Visualization and Enhancement Methods for High-Dimensional Multi-Label Network Embedding Results

Abstract

A set-based method for visualizing and enhancing high-dimensional multi-label network embedding results includes: cleaning and preprocessing self-built or publicly available heterogeneous multi-label graph datasets; running a multi-label classification model suitable for heterogeneous graph data to obtain high-dimensional heterogeneous network embedding results; applying hierarchical dimensionality reduction techniques to the high-dimensional heterogeneous network embedding results to obtain hierarchical two-dimensional embedding results; extracting multi-label attributes from the data; constructing a set-element-intersection relationship model; performing data statistics on sets and intersections; and linking the statistical data with the embedding results; visualizing the two-dimensional embedding results using scatter plots; and implementing density-based and geometry-based layout enhancement methods to support user interaction; and visualizing set information to display rich information about sets and intersections, and implementing interactive means to link sets, intersections, and the scatter plot of the embedding results.

Description

Technical Field

[0001] This invention proposes a set-based visualization and enhancement method for high-dimensional multi-label network embedding results. This method is designed for high-dimensional multi-label embedding results of heterogeneous networks. It constructs a set space for multi-label attributes and links the embedding space with the set space, thus solving the complexity problem of multi-labels and providing enhancement techniques for different tasks. Background Technology

[0002] Many heterogeneous networks exist in the real world, such as social networks and academic networks containing different types of nodes. The complexity and large scale of heterogeneous networks significantly increase the difficulty of their analysis. Recently, network embedding techniques have become an effective method for analyzing and mining heterogeneous networks. These techniques compute representative vectors of the original network nodes and edges through representation learning. By processing and visualizing the learned node and edge embedding vectors, the network structure and key information can be effectively analyzed. However, due to the inherent complexity of representation learning, the process is like a "black box," posing challenges not only in understanding the learning process but also in understanding the embedding results. Against this research backdrop, how to use an intuitive method to enhance the understanding of the learned embedding results, helping researchers better understand and improve networks, has become an important question.

[0003] Most previous work typically uses dimensionality reduction techniques to reduce high-dimensional embedding results to lower dimensions, and then uses two-dimensional scatter plots for visualization and analysis. However, complex heterogeneous networks often exhibit large scale and multiple attributes. As complexity increases, the limitations of traditional dimensionality reduction techniques become increasingly apparent. First, dimensionality reduction inevitably introduces distortion. Second, for large-scale data, traditional scatter plots are constrained by layout issues, leading to point overlap within a limited screen space. Therefore, the primary goal of this invention is to provide a comprehensive method for visualizing embedding results, enabling the interpretation and enhancement of these results.

[0004] Furthermore, existing research on the interpretation and enhancement of embedding visualizations largely focuses on multidimensional single-label attributes. However, heterogeneous network data often contains multi-label attributes; for example, a movie typically has multiple genres, and a product often has multiple functions or application scenarios. Multi-label attributes involve not only the increase of a single label but also rich combinations between labels, which brings more challenges. First, as the number of label categories increases, the combinations of multi-label attributes also grow exponentially. Moreover, these label categories are not entirely independent but have different correlations. The implicit correlations between large-scale label categories lead to the proximity or overlap of the embedding space, posing a significant challenge to visualizing and interpreting them. Therefore, visualizing multi-label data is the second problem that this invention aims to address. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, this invention proposes a set-based method for visualizing and enhancing the embedding results of high-dimensional multi-label networks.

[0006] The present invention provides a method for visualizing and enhancing the embedding results of high-dimensional multi-label networks based on sets, comprising the following steps:

[0007] This invention proposes a method for visualizing the embedding results of high-dimensional, multi-label heterogeneous networks based on set theory. First, addressing the initial problem, this invention uses a hierarchical DR method to project the heterogeneous network embedding results onto an embedding space and visualizes it as a hierarchical scatter plot, serving as a more scalable foundational solution. Second, to address the issue of multi-label attribute data, this invention constructs a set space for multi-label attributes and, based on implicit correlation rules, proposes a strategy for set projection and color mapping using a fully ordered radial coordinate system. Finally, this invention connects these two spaces by designing relationships between high-dimensional multi-label attributes and low-dimensional embedding positions to improve interpretability. Furthermore, this invention employs various layout enhancement strategies combining statistical and geometric methods to reduce the limitations of traditional scatter plots when applied in different ways to large-scale, multi-label complexities, and to improve the scalability and interpretability of user exploration. Case studies and user experiments on two real-world datasets demonstrate the effectiveness of this invention.

[0008] Step 1: Clean and preprocess the data of the self-built or publicly available heterogeneous multi-label graph dataset, run the multi-label classification model suitable for heterogeneous graph data, and obtain high-dimensional heterogeneous network embedding results;

[0009] Step 2: Use hierarchical dimensionality reduction techniques to embed the high-dimensional heterogeneous network results into hierarchical two-dimensional embedding results;

[0010] Step 3: Extract multi-label attributes from the data, construct a set-element-intersection relationship model, perform data statistics on the set and intersection, and link the statistical data with the embedding results;

[0011] Step 4: Visualize the 2D embedding results using a scatter plot, and then implement density-based and geometry-based layout enhancement methods to support user interaction.

[0012] Step 5: Visualize the set information extracted in Step 3. Use novel and reasonable visualization design to display the rich information of sets and intersections, and implement interactive means to connect sets, intersections and embedded result scatter plots.

[0013] Furthermore, step 1 specifically includes:

[0014] 1.1 Preparation of Heterogeneous Multi-Label Graph Datasets (Self-built or Publicly Available). This invention uses the DBLP public literature citation dataset from the Aminer website, extracting 16 conferences as venue nodes and dividing them into four domains: database, data mining, machine learning, and information retrieval. Then, this invention extracts 1600 papers from these 16 conferences as paper nodes and the corresponding 4420 authors as author nodes. This invention defines the features of a paper as its set of keywords, and the features of an author as the set of keywords from all their papers; the label of a paper is determined by the domain in which it was submitted, and the label of an author is determined by the labels of their papers (an author may have multiple labels, i.e., the author has published papers in multiple domains).

[0015] In addition, this invention crawled a large amount of movie and filmmaker data from Douban Movies and extracted some data to create a self-built dataset for experiments. This dataset contains two types of heterogeneous graph datasets: movies and related filmmakers, such as actors and directors. This dataset contains 3416 movie nodes and 5107 filmmaker nodes. A movie can belong to multiple genres, therefore the "genre" attribute of a movie is multi-labeled. The "genre" attribute of a filmmaker is determined by the movies they have participated in, and is also multi-labeled. This invention defines the features of movie nodes as "the tags users give to movies on the movie details page of Douban Movies," and the features of filmmaker nodes as the set of features of the movies they have participated in.

[0016] 1.2 Running the Heterogeneous Graph Embedding Algorithm. Theoretically, this invention supports all types of network embedding algorithms. To better adapt to multi-label classification tasks in heterogeneous networks, this invention uses RANCH (Representation learning model using AttentionNetwork and CNN for HINs), a representation learning model for heterogeneous networks and convolutional neural networks, as the heterogeneous graph embedding algorithm to generate multi-label embedding results.

[0017] Furthermore, step 2 specifically includes: To address the problem of overlapping embedding results in large-scale heterogeneous networks, this invention uses hierarchical embedding technology for multi-level dimensionality reduction to overcome visual confusion caused by large-scale data. This invention uses HUMAP (Hierarchical Uniform Manifold Approximation and Projection), a hierarchical embedding technology that performs well in terms of runtime, preservation of mind maps, and maintenance of global and local relationships.

[0018] HUMAP consists of two main parts: hierarchy construction and projection. In the hierarchy construction part, the locality of each edge is determined by creating a k-nearest neighbor graph, and then the most visited node in the k-nearest neighbor graph is identified as a landmark. Based on the similarity between landmarks, a tree-like hierarchy can be built from bottom to top. In the projection part, HUMAP embeds the hierarchy into a user-defined data space.

[0019] This invention utilizes HUMAP to transform high-dimensional embedding results into a three-level two-dimensional embedding representation. In the three-level structure of this invention, the data volume of each level is 1 / 5 of that of the level below it. Through this hierarchical structure, this invention achieves a transition from overview to detail, which helps users better observe and interact with the reduced-dimensional embedding.

[0020] Furthermore, step 3 specifically includes the construction of the set space. This invention uses a set model to solve the multi-label problem and enhances the layout of the scatter plot on the multi-label attributes. Therefore, in step 3, the set space is constructed first to prepare for steps 4 and 5.

[0021] This invention employs three basic set elements—sets, elements, and the intersection of sets—to construct a set model for multi-label embedding visualization. First, each sample in the dataset is defined as an element. Second, each label of the multi-label attribute is segmented, with each label forming a set; elements with the same label belong to the same set. Therefore, the intersection of multiple sets represents the multi-label attribute. Taking a movie dataset as an example, each movie has a multi-label attribute named "genre." By collecting and segmenting all types appearing in the dataset, 31 independent labels are obtained, corresponding to 31 sets, such as "comedy," "romance," and "action." Taking a movie with the genre "romance, comedy" as an example, since this movie belongs to both the "romance" and "comedy" sets, it belongs to the intersection of the "romance" and "comedy" sets.

[0022] Furthermore, step 4 specifically includes:

[0023] Traditional scatter plots suffer from limitations such as overlap, approximation, and misinterpretation when applied to large-scale, multi-label, and complex scenarios. This invention enhances traditional scatter plots through two set-based layout enhancement methods. These methods not only establish relationships between sets and embeddings but also improve the overall structure and outlier identification in scatter plots through set enhancement.

[0024] Specifically, this invention proposes two methods for different enhancement tasks. One is a statistical contour plotting method, which presents the density distribution of a scatter plot like contour lines in geography, facilitating the discovery of global structure. The other is a geometric non-convex hull plotting method, which enhances the scatter plot layout in a semi-transparent non-convex hull form by calculating Delaunay triangulation, helping to explore outliers. In addition, this invention also utilizes interactive means between views for direct enhancement as a supplementary enhancement method.

[0025] 4.1 Contour drawing method based on statistics.

[0026] Most existing embedding visualization methods do not fully consider the structural relationships within high-dimensional embeddings. However, in the case of multi-label high-dimensional embeddings discussed in this invention, there are often more important or richer structural relationships between multiple labels. Because multiple labels belong to the same attribute, they often exhibit a closer relationship. Unfortunately, these structural relationships between multi-label embeddings have received little attention. Therefore, this invention proposes a set-based contour layout enhancement method that incorporates hierarchical information to reveal and enhance the potential structural and relational patterns within and between multiple labels in high-dimensional data.

[0027] This invention uses the `contour` method from the visualization library `d3.js`, based on kernel density estimation, to calculate and draw contour lines. A kernel function is used to calculate the value per unit area based on point or polyline features to fit each point or polyline to a smooth conical surface. Furthermore, this invention optimizes the selection of embedding points. Considering that the purpose of using contour lines in this invention is to highlight the overall structural relationships of the set, more attention should be paid to the overall structure, and deviations caused by outliers should be minimized. Therefore, this invention applies landmark elements calculated using hierarchical embedding technology to kernel density estimation. Landmarks are the most visited nodes in the neighborhood, reflecting the connectivity of the area, and thus can be considered representative nodes of the neighborhood. This invention also considers the differences in set size, selecting the range of embedding points in different ways. For larger sets, this invention uses only landmark elements for contour line calculation, while for smaller sets (this invention considers sets without landmark elements as small sets), all elements in the set are used for contour line drawing.

[0028] 4.2 Geometry-based non-convex hull drawing method.

[0029] While contour plotting can provide a comprehensive enhancement of the overall structure, outliers are equally important for the analysis of embedding results. Therefore, this invention proposes a geometry-based non-convex hull plotting method to enhance the representation of outliers, enabling users to more effectively discover and analyze them.

[0030] This invention continues to use the set space construction method from step 3, dividing the multi-label attributes into different sets. Sets are constructed by dividing the attribute values ​​into intervals. Then, the attribute value for each element is determined based on the relationship between the element and the set: within each set, each sample is assigned a value of 1 or 0 depending on whether the element belongs to that set. Next, this invention uses Python's shapely library to draw Delaunay triangles for each node in each set, thus forming a non-convex hull, and outliers are highlighted by increasing the element radius. To handle sets of different sizes, this invention introduces an adjustable threshold to determine the standard for Delaunay triangulation. Increasing the threshold strengthens the connectivity of the regions, while decreasing the threshold forms more and smaller triangles.

[0031] With these two threshold-adjustable enhancement methods, users can flexibly explore embedding visualizations and discover regions in the embedding space that are more tightly or loosely connected. Furthermore, both of these enhanced visualizations are semi-transparent and can be overlaid on the original scatter plot to clearly and intuitively reveal the intersections and repulsions between sets.

[0032] Furthermore, step 5 specifically includes: proposing a novel set-based multi-label visualization method that solves the problems of traditional set visualization in visualizing set intersections and improving scalability.

[0033] 5.1 Set and color radial projection algorithms for visualizing set intersections.

[0034] The core task of set visualization is to visualize the intersection of sets. However, previous methods for visualizing intersections have limitations in terms of scalability and application scenarios. This invention aims to propose a new method for visualizing set intersections. On the one hand, it is necessary to design a reasonable visualization scheme for high-dimensional set spaces, allowing people to "see" the relationships between sets and their intersections. On the other hand, it is necessary to establish a logically intuitive visual channel for the embedded scatter plot in step 4, displaying the multi-label attribute categories of the embedded points, thereby enhancing the interpretability of the embedded space.

[0035] This invention develops a radial coordinate system for set space to obtain the projected position of each intersection, called SetRadviz. (See attached...) Figure 3As shown in (b), this invention divides the radial plane into several equal parts corresponding to each set. The position of each intersection is influenced by the set that produces the intersection. To visualize these influences, this invention places multiple springs at the intersection points to represent the influence from different sets. One end of each spring is fixed to the outer ring of the set it represents, with equal spacing between the endpoints of each set, and the other end is fixed to the intersection of the sets. When the forces are in equilibrium, the projected position of the intersection point is determined. SetRadviz not only solves the projection problem of multi-tag attributes but also preserves the relationship between the intersection of sets and their related sets, i.e., the relationship between sets.

[0036] Since color is the most efficient visual channel for encoding categorical values, this invention uses color to encode the multi-label attributes of nodes, i.e., the categories of set intersections. However, due to the large scale of set intersections (e.g., the Douban Movie dataset used in this invention contains thousands of set intersections), traditional categorical color encoding methods face significant scalability challenges. This invention converts the three-dimensional HSL color space into a two-dimensional radial color plane, called a Colormap, by fixing the brightness of the HSL color space. Both the Colormap and SetRadviz are two radial planes, and they both perform equidistant divisions based on sets, exhibiting good alignment. Therefore, this invention combines them, determining the position of each set intersection on the Colormap by the position of the set intersections on these radial coordinates, thereby determining its color mapping.

[0037] By combining Colormap and SetRadviz, this invention achieves a perfect combination of spatial location and color mapping, as shown in the attached figure. Figure 3 (d) shows the inside of the ColorSet. This design for visualizing sets is very effective because the two items naturally correspond to the design of the set space; they are closely integrated and mutually reinforcing. On one hand, the color mapping scheme of the set intersection is determined by the category of the set intersection and is related to the sets involved, consistent with the projection of the set intersection location. See attached... Figure 3 As shown in (d), the color assignment of the "Sports, Family, Action" multi-label nodes depends on the color assignment of the "Sports," "Family," and "Action" sets. On the other hand, the mapping result of the location projection uses color, the most intuitive visual element, to represent the category of the intersection of sets. This color coding is uniformly used in other views such as embedded scatter plots, making understanding more convenient and effective.

[0038] Using ColorSet, the intersection of sets is assigned a color and displayed in each view. To better assign colors to sets and their intersection, this invention further reorders all sets based on relevance before using ColorSet; sets with stronger positive correlations are placed closer together, thus assigning more similar colors. This reordering reduces visual burden and interprets structure more effectively and accurately. This invention uses a hierarchical clustering algorithm, gradually merging the most similar dimensions into a cluster until all dimensions are clustered together. The order of the dimensions at this point is the final sorting result, thus achieving the reordering of dimensions. This invention chooses the full connectivity method as the strategy for merging clusters and uses the optimal leaf order method to process the resulting sequence of reordered sets.

[0039] 5.2 Aggregation-based set visualization and optimization methods.

[0040] Traditional set visualization methods often suffer from poor scalability, especially at the element level. Therefore, this invention aggregates elements based on their degree within each set, significantly improving scalability by aggregating elements with similar characteristics. For a set S containing m sets... 1≤j≤m and n elements E = {e i The set space of 1 ≤ i ≤ n, with element e i The degree of an element represents the number of sets it belongs to, and the formula is as follows:

[0041] degree(e i )=|{S j :1≤j≤m∧e i ∈S j}| (1)

[0042] The degree of each set is used to calculate the degree distribution of that set: Degree(S) j )={d a ,d b ..., 1≤a≤b≤m}. Next, we classify and aggregate the elements according to their degree, and then group the sets S. j Divided into different intervals according to degree, totaling D. j =|Degree(S j )| each interval b jk Contains the set (S) j All degrees in the range are equal to that degree (d) i =k,e i ∈S j ) elements:

[0043] b jk ={e∈S j:degree(e)=k} (2)

[0044] Finally, the set space is visualized. (See attached image) Figure 3 (c) In this invention, the outer ring of the ColorSet is divided equally according to the number of sets, with each block representing one set. Since the sizes of the sets can vary significantly, this invention uses color opacity to encode the set sizes for better alignment and comparison. Then, in each set block, this invention uses several radial bars to draw the degree-based aggregation interval for each set, as shown in the appendix. Figure 3 (c) As shown in the middle, the width of the bar represents the size of the interval, i.e., the number of elements contained. Since the degree distribution of each set can vary greatly, for better alignment and comparison, this invention first calculates the maximum and minimum degrees of all sets as the interval range for drawing the degree histogram, thereby achieving horizontal alignment of degrees. That is, each radial bar in the outer ring of the ColorSet represents a set of elements with the same degree. This invention follows Gestalt design principles, encoding the bars from minimum to maximum degree from the outside in, corresponding to the transition from set independence to sharing, indicating that the intersection of this set with other sets tends to be less or more.

[0045] This invention also optimizes the radial bar chart of ColorSet for issues related to the poor performance of the set's degree distribution when it is diverse or unbalanced. In cases of diverse degree distributions, since adjacent degree distributions often exhibit similarities, this invention optimizes the degree intervals by merging adjacent degree intervals, effectively mitigating the scalability problem without introducing new errors.

[0046] For cases of unbalanced set sizes, this invention combines an adjustable scaling ratio with stacked bar charts of varying colors from light to dark. This allows users to freely adjust the scaling ratio, while portions exceeding the current scaling ratio are transformed into a new, darker bar chart overlaid on the original bar chart area. In this case, for the intersection of sets within a ColorSet, this invention uses an exponential scale instead of the original linear scale to map the size of the set intersection, reducing the visual impact of significant differences in set sizes.

[0047] This invention primarily addresses the following three issues: 1. It realizes a complete workflow combining embedding visualization and set visualization, achieving interpretability of high-dimensional multi-label embedding; 2. It proposes a set-based method to solve complex multi-label problems, constructing a correlation-based radial projection and color mapping for the set space; 3. It proposes a hierarchical DR technique and various set-based layout enhancement strategies to improve the scalability and interpretability of embedding visualization; 4. It conducts user experiments and case studies on two real-world datasets to demonstrate the effectiveness of the visualization system incorporating the above design.

[0048] The advantages of this invention can be summarized as follows: (1) It is easy to use, the effect is intuitive and effective, and the expressive power is strong. This invention realizes the visual analysis of high-dimensional multi-label network embedding results based on sets through a front-end and back-end connected system, giving users an intuitive visual display and supporting rich interactive operations. (2) It is highly innovative. At present, there is no general method for visualization of multi-label data. This invention proposes a set-based method to solve complex multi-label problems, and constructs radial projection and color mapping based on correlation for the set space. At present, there is also no visualization for multi-label embedding results. This invention proposes a complete workflow for high-dimensional embedding results containing multi-label attributes. By introducing the set space, it realizes the combination of embedding visualization and set visualization, realizes the connection between low-dimensional embedding position and high-dimensional multi-label attributes, and realizes the interpretability of high-dimensional multi-label embedding. (3) Practical significance. This invention uses two real-world datasets for verification and case analysis, which proves the effectiveness and feasibility of this invention. Attached Figure Description

[0049] Figure 1 This is the overall flowchart of the method of the present invention.

[0050] Figure 2 (a)- Figure 2 (d) is a diagram of the actual system interface of the method of the present invention, wherein Figure 2 (a) is the control panel and information list of the visualization system. Figure 2 (b) is the embedded scatter plot. Figure 2 (c) is a collection view with multiple labels. Figure 2 (d) is the view of node connection relationships.

[0051] Figure 3 (a)- Figure 2 (d) is a schematic diagram of step 5 of the method of the present invention, wherein Figure 3 (a) is the color mapping method (Colormap). Figure 3 (b) is the position projection method for the intersection of sets (SetRadviz). Figure 3 (c) is an aggregation-based method for visualizing collections. Figure 3 (d) combined Figure 3 (a) Figure 3 (b) Figure 3 (c) is a set-based multi-label visualization method (ColorSet).

[0052] Figure 4 (a)- Figure 4 (b) is a schematic diagram of step 4 of the method of the present invention, wherein Figure 4 (a) is a contour drawing method based on statistics. Figure 4 (b) is a geometry-based non-convex hull drawing method. Detailed Implementation

[0053] Example 1

[0054] This invention can be applied to graph networks of different sizes. This embodiment uses the Douban movie dataset as an example. The following, with reference to the accompanying drawings, further illustrates a movie recommendation method based on high-dimensional multi-label network embedding result visualization and enhancement.

[0055] Referring to the overall flowchart of the technical solution, this invention comprises six stages: heterogeneous graph embedding algorithm, hierarchical dimensionality reduction algorithm, construction of set space, set-based scatter plot layout enhancement method, set-based multi-label visualization method, and specific application scenarios of the visualization system.

[0056] Step 1: Heterogeneous graph embedding algorithm; clean and preprocess the data of self-built or publicly available heterogeneous multi-label graph datasets, run a multi-label classification model suitable for heterogeneous graph data, and obtain high-dimensional heterogeneous network embedding results;

[0057] 1.1 Preparation of a self-built or publicly available heterogeneous multi-label graph dataset. This invention crawled a heterogeneous graph dataset containing nodes of two types: movies and filmmakers. The filmmaker type refers to the filmmakers associated with a movie, such as actors and directors. This dataset contains 3416 movie nodes and 5107 filmmaker nodes. A movie can belong to multiple types, therefore the "type" attribute of a movie is multi-labeled. The "type" attribute of a filmmaker is determined by the movies they have participated in, and is also multi-labeled. This invention defines the feature of a movie node as "the tags users have given to the movie on the movie details page of Douban Movie," and the feature of a filmmaker node as the set of features of the movies they have participated in. The Douban Movie dataset used in this invention contains a total of 2836 multi-label cases.

[0058] Similar methods are used on other datasets, such as the publicly available citation dataset DBLP. This invention uses the DBLP dataset from the Aminer website, extracting 16 conferences as venue nodes and dividing them into four domains: databases, data mining, machine learning, and information retrieval. Then, this invention extracts 1600 papers from these 16 conferences as paper nodes and their corresponding 4420 authors as author nodes. This invention defines the features of a paper as its set of keywords, and the features of an author as the set of keywords from all their papers; the label of a paper is determined by the domain in which it was submitted, and the label of an author is determined by the labels of their papers. Therefore, an author may have multiple labels, meaning that the author has published papers in multiple domains. The DBLP dataset used in this invention contains a total of 14 types of multi-label cases.

[0059] During the development of this invention, two datasets of similar size but different complexity were used for testing. The more complex Douban movie dataset will be used to illustrate the specific implementation method described below.

[0060] 1.2 Running the Heterogeneous Graph Embedding Algorithm. This invention supports all types of network embedding algorithms. To better adapt to multi-label classification tasks in heterogeneous networks, this invention uses the RANCH network embedding algorithm, a representation learning model combining attention networks and convolutional neural networks for heterogeneous networks, as the heterogeneous graph embedding algorithm to generate multi-label embedding results. This invention runs the RANCH network embedding algorithm on the Douban Movie dataset after data cleaning and processing, obtaining high-dimensional embeddings of 8523 heterogeneous nodes, i.e., 64-dimensional vector representations.

[0061] For the RANCH model parameter settings, this invention sets the embedding vector dimension to 128. For the first part of the RANCH, this invention sets the learning rate to 0.005, the regularization parameter to 0.001, the number of heads for multi-head attention to 16, and the dropout probability to 0.6. For the second part of the RANCH, in the step of generating node sequences through random walks, this invention performs 5 random walks of length 10 on each type of edge at each node, with a return probability set to 0.3. This invention sets the learning rate for this part to 0.001, the dropout probability to 0.2, and the convolution kernel sizes to 3, 4, and 5, respectively, with 10 convolution kernels for each size. For the optimization steps in both parts, this invention uses the Adam algorithm for optimization. This invention uses 80% of the data for training and 20% of the data for testing.

[0062] Step 2: Hierarchical dimensionality reduction algorithm; The high-dimensional heterogeneous network embedding results are used with the hierarchical dimensionality reduction technique HUMAP to obtain hierarchical two-dimensional embedding results;

[0063] HUMAP consists of two main parts: hierarchy construction and projection. In the hierarchy construction part, the locality of each edge is determined by creating a k-nearest neighbor graph, and then the most visited node in the k-nearest neighbor graph is identified as a landmark. Based on the similarity between landmarks, a tree-like hierarchy can be built from bottom to top. In the projection part, HUMAP embeds the hierarchy into a user-defined data space.

[0064] This invention utilizes HUMAP to transform the 64-dimensional high-dimensional embedding results of the Douban Movie dataset into a three-level two-dimensional embedding representation. In the three-level structure of this invention, the bottom layer contains all data points, and the amount of data in each upper layer is 1 / 5 of that in the layer below it. Through this hierarchical structure, this invention achieves a transition from overview to detail, which helps users better observe and interact with the reduced-dimensional embedding.

[0065] Step 3: Constructing the collection space;

[0066] The feature model data obtained based on the above steps are mapped to different visualization views, as shown in the following steps:

[0067] This invention employs three basic set elements—sets, elements, and the intersection of sets—to construct a set model for multi-label embedding visualization. First, each sample in the dataset is defined as an element. Second, each label of the multi-label attribute is segmented, with each label forming a set; elements with the same label belong to the same set. Therefore, the intersection of multiple sets represents the multi-label attribute. Taking the Douban movie dataset as an example, each movie has a multi-label attribute named "genre." By collecting and segmenting all types appearing in the dataset, 31 independent labels are obtained, corresponding to 31 sets, such as "comedy," "romance," and "action." Taking a movie with the genre "romance, comedy" as an example, since this movie belongs to both the "romance" and "comedy" sets, it belongs to the intersection of the "romance" and "comedy" sets.

[0068] Step 4: Set-based scatter plot layout enhancement method; visualize the 2D embedding results using a scatter plot, and implement density-based and geometry-based layout enhancement methods on this basis, supporting user interaction, as shown in the appendix. Figure 4 As shown;

[0069] 4.1 A Statistically Based Contour Line Drawing Method. This invention proposes a set-based contour layout enhancement method, the effect of which is shown in the attached figure. Figure 4As shown in (a), this method combines hierarchical information to reveal and enhance the potential structure and relationship patterns within and between multiple labels in high-dimensional data. This invention uses the `contour` method from the visualization library `d3.js`, based on kernel density estimation, to calculate and draw contour lines. Furthermore, this invention optimizes the selection of embedding points. Considering that the purpose of using contour lines in this invention is to highlight the overall structural relationships of the set, more attention should be paid to the overall structure, and the bias caused by outliers should be minimized. Therefore, this invention applies the landmark elements calculated by hierarchical embedding technology to kernel density estimation. Landmarks are the most visited nodes in the neighborhood, reflecting the connectivity of the area, and thus can be regarded as representative nodes of the neighborhood. This invention also considers the differences in set size, selecting the range of embedding points in different ways. For larger sets, this invention only uses landmark elements for contour line calculation, while for smaller sets (this invention considers sets without landmark elements as small sets), all elements in the set are used for contour line drawing.

[0070] 4.2 Geometry-Based Non-Convex Hull Drawing Method. This invention proposes a geometry-based non-convex hull drawing method to enhance the representation of outliers, enabling users to more effectively discover and analyze outliers. The results are shown in the attached figure. Figure 4 As shown in (b), this invention continues to use the set space construction method of step 3, dividing the multi-label attribute into different sets. Sets are constructed by dividing the attribute values ​​into intervals. Then, the attribute value of each element on that attribute is determined according to the relationship between the element and the set: in each set, each sample is assigned a value of 1 or 0 depending on whether the element belongs to that set. Next, this invention uses Python's shapely library to draw Delaunay triangles for each node in the set, thus forming a non-convex hull, and outliers are highlighted by increasing the element radius. To handle sets of different sizes, this invention introduces an adjustable threshold to determine the standard for Delaunay triangulation. Increasing the threshold makes the connectivity of the regions stronger, while decreasing the threshold forms more and smaller triangles.

[0071] Using these two threshold-adjustable enhancement methods, users can flexibly explore embedding visualizations, discovering denser or sparser regions within the embedding space. Furthermore, both of these enhanced visualizations are semi-transparent and can be overlaid on the original scatter plot, clearly and intuitively revealing the intersections and repulsion relationships between sets. (See attached image.) Figure 4 As shown, Figure 4 (a) Three highly correlated sets, namely “history”, “war” and “biography”, were selected and enhanced with contour lines. The outlines of the three sets are within the same range, indicating that the distribution of these three sets in the embedding space is also highly similar. Figure 4(b) Two sets with low correlation, “Romantic” and “Action”, were selected and enhanced using a geometric non-convex hull. After adjusting the threshold, it was found that the densely distributed embedding space regions of the two sets showed strong separation, revealing the separation of the two sets in the embedding distribution.

[0072] Step 5: Multi-label visualization method based on sets; visualize the set information extracted in Step 3, use novel and reasonable visualization design to display the rich information of sets and intersections, and implement interactive means to connect sets, intersections and embedded result scatter plots;

[0073] 5.1 Set and color radial projection algorithms for visualizing set intersections.

[0074] This invention develops a radial coordinate system for set space to obtain the projected position of each intersection, called SetRadviz. (See attached...) Figure 3 As shown in (b), this invention divides the radial plane into several equal parts corresponding to each set, which in the Douban movie dataset corresponds to various movie genres. This invention places multiple springs at the intersection points to represent the influence from different sets. One end of each spring is fixed to the outer ring of the set it represents, with equal spacing between the endpoints of each set, and the other end is fixed to the intersection of the sets. When the forces are in equilibrium, the projected position of the intersection point is determined. Figure 3 Taking the intersection of "Motion, Family, Action" in (d) as an example, this intersection is the intersection of the three sets "Motion," "Family," and "Action." It is subject to forces from these three sets and reaches equilibrium near the center point; therefore, this position is used as the projection location of the intersection. This invention not only solves the projection problem of multiple tag attributes but also preserves the relationship between the intersection of sets and their related sets, that is, the relationship between sets. Figure 3 (d) indicates this relationship by connecting the intersection with the line.

[0075] Since color is the most efficient visual channel for encoding classification values, this invention uses color to encode the multi-label attributes of nodes, i.e., the category of the intersection of sets. However, due to the large scale of the set intersections, traditional category color encoding methods face significant scalability challenges. This invention converts the three-dimensional HSL color space into a two-dimensional radial color plane, called a Colormap, by fixing the brightness of the HSL color space. Both the Colormap and SetRadviz are two radial planes, and they are both equally spaced based on sets, exhibiting good alignment. Therefore, this invention combines them, determining the position of each set intersection on the Colormap by the position of the set intersection on these radial coordinates, thereby determining its color mapping. Figure 3 As shown, Figure 3(b) The projection position of the intersection obtained by SetRadviz projection on the radial coordinate, combined with... Figure 3 In (a), the position of the intersection of the color wheel planes on the Colormap is the color map of the intersection.

[0076] By combining Colormap and SetRadviz, this invention achieves a perfect combination of spatial location and color mapping, as shown in the attached figure. Figure 3 (d) shows the inside of the ColorSet. Using the ColorSet, the intersection of sets is assigned a color and displayed in each view. To better assign colors to sets and their intersection, this invention further reorders all sets according to their relevance before using the ColorSet; sets with stronger positive correlations should be placed closer together, thus assigning more similar colors. This reordering reduces visual burden and interprets the structure more effectively and accurately. This invention uses a hierarchical clustering algorithm, gradually merging the most similar dimensions into a cluster until all dimensions are clustered together. The order of the dimensions at this point is the final sorting result, thus achieving the reordering of dimensions. This invention chooses the full connectivity method as the strategy for merging clusters and uses the optimal leaf order method to process the resulting sequence of reordered sets.

[0077] 5.2 Aggregation-based set visualization and optimization methods.

[0078] This invention aggregates elements based on their degree within each set, significantly improving scalability by aggregating elements with similar characteristics. For a set S containing m sets... 1≤j≤m and n elements E = {e i The set space of 1 ≤ i ≤ n, with element e i The degree represents the number of sets to which the element belongs. This invention calculates the degree of each set as its degree distribution. For example, the Douban Movie dataset contains seven degree distributions ranging from 1 to 7. Next, the elements are categorized and aggregated according to their degree, and each set S... j Divided into different intervals according to different degrees, each interval b jk Contains the set (S) j All degrees in the range are equal to that degree (d) i =k,e i ∈S j () elements.

[0079] Finally, the set space is visualized. (See attached image) Figure 3(c) In this invention, the outer ring of the ColorSet is divided equally according to the number of sets, with each block representing one set. Since the sizes of the sets can vary significantly, this invention uses color opacity to encode the set sizes for better alignment and comparison. Then, in each set block, this invention uses several radial bars to draw the degree-based aggregation interval for each set, as shown in the appendix. Figure 3 (c) As shown in the middle, the width of the bar represents the size of the interval, i.e., the number of elements contained. Since the degree distribution of each set can vary greatly, for better alignment and comparison, this invention first calculates the maximum and minimum degrees of all sets as the interval range for drawing the degree histogram, thereby achieving horizontal alignment of degrees. That is, each radial bar in the outer ring of the ColorSet represents a set of elements with the same degree. This invention follows Gestalt design principles, encoding the bars from minimum to maximum degree from the outside in, corresponding to the transition from set independence to sharing, indicating that the intersection of this set with other sets tends to be less or more.

[0080] This invention also optimizes the radial bar chart of ColorSet for issues related to the poor performance of the set's degree distribution when it is diverse or unbalanced. In cases of diverse degree distributions, such as the Douban Movies actor dataset which contains up to 26 different degrees, adjacent degree distributions often exhibit similarities. This invention optimizes the degree intervals in such cases by merging adjacent degree intervals, effectively mitigating the scalability issue without introducing new errors.

[0081] For cases of unbalanced set sizes, this invention combines an adjustable scaling ratio with stacked bar charts of varying colors from light to dark. This allows users to freely adjust the scaling ratio, while portions exceeding the current scaling ratio are transformed into a new, darker bar chart overlaid on the original bar chart area. In this case, for the intersection of sets within a ColorSet, this invention uses an exponential scale instead of the original linear scale to map the size of the set intersection, reducing the visual impact of significant differences in set sizes.

[0082] Step 6: Achieve better movie recommendations based on a visual analytics system. A web-based visualization system will intuitively display the learning results of the heterogeneous graph embedding model, supporting user interaction, providing insights for model optimization, improving model performance, and applying it to the movie recommendation system.

[0083] As attached Figure 2As shown, the visualization system in this embodiment supports adjustments to various embedding algorithms and selection of datasets. It uses interactive scatter plots to display embedding results at different levels, supports selection, detailed viewing, and comparative analysis of data at different granularities, supports the display and interaction of multi-label information, and supports two adjustable parameter-based multi-label scatter plot enhancement algorithms. Through the visualization system in this embodiment, one can not only intuitively understand the model's learning results but also gain insights into model optimization through analysis.

[0084] Taking the Douban movie dataset as an example, this embodiment can enhance the selection and embedding of multi-label information through scatter plots, compare the embedding distribution of different relevance labels, and analyze the distribution characteristics of the multi-label attribute "type" in terms of relevance. It discovers the internal correlations between the original 31 multi-labels for "type," thus providing insights and inspiration for feature construction during model initialization. For example, multi-label attributes can be decomposed into smaller sub-attributes according to their positive and negative correlation, reducing redundancy within multi-label attributes and improving the performance of the network embedding algorithm in downstream multi-label classification tasks.

[0085] The node representation obtained by the optimized network embedding algorithm is in vector form, which has high versatility and can be well applied to downstream tasks such as recommendation systems, node classification, and link prediction. For example, this embodiment can be applied to a movie recommendation system to recommend more accurate and reasonable movies to users based on more accurate multi-label attribute information.

[0086] The embodiments described in this specification are merely examples of implementations of the inventive concept. The scope of protection of this invention should not be considered as limited to the specific forms stated in the embodiments. The scope of protection of this invention also extends to equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

Claims

1. A method for visualizing and enhancing the embedding results of high-dimensional multi-label networks based on sets, comprising the following steps: Step 1: Clean and preprocess the data of the self-built or publicly available heterogeneous multi-label graph dataset, run the multi-label classification model suitable for heterogeneous graph data, and obtain high-dimensional heterogeneous network embedding results; Step 2: Use hierarchical dimensionality reduction techniques to embed the high-dimensional heterogeneous network results into hierarchical two-dimensional embedding results; Step 3: Extract multi-label attributes from the data, construct a set-element-intersection relationship model, perform data statistics on the set and intersection, and link the statistical data with the embedding results; Step 4: Visualize the 2D embedding results using a scatter plot, and then implement density-based and geometry-based layout enhancement methods to support user interaction. Step 5: Visualize the set information extracted in Step 3. Use novel and reasonable visualization design to display the rich information of sets and intersections, and implement interactive means to connect sets, intersections and embedded result scatter plots.

2. The method for visualizing and enhancing the embedding results of high-dimensional multi-label networks based on sets as described in claim 1, characterized in that, Step 1 specifically includes: 1.1 Prepare a self-built or publicly available heterogeneous multi-label graph dataset; use the DBLP public literature citation dataset from the Aminer website, extract conferences as venue nodes, and divide them into 4 domains: database, data mining, machine learning, and information retrieval; then extract papers from these conferences as paper nodes and their corresponding authors as author nodes; define the features of a paper as its set of keywords, and define the features of an author as the set of keywords from all their papers; the label of a paper is determined by the domain in which it was submitted, and the label of an author is determined by the labels of their papers; In addition, we crawled movie and filmmaker data from Douban Movies and extracted some data to create a self-built dataset for experiments; the dataset contains two types of heterogeneous graph datasets with two nodes: movies and related filmmakers. 1.2 Running the Heterogeneous Graph Embedding Algorithm; To adapt to multi-label classification tasks in heterogeneous networks, the RANCH model, which combines attention networks and convolutional neural networks for heterogeneous networks, is used as the heterogeneous graph embedding algorithm to generate multi-label embedding results.

3. The method for visualizing and enhancing the embedding results of high-dimensional multi-label networks based on sets as described in claim 1, characterized in that, Step 2 specifically includes: to solve the problem of overlapping embedding results in large-scale heterogeneous networks, hierarchical embedding technology is used to perform multi-level dimensionality reduction to overcome the visual confusion caused by large-scale data; the hierarchical embedding technology HUMAP is used. HUMAP includes hierarchical structure construction and projection. In the hierarchical structure construction part, the locality of each edge is determined by creating a k-nearest neighbor graph, and then the node with the most visits in the k-nearest neighbor graph is identified as a landmark. Based on the similarity between landmarks, a tree-like hierarchical structure can be built from bottom to top. In the projection part, HUMAP embeds the hierarchical structure into a user-defined data space. HUMAP is used to transform high-dimensional embedding results into a three-level two-dimensional embedding representation; in the three-level structure, the amount of data in each level is 1 / 5 of that in the next level; through the hierarchical structure, a transition from overview to detail is achieved, which helps users observe and interact with the dimensionality-reduced embedding.

4. The method for visualizing and enhancing the embedding results of high-dimensional multi-label networks based on sets as described in claim 1, characterized in that, Step 3 specifically includes: constructing a set space; using a set model to solve the multi-label problem and enhancing the layout of the scatter plot on the multi-label attributes, therefore, the set space is constructed first to prepare for subsequent steps; We use three basic set elements—set, element, and set intersection—to construct a set model for multi-label embedding visualization. First, each sample in the dataset is defined as an element. Second, each label of the multi-label attribute is segmented, and each label constitutes a set, meaning that elements with the same label belong to the same set. Therefore, the intersection of multiple sets represents the attributes of the multi-label. By collecting all types that appear in the dataset and segmenting them, we can obtain independent labels corresponding to different sets.

5. The method for visualizing and enhancing the embedding results of high-dimensional multi-label networks based on sets as described in claim 1, characterized in that, Step 4 specifically includes: Because traditional scatter plots have limitations such as overlap, approximation, and misreading when applied to large-scale, multi-label complex scenarios, two set-based layout enhancement methods are used to enhance traditional scatter plots; the relationship between sets and embeddings is established to enhance the overall structure of multi-label embeddings and the identification of outliers in scatter plots. Specifically, two methods are proposed for different enhancement tasks: one is a statistical contour plotting method, which presents the density distribution of scatter plots like "contour lines" in geography, making it easier to discover global structures; the other is a geometric non-convex hull plotting method, which enhances the layout of scatter plots in the form of a semi-transparent non-convex hull by calculating Delaunay triangulation, helping to explore outliers; in addition, direct enhancement is also performed using interactive means between views as a supplementary enhancement method. 4.1 Statistically based contour drawing method; A set-based contour layout enhancement method is proposed, which combines hierarchical information to reveal and enhance the potential structure and relationship patterns within and between multiple labels in high-dimensional data. Using the `contour` method from the visualization library `d3.js`, contour lines are calculated and drawn based on kernel density estimation. A kernel function is used to calculate the magnitude per unit area based on point or polyline features to fit each point or polyline to a smooth conical surface. The selection of embedding points has been optimized. Landmark elements calculated using hierarchical embedding techniques are applied to kernel density estimation. Landmarks are the most visited nodes in a neighborhood, reflecting the connectivity of that neighborhood, and therefore can be considered representative nodes of that neighborhood. The differences in set size are also considered, with different embedding point ranges selected. For sets containing landmark elements, only the landmark elements are used for contour line calculation, while for sets without landmark elements, all elements in the set are used for contour line drawing. 4.2 Geometry-based Non-convex Hull Drawing Method; A geometry-based non-convex hull rendering method is proposed to enhance the representation of outliers, enabling users to discover and analyze outliers; Continuing with the set space construction method from step 3, the multi-label attribute is divided into different sets. Sets are constructed by dividing the attribute values ​​into intervals. Then, the attribute value of each element on that attribute is determined based on the relationship between the element and the set: in each set, each sample is assigned a value of 1 or 0 depending on whether the element belongs to that set; next, Delaunay triangles are drawn for each node in each set using Python's shapely library, thus forming a non-convex hull, and outliers are highlighted by increasing the element radius; to handle sets of different sizes, an adjustable threshold is introduced to determine the standard for Delaunay triangulation. Increasing the threshold enhances the connectivity of the regions, while decreasing the threshold results in more triangles being formed; With the two threshold-adjustable enhancement methods mentioned above, users can flexibly explore embedding visualizations and discover densely or sparsely connected regions in the embedding space. Furthermore, both of these enhanced visualizations are semi-transparent and can be overlaid on the original scatter plot to clearly and intuitively reveal the intersection and repulsion relationships between sets.

6. The method for visualizing and enhancing the embedding results of high-dimensional multi-label networks based on sets as described in claim 1, characterized in that, Step 5 specifically includes: 5.1 Set and Color Radial Projection Algorithms for Visualizing Set Intersections; The core task of set visualization is to visualize the intersection of sets; however, previous work on intersection visualization has limitations in terms of scalability and application scenarios. This paper aims to propose a new method for visualizing set intersections. On the one hand, it is necessary to design a reasonable visualization scheme for high-dimensional set spaces so that people can "see" the relationships between sets and their intersections; on the other hand, it is necessary to establish a logically intuitive visual channel for the embedded scatter plot in step 4, displaying the multi-label attribute categories of the embedded points, thereby enhancing the interpretability of the embedded space. A radial coordinate system, SetRadviz, was developed for the set space to obtain the projected position of each intersection. The radial plane is divided into several equal parts corresponding to each set. The position of each intersection is influenced by the set that produced the intersection. To visualize these influences, multiple springs are placed at the intersection to represent the effects from different sets. One end of each spring is fixed to the outer ring of the set it represents, with equal spacing between the endpoints of each set, and the other end is fixed to the intersection of the sets. When the forces are in equilibrium, the projected position of the intersection is determined. SetRadviz not only solves the projection problem of multi-tag attributes but also preserves the relationship between the intersection of sets and their related sets, i.e., the relationship between sets. Since color is the most efficient visual channel for encoding categorical values, it is used to encode the multi-label attributes of nodes, i.e., the category of the intersection of sets. By fixing the brightness of the HSL color space, the three-dimensional HSL color space is converted into a two-dimensional radial color plane, Colormap. Colormap and SetRadviz are both two radial planes, and they are both equally spaced based on sets, exhibiting good alignment. Therefore, they are combined, and the position of each set intersection on the Colormap is determined by the position of the set intersection on these radial coordinates, thereby determining its color mapping. By combining Colormap and SetRadviz, a combination of spatial location and color mapping of sets is achieved. On the one hand, the color mapping scheme of the set intersection is determined by the category of the set intersection and is related to the sets involved, and is consistent with the projection of the set intersection location. On the other hand, the mapping result of the location projection uses color, the most intuitive visual element, to represent the category of the set intersection. This color encoding is uniformly used in embedding scatter plots and other views for easy and effective understanding. Using ColorSet, the intersection of sets is assigned a color and displayed in each view. Before using ColorSet, all sets are further reordered dimensionally based on relevance; sets with strong positive correlations should be placed closer together to assign similar colors. This reordering reduces visual burden and interprets the structure. Hierarchical clustering is used to gradually merge the most similar dimensions into a cluster until all dimensions are clustered together. The order of the dimensions at this point is the final sorting result, thus achieving dimensional reordering. Full connectivity is chosen as the strategy for merging clusters, and optimal leaf ordering is used to process the resulting sequence of reordered sets. 5.2 Aggregation-based set visualization and optimization; Elements are aggregated based on their degree within each set. By aggregating elements with similar characteristics, scalability is significantly improved. For a set containing m sets... and n elements The set space, elements The degree of an element represents the number of sets it belongs to, and the formula is as follows: （1） The degree of each element in a set is used to determine the degree distribution of that set. Next, the elements are categorized and aggregated according to their degree, and the sets are grouped together. Divided into different intervals according to different degrees, a total of Each interval Includes this set ( All degrees in the range are equal to that degree. , ) elements: （2） Finally, the set space is visualized. The outer ring of the ColorSet is divided equally according to the number of sets, with each block representing a set. Since the sets vary greatly in size, color opacity is used to encode the set size for alignment and comparison. Then, several radial bars are used in each set block to draw the aggregation interval of each set based on degree. The width of the bar represents the size of the interval, i.e., the number of elements contained. Since the degree distribution of each set varies greatly, the maximum and minimum degrees of all sets are first calculated as the range for drawing the degree histogram, thus achieving horizontal alignment of degrees. That is, each radial bar in the outer ring of the ColorSet represents a set of elements with the same degree. Following Gestalt design principles, the bars from the minimum to the maximum degree are encoded from the outside in, corresponding to the transition from set independence to sharing, indicating that the intersection of this set with other sets tends to be less or more. Optimizations were made to address the poor performance of the radial bar chart in ColorSet when the degree distribution of the sets is diverse and unbalanced. In cases of diverse degree distribution, since adjacent degree distributions often have similarities, the degree intervals were optimized by merging adjacent intervals, alleviating scalability issues without introducing new errors. For cases of unbalanced degree distribution, an adjustable scaling ratio and stacked bars of varying colors from light to dark were used. This allows users to freely adjust the scaling ratio, and portions exceeding the current scaling ratio are converted into a new dark bar chart overlaid on the original bar chart area. In this case, for the intersection of sets within a ColorSet, an exponential scale was used instead of the original linear scale to map the size of the intersection, reducing the visual impact of significant differences in set sizes.

Images