein, loss shape Representing the second loss function, E circle For the edge set of all rings in two-dimensional space, ω 1ij Is d_shape ij Related parameters, x i X is the current layout coordinate of the ith skeleton node j M is the current layout coordinate of the j-th skeleton node Is an affine matrix, x_index i X_ideal is the ideal layout coordinate of the skeleton node i j D_shape is the ideal layout coordinate of the skeleton node j ij Is a first target edge vector between the skeleton node i and the skeleton node j.
9. The method of dimension reduction of high-dimensional data maintaining one-dimensional topological features according to claim 6, wherein the third part is determined by a third loss function, and wherein the third loss function satisfies the following relationship:
wherein, loss overlap Representing the third loss function, ω 2ij Is d_overlap with ij Related parameters, x 1i For the current layout coordinates of skeleton node i in the first one of the two one-dimensional topological features with overlap, x 2j D_overlap for the current layout coordinates of skeleton node j in the second one of the two one-dimensional topological features with overlap ij For the second target edge vector between the skeleton node i in the first one-dimensional topological feature and the skeleton node j in the second one-dimensional topological feature in the two overlapped one-dimensional topological features, circle a For the first of two said one-dimensional topological features with overlap, circle b For a second of the two one-dimensional topological features where there is overlap.
10. A high-dimensional data dimension reduction system that maintains one-dimensional topological features, the system using the high-dimensional data dimension reduction method of one-dimensional topological features of any one of claims 1 to 9, comprising:
the framework extraction module is used for constructing a reeb graph of the high-dimensional data as a data framework;
the feature extraction module is used for extracting one-dimensional topological features of the data skeleton to obtain one-dimensional topological features of the data skeleton;
the constraint layout module is used for carrying out constraint graph layout aiming at skeleton nodes contained in the one-dimensional topological features to obtain the optimal constraint layout of the skeleton nodes;
and the mapping dimension reduction module is used for projecting other nodes except the skeleton node by using an improved L-Isomap algorithm based on the optimal constraint layout, so as to realize dimension reduction of high-dimension data.
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Citations (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20070036434A1 (en) * | 2005-08-15 | 2007-02-15 | Peter Saveliev | Topology-Based Method of Partition, Analysis, and Simplification of Dynamical Images and its Applications |
| US20080181503A1 (en) * | 2007-01-30 | 2008-07-31 | Alon Schclar | Diffusion bases methods for segmentation and clustering |
| FR2914757A1 (en) * | 2007-04-06 | 2008-10-10 | France Telecom | METHOD FOR ESTIMATING MORPHOLOGICAL CHARACTERISTICS OF A GEOMETRIC FORM |
| CN107153839A (en) * | 2017-04-20 | 2017-09-12 | 电子科技大学 | A kind of high-spectrum image dimensionality reduction processing method |
| CN110648276A (en) * | 2019-09-25 | 2020-01-03 | 重庆大学 | High-dimensional image data dimension reduction method based on manifold mapping and dictionary learning |
| CN111340108A (en) * | 2020-02-25 | 2020-06-26 | 重庆邮电大学 | High-dimensional data visualization method based on optimal transmission theory |
| CN111950651A (en) * | 2020-08-21 | 2020-11-17 | 中国科学院计算机网络信息中心 | High-dimensional data processing method and device |
| CN112991424A (en) * | 2021-04-07 | 2021-06-18 | 重庆大学 | Fractal dimension calculation method and device based on octree algorithm |
| CN113628339A (en) * | 2021-08-17 | 2021-11-09 | 电子科技大学 | Broken layer slice extraction method based on local reservation projection |
| CN115229813A (en) * | 2022-07-20 | 2022-10-25 | 神华准格尔能源有限责任公司 | Welding hand-eye calibration system and calibration method based on machine vision |
-
2023
- 2023-09-20 CN CN202311215687.6A patent/CN117173496B/en active Active
Patent Citations (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20070036434A1 (en) * | 2005-08-15 | 2007-02-15 | Peter Saveliev | Topology-Based Method of Partition, Analysis, and Simplification of Dynamical Images and its Applications |
| US20080181503A1 (en) * | 2007-01-30 | 2008-07-31 | Alon Schclar | Diffusion bases methods for segmentation and clustering |
| FR2914757A1 (en) * | 2007-04-06 | 2008-10-10 | France Telecom | METHOD FOR ESTIMATING MORPHOLOGICAL CHARACTERISTICS OF A GEOMETRIC FORM |
| CN107153839A (en) * | 2017-04-20 | 2017-09-12 | 电子科技大学 | A kind of high-spectrum image dimensionality reduction processing method |
| CN110648276A (en) * | 2019-09-25 | 2020-01-03 | 重庆大学 | High-dimensional image data dimension reduction method based on manifold mapping and dictionary learning |
| CN111340108A (en) * | 2020-02-25 | 2020-06-26 | 重庆邮电大学 | High-dimensional data visualization method based on optimal transmission theory |
| CN111950651A (en) * | 2020-08-21 | 2020-11-17 | 中国科学院计算机网络信息中心 | High-dimensional data processing method and device |
| CN112991424A (en) * | 2021-04-07 | 2021-06-18 | 重庆大学 | Fractal dimension calculation method and device based on octree algorithm |
| CN113628339A (en) * | 2021-08-17 | 2021-11-09 | 电子科技大学 | Broken layer slice extraction method based on local reservation projection |
| CN115229813A (en) * | 2022-07-20 | 2022-10-25 | 神华准格尔能源有限责任公司 | Welding hand-eye calibration system and calibration method based on machine vision |
Non-Patent Citations (5)
| Title |
|---|
| HARISH DORAISWAMY 等: "TopoMap: A 0-dimensional homology preserving projection of High-Dimensional Data", 《HTTPS://ARXIV.DOSF.TOP/PDF/2009.01512》, 3 September 2020 (2020-09-03) * |
| 张义宽;张晓鹏;查红彬;张讲社;: "3维点云的拓扑结构表征与计算技术", 中国图象图形学报, no. 08, 15 August 2008 (2008-08-15) * |
| 李燕燕 等: "自适应邻域选择的I somap算法", 《河北建筑工程学院学报》, 31 December 2014 (2014-12-31) * |
| 祝铭阳;孙怀江;: "人脸动画关键点最优化算法", 计算机辅助设计与图形学学报, no. 01, 15 January 2013 (2013-01-15) * |
| 秦红星 等: "深度学习刚性点云配准前沿进展", 《中国图象图形学报》, 28 February 2022 (2022-02-28) * |
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