Human activity intensity prediction method based on generalized spatial heterogeneity learning

Abstract

The invention provides a human activity intensity prediction method based on generalized spatial heterogeneity learning. The human activity intensity prediction method comprises node-to-node propagation learning, node-to-partition propagation learning, a graph learning module guided by mobility, and combination of a mobility model for spatial interaction modeling and graph information propagation. Introducing a radiation model to calculate a movement probability matrix between nodes, and capturing a random process of a local mobility decision; the migration volume of inflow and outflow is introduced to optimize fitting of motion possibilities; the problem of local heterogeneity is solved from the perspective of mobility cost; using a spectrum attention module to dynamically group nodes based on node attributes, and performing adaptive adjustment according to a time evolution mode; establishing dynamic interaction between nodes and partitions by using linearized transformer attention, and taking spatial partition features as additional channel parameters; according to the method, the prediction precision is improved, the real human movement rule can be more effectively captured and simulated, and the prediction result is more practical and reliable.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of human activity intensity prediction and machine learning, and particularly to a human activity intensity prediction method based on generalized spatial heterogeneity learning. BACKGROUND

[0002] Accurate prediction of the future human activity intensity in a specific area of a city, i.e., prediction of the crowd gathering scale and activity level at a certain location at a certain time point, has vital practical significance and application value for modern city management, business decision-making and public services.

[0003] For example, in terms of business operation, retailers or catering enterprises can optimize new store location selection, dynamically adjust inventory and personnel scheduling according to activity intensity prediction; shared travel service providers (such as shared bicycles and online taxis) can achieve precise deployment and scheduling of vehicles to cope with upcoming demand peaks and maximize resource utilization efficiency. In city planning and traffic management, activity intensity prediction is a key data basis for optimizing public transportation routes and dynamically adjusting traffic signal timing.

[0004] Because this task has broad application prospects and great social and economic value, academia and industry have invested a lot of research. In recent years, with the progress of deep learning technology, spatio-temporal graph neural networks (ST-GNN) have gradually replaced traditional statistical methods and machine learning methods and become the mainstream method for spatio-temporal prediction tasks. These methods combine graph neural networks with time series analysis models to effectively capture the potential spatio-temporal correlations in the data, thereby improving performance and efficiency.

[0005] Early ST-GNN methods tend to simulate static spatio-temporal dependencies, in which spatial relationship weights (such as spatial distance) or temporal learning weights (such as learned convolution kernels) remain fixed. As researchers pursue improvements in performance and efficiency, they attempt to optimize spatio-temporal feature modeling based on features such as dynamic spatio-temporal evolution and spatio-temporal scale effects, achieving dynamic optimization, embedding improvement, adaptive learning, multi-granularity learning and neural architecture search.

[0006] Although ST-GNN has been widely applied to human activity intensity prediction tasks due to its strong spatio-temporal dynamic modeling capability, there are still some challenges. The core challenge of this task is to capture complex spatial relationships, but this challenge is particularly severe due to the inherent characteristics of the data itself. Unlike comprehensive crowd flow data that contains crowd mobility, activity intensity data describes more precise and static behavior. This precision leads to more obvious spatial heterogeneity, even sparsity in remote areas, thereby posing significant difficulties for standard models. This gives rise to a class of problems - spatial heterogeneity problems.

[0007] In most ST-GNN research, the model usually learns a general mapping relationship for historical and future data. However, the existence of spatial heterogeneity phenomenon will make this mapping relationship invalid, resulting in poor performance in specific partitions. In addition to spatial heterogeneity, temporal heterogeneity and even synchronous spatio-temporal heterogeneity also exist, further increasing the difficulty of prediction.

[0008] To alleviate these phenomena, researchers try to use meta-learning, external variables, self-supervised learning, memory pool enhancement, and differentiated parameter learning methods to distinguish the mapping relationship between different nodes, ensuring that the model no longer relies on completely shared relationships. Despite this, the existing spatial heterogeneity modeling methods in human activity prediction tasks still face challenges, such as: spatial autocorrelation of errors near heterogeneous nodes.

[0009] Recently, researchers have proposed a generalized heterogeneity model that models spatial local heterogeneity and spatial hierarchical heterogeneity together for geostatistical analysis, thereby reducing the spatial autocorrelation of partition errors at partition boundaries. (The existing heterogeneity-aware spatio-temporal prediction framework is shown in Table 1).

[0010] Table 1 Existing heterogeneity-aware spatio-temporal prediction framework

[0011]

[0012] Among the existing modeling methods, most only consider one type of spatial heterogeneity phenomenon (mainly spatial local heterogeneity), lacking modeling of generalized spatial heterogeneity phenomena. This leads to the model being prone to redundant or over-smoothed estimates when learning spatial correlations, and severely lacking in physical world interpretability. There are also a small number of studies that consider movement patterns (e.g.: STDEN, ST-PEFs), but these methods require the use of additional high-precision data to predict low-precision data, which is high in data acquisition cost in practical applications, and is logically counterproductive. Even if researchers try to directly use classic movement mechanism models (such as gravity models, radiation models) to guide the network, these classic models are designed for low-dimensional data, and it is difficult to be directly modified to adapt to the high-dimensional tensor calculation of end-to-end in deep learning, leading to integration difficulties.

[0013] Two major challenges facing spatial heterogeneity modeling methods in human activity prediction tasks:

[0014] (1) For hierarchical spatial heterogeneity modeling, existing hierarchical heterogeneity division is mostly static and predefined. This static division cannot adapt to the dynamic change patterns of human activities, and inappropriate static partitions will introduce serious prediction bias at the partition boundary.

[0015] (2) For modeling local spatial heterogeneity, most methods focus on node-level meta-learning or spatial correlation weighting. Although these methods improve flexibility, they are essentially data-driven "black box" fitting, ignoring human mobility patterns and rules that lead to local heterogeneity. This leads to a model that may perform well on the training set, but the spatial interaction it learns lacks physical meaning in the real world, and its generalization ability and robustness are insufficient. SUMMARY

[0016] The present application proposes a human activity intensity prediction method based on generalized spatial heterogeneity learning, which improves prediction accuracy and more effectively captures and simulates real human mobility patterns, making the prediction results more realistic and reliable.

[0017] The present application adopts the following technical solutions.

[0018] The human activity intensity prediction method based on generalized spatial heterogeneity learning comprises node-to-node propagation learning and node-to-partition propagation learning.

[0019] In node-to-node propagation learning, a mobility-guided graph learning module is used to combine mobility models for spatial interaction modeling and graph information propagation. A radiation model is introduced to calculate the mobility probability matrix between nodes to capture the random process of local liquidity decisions. Inspired by the gravity model, the inflow and outflow migration volume is introduced to optimize the fitting of movement possibilities. The local heterogeneity problem is solved from the perspective of mobility cost.

[0020] In node-to-partition propagation learning, a spectral attention module is used to dynamically group nodes based on node attributes and adaptively adjust according to time evolution patterns. Spectral attention is also used to establish dynamic interaction between nodes and partitions using linearized transformer attention, and the spatial partition features are used as additional channel parameters to realize dynamic and adaptive adjustment of node-partition membership.

[0021] The prediction method further comprises a spatiotemporal embedding module, which is an initial module for encoding spatiotemporal features from input data, used to generate preliminary dynamic space and time partitions as the basis for spatial hierarchical heterogeneity modeling.

[0022] Node-to-node propagation learning (N2NPL) uses a node-to-node propagation learning module, which is an N2NPL submodule that models the different contributions of individual node interactions to capture spatial local heterogeneity and improves the end-to-end formula of the radiation model by introducing a neural network tensor to simulate how human mobility costs guide information propagation between locations.

[0023] Node-to-Partition Propagation Learning (N2PPL) uses a node-to-partition propagation learning module, specifically: the module is an N2PPL submodule, which learns the dynamic relationship between individual nodes and the broader internal homogeneous partitions to which they belong to address spatially hierarchical heterogeneity, and uses spectral attention to explicitly model these node-to-partition associations.

[0024] The human activity intensity prediction method uses a human activity intensity prediction model, the main body of which is Proformer, which is used to learn the complex relationship between space and time, and each layer contains two main submodules, namely a node-to-node propagation learning module N2NPL and a node-to-partition propagation learning module N2PPL;

[0025] The N2NPL submodule is responsible for combining mobility models that model spatial interactions with graph information propagation, including a mobility-guided graph learning module; its internal components include: an improved radiation model (IRM) component for physical inspiration, which is mainly used to calculate a prior propagation weight matrix based on the geographic / attractive force information between input data nodes and pass it into the graph convolution component; a graph propagation (Graph Propagate) component for graph network propagation, which aggregates messages for the current node features and adjacency relationships; a replacement component that fuses the adjacency relationships in the IRM component and the graph convolution;

[0026] The N2PPL submodule mainly captures the interaction patterns between nodes and partitions through learned dynamic partitions, including a spectral attention module; its internal components include: a projection layer (K / Q / V Projection) responsible for transforming the original features into a representation suitable for attention calculation; a temporal region (Temporal Region) representation that divides the node's historical sequence into several time periods with similar dynamic characteristics in the time dimension; a spatial region (Spatial Region) representation that divides nodes into several regions with similar functions or interaction patterns in the spatial dimension; a temporal region attention mechanism (TR Attention) that learns the dependency relationship between different time slices in the time dimension to strengthen time pattern modeling; a spatial region attention mechanism (SR Attention) that learns the interaction relationship and dependency strength between different spatial regions in the spatial dimension (i.e., the node dimension) to strengthen spatial pattern modeling; a linear feature mapping (Projection) that converts input features into a new feature space for data transmission;

[0027] In the human activity intensity prediction model, the forward propagation of GLU (GLU-FFN) is equivalent to "letting a part of neurons control the output of another part", which adjusts the information flow through "gates" and helps to selectively activate or inhibit features, improving the model's nonlinear expression ability and computational performance;

[0028] In the human activity intensity prediction model, the value output by the Propformer is processed by a multi-layer perception with memory enhancement (MA-MLP), the stacked high-level spatio-temporal representation is converted into the final prediction, and the "memory" mechanism is introduced to retain long-term or global patterns (the overall framework diagram is as follows Figure 1 ).

[0029] The human activity intensity prediction method comprises the following steps.

[0030] Step S1: In the data transmission stage, prepare the data required for the subsequent process.

[0031] Step S2: In the spatio-temporal embedding stage, the input data is encoded for spatio-temporal features;

[0032] Step S3: In the N2NPL stage, the mobility model of spatial interaction modeling is combined with the graph information propagation;

[0033] Step S4: In the N2PPL stage, nodes are dynamically grouped based on node attributes, and these groups are adaptively adjusted according to the time evolution pattern;

[0034] Step S5: In the GLU-FNN and hierarchical normalization stage, high-performance prediction is performed;

[0035] Step S6: In the MA-MLP stage, the data output by the entire Propformer is processed by residual jump connection and memory enhancement to enhance the ability to handle spatial and temporal uncertainty, and then MLP decoding is performed for the final spatio-temporal prediction.

[0036] Step S1 comprises the following steps.

[0037] Step S11, data definition; define the overall structure of the built-up area as a graph , where the edge is weighted by distance; based on the constructed graph structure, the intensity of human activity over time can be regarded as a signal acting on each node, denoted as ;

[0038] where represents the signal feature component of all nodes at the Tth time step;

[0039] For each time snapshot, there is also a dynamic spatial division ;

[0040] where represents the soft assignment of N nodes to M partitions at each time step, T represents the total number of time steps, and a mobility cost matrix , represents the moving cost from one node to another in the N nodes at time point T, which is used to encode the travel cost prior knowledge between units; step S12, input data; given the human activity and flow data of the past

[0041] human activity intensity

[0042] inflow

[0043] outflow

[0044] where t represents the current time index, q represents the length of the historical sequence, and C represents the feature dimension; step S13, input the data in step S12 into the space-time embedding module.

[0045] Step S2 includes the following steps.

[0046] Step S21, generate a spatial relationship embedding representation; encode the spatial attributes (belonging area, geographic coordinates, and learnable node vector) of the node into a vector, and the calculation expression is as follows:

[0047]

[0048]

[0049]

[0050] is a learnable parameter;

[0051]

[0052] represents the feature dimension, which is a hyperparameter;

[0053] Step S22, generate a time relationship embedding representation; encode the time periodicity and holiday information into a vector, and the calculation expression is as follows:

[0054]

[0055] is a learnable parameter in learning partition and meta-learning; represents a channel-level connection, is a meta timestamp, which is used as an input of the time sequence meta learning;

[0056] where T is the number of time steps, and w is the number of time partitions. ​​​​; Step S23, in combination with steps S21, S22, all embedded features are connected and Hadamard mapper is applied to effectively convert features into linear space while reducing noise, so as to obtain a complete spatio-temporal representation As the input of Propformer, its calculation expression is as follows:

[0057]

[0058] Wherein is a learnable parameter for changing the dimension of the feature, is a learnable parameter in Harmard projection;

[0059] is a hyperparameter representing the dimension of the input feature;

[0060] H0 is initially 1.

[0061] Step S3 includes the following steps:

[0062] Step S31, inspired by the gravity model, combines the migration tensor and mobility tensor Z flowing into and flowing out , and optimizes the fitting of motion possibility, and its calculation expression is as follows:

[0063]

[0064] is the data of step S12, representing the migration amount flowing into and flowing out of each place;

[0065] is a learning parameter for converting the migration amount into a high-dimensional tensor, is a Softplus activation function to ensure the nonlinear fitting of the quality parameter;

[0066] are two power-law learning parameters to realize flexible scale adjustment of part of the quality term;

[0067] and respectively represent the migration tensors flowing in and out,

[0068] Step S32, through the IRM component; according to the radiation model, the calculation is a flow distribution process with inherent uncertainty, and its expression is as follows:

[0069]

[0070] Wherein , respectively represent the positions and population size or attractiveness; denotes the center of the circle, is located in the circular area on the circumference (excluding itself), the opportunity and uncertainty factors of all positions;

[0071] is the moving probability from node i to node j;

[0072] Step S33, in combination with steps S31 and S32, uses graph information propagation to transmit the motion pattern back to the tensor of each place, simulates the influence of the corresponding moving behavior on the activity, and adds a simple but learnable importance parameter during the graph propagation process, realizes differentiated scaling across nodes, and thus the final tensor calculation expression is as follows:

[0073]

[0074] wherein denotes a Softmax activation function used to normalize the moving cost matrix;

[0075] Step S34, normalizing each feature of the sample through a LayerNorm layer.

[0076] Step S4 comprises the following steps.

[0077] Step S41: pre-compute the query, key and value tensors of the Propformer, and the calculation expression is as follows:

[0078]

[0079] are learnable parameters in the transformer layer;

[0080] wherein h represents the number of attention heads, denotes the feature dimension of each attention head;

[0081] Step S42: the adaptive spectral adjacency matrix calculated through a series of activation functions, and the calculation expression is as follows:

[0082]

[0083] wherein is a tanh activation function; is a ReLU activation function; is a linear transformation operation,

[0084] , ​These are learnable adaptive node vectors used to obtain the adaptive adjacency matrix;

[0085] Step S43: Combining steps S21, S41, and S42, this formula defines the graph information propagation function in the spectral attention layer. That is, it realizes cross-node feature diffusion through the spectral adjacency matrix As and the geospatial feature Sspatial, and calculates the spatial partitioning features of each layer. Its calculation expression is as follows:

[0086]

[0087] in These are the learnable parameters in the graph pooling layer; It is the Softmax activation function used for tensor normalization;

[0088] Step S44: Combining with step S22, calculate the temporal features according to the method for obtaining spatial partitioning features. The calculation expression is as follows:

[0089]

[0090] O T It is the output feature tensor that captures temporal dependencies; R T It is the input tensor in time feature calculation, used to interact with query Q and key K;

[0091] Step S45: Combining steps S44 and S43, based on the obtained spatiotemporal features, we use the concept of channel focus for weighted fusion, and finally, we perform... Channel dimension mapping yields the output features of N2PPL, and its calculation expression is as follows:

[0092]

[0093] in These are channel parameters used for spatiotemporal data fusion; These are the learnable parameters of the mapping layer; This represents a depthwise convolution used to assist in a better gradient flow.

[0094] r is a dimension scaling factor used to control the degree of dimensional expansion of features within the model; and These represent the temporal feature channel weights and spatial feature channel weights, respectively, used for channel-level adaptive fusion of the output temporal and spatial features; It is an intermediate feature that integrates temporal and spatial attention information. It is the final output feature of the module.

[0095] Step S5 includes the following steps;

[0096] Step S51: High-performance prediction is achieved using a feedforward network (FFN) and layer normalization (LayerNorm), and effective information filtering is performed using a gated linear unit feedforward network (GLU-FFN) based on this; its calculation expression is as follows:

[0097]

[0098] in Indicates GLU-FFN; Represents the GELU activation function. This represents the learnable parameters in FFN;

[0099] Step S6 includes the following steps;

[0100] Step S61: Perform residual skip joins on the data output from each layer of the Propformer. The calculation expression is as follows:

[0101]

[0102] in These are the learnable parameters of the (l-1) layer of the residual skip connection. It is the output of the l-level Propformer;

[0103] It is a dimensional hyperparameter representing the feature dimension in the residual skip connection;

[0104] Step S62: Decode these features using a multilayer perceptron (MLP) head and employ a memory bank method before the MLP head to enhance the ability to handle spatial and temporal uncertainties, obtaining the final prediction; its calculation expression is as follows:

[0105]

[0106] in , M is the learnable parameter that the decoder ultimately predicts. s M t It is a spatial / temporal memory module that enhances the input features; M s Capturing spatial uncertainty / heterogeneity, M t Capture the uncertainty of time / the impact of events;

[0107] Finally, L1 loss was chosen as the loss function to train the model, expressed by the following formula:

[0108]

[0109] in This represents the actual ground-level value of human activity intensity. This is the Hermes prediction result;

[0110] n represents the total number of samples, and i is the sample index. Let i be the true value of the i-th sample. for The predicted value of the i-th sample.

[0111] The prediction method uses historical human activity intensity, inflow and outflow information based on large-scale mobile phone data to predict the scale and activity level of the population in a census tract within the next two hours, with a preset time granularity of 30 minutes.

[0112] This invention proposes node-to-node propagation learning, a mobility-guided graph learning module that combines a mobility model for spatial interaction modeling with graph information propagation. Existing methods often select nearby locations to meet activity needs, leading to local heterogeneity in spatial interactions. Therefore, this proposal introduces a radiation model to calculate the mobility probability matrix between nodes, capturing the stochastic process of local mobility decisions. Inspired by gravity models, it introduces inflow and outflow migration quantities to optimize the fitting of movement probabilities, addressing the local heterogeneity problem from the perspective of mobility cost. Experiments demonstrate that the spatial interaction relationships learned by this module are highly interpretable. The node-to-node interaction matrix generated by this module exhibits sparsity, which closely matches real-world human mobility behavior—that is, people's activities are usually concentrated in a few functional core areas, while interactions between most areas are relatively few. Furthermore, this interaction relationship exhibits a significant "distance decay" effect, meaning that the interaction intensity weakens with increasing geographical distance, which conforms to the first law of geography. More importantly, the interaction scale learned by this module is highly consistent with the human community-scale travel distance observed in sociological research, proving that this module not only improves prediction accuracy but also effectively captures and simulates real human movement patterns, making its prediction results more realistic and reliable.

[0113] This invention proposes a node-to-partition propagation learning method, which is a spectral attention module that dynamically groups nodes based on node attributes and adaptively adjusts according to temporal evolution patterns. Existing methods rely solely on pre-existing static partitions for human activity prediction, failing to capture temporal dynamics and requiring additional external data, thus increasing data collection costs. Therefore, this proposal introduces spectral attention, which, instead of having nodes directly focus on other nodes, uses linearized transformer attention to establish dynamic interactions between nodes and partitions. Unlike traditional linear attention, it uses spatial partition features as additional channel parameters, achieving dynamic and adaptive adjustment of node-partition affiliation relationships.

[0114] The advantages of this invention are:

[0115] (1) Collaborative modeling of generalized spatial heterogeneity is achieved, resulting in superior and more stable technical performance. This proposal considers both local spatial heterogeneity and hierarchical spatial heterogeneity through the aforementioned N2NPL and N2PPL. Ablation experiments demonstrate that both modules are indispensable for improving model performance and outperform traditional attention mechanisms or simple graph convolution. This dual modeling mechanism enables the model to have better predictive stability, especially when predicting peaks and troughs of drastic changes in activity intensity.

[0116] (2) An effective fusion of physical mechanisms and deep learning is achieved without relying on additional data. Compared to existing techniques that consider transfer patterns (e.g., STDEN, ST-PEFs), this proposal introduces a method based on a gravity model and uses important parameters for graph propagation. While ensuring that migration costs are taken into account, this method successfully injects prior knowledge of mobile physics into graph neural networks without relying on any additional, expensive fine-grained OD flow data. This solves the "counterproductive" problem of such methods and has extremely high application flexibility and practical value. Attached Figure Description

[0117] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0118] Appendix Figure 1 This is a schematic diagram illustrating the principle framework of the human activity intensity prediction model in this embodiment of the invention. Detailed Implementation

[0119] As shown in the figure, a method for predicting human activity intensity based on generalized spatial heterogeneity learning includes node-to-node propagation learning and node-to-partition propagation learning.

[0120] In node-to-node propagation learning, a mobility-guided graph learning module is used to combine the mobility model of spatial interaction modeling with graph information propagation; a radiation model is introduced to calculate the mobility probability matrix between nodes, capturing the stochastic process of local mobility decisions; inspired by the gravity model, inflow and outflow migration amounts are introduced to optimize the fitting of motion probability; and the problem of local heterogeneity is addressed from the perspective of mobility cost.

[0121] In the node-to-partition propagation learning, a spectral attention module is used to dynamically group nodes based on node attributes and adaptively adjust according to the temporal evolution pattern. Furthermore, through spectral attention, a linearized transformer attention is used to establish dynamic interactions between nodes and partitions, and spatial partition features are used as additional channel parameters to achieve dynamic and adaptive adjustment of node-partition affiliation.

[0122] The prediction method also includes a spatiotemporal embedding module, which is an initial module that encodes spatiotemporal features from the input data. It is used to generate preliminary dynamic spatial and temporal partitions as the basis for spatial hierarchical heterogeneity modeling.

[0123] Node-to-Node Propagation Learning (N2NPL) uses a node-to-node propagation learning module, which is a submodule of N2NPL. It captures spatial local heterogeneity by modeling the different contributions of interactions between individual nodes and improves the end-to-end formula of the radiation model by introducing neural network tensors to simulate how the cost of human movement guides the propagation of information between locations.

[0124] Node-to-Partition Propagation Learning (N2PPL) uses the Node-to-Partition Propagation Learning module, which is a submodule of N2PPL. It addresses the heterogeneity of spatial stratification by learning the dynamic relationships between individual nodes and the broader internal homogeneous partitions to which they belong, and explicitly models these node-to-partition associations using spectral attention.

[0125] The human activity intensity prediction method uses a human activity intensity prediction model, whose main body is Proformer, which is used to learn the complex relationship between space and time. Each layer contains two main sub-modules, namely the node-to-node propagation learning module N2NPL and the node-to-partition propagation learning module N2PPL.

[0126] The N2NPL submodule is responsible for combining the mobility model of spatial interaction modeling with graph information propagation, including a mobility-guided graph learning module. Its internal components include: an Improved Radiation Model (IRM) component for physical inspiration, whose main function is to calculate a prior propagation weight matrix based on the geographic / attraction information between input data nodes and pass it into the graph convolution component; a Graph Propagate component for graph network propagation, which aggregates the current node features and adjacency relationships; and Replacement, which represents the weighted fusion of the adjacency relationships in the IRM component and the graph convolution component.

[0127] The N2PPL submodule primarily captures the interaction patterns between nodes and partitions through learned dynamic partitioning, including a spectrum attention module. Its internal components include: a projection layer (K / Q / V Projection) that transforms the original features into a representation suitable for attention computation; a temporal region that divides the historical sequence of nodes into several time periods with similar dynamic features; a spatial region that divides nodes into several regions with similar functions or interaction patterns; a temporal region attention mechanism (TR Attention) that learns the dependencies between different time slices in the temporal dimension, strengthening temporal pattern modeling; a spatial region attention mechanism (SR Attention) that learns the interaction relationships and dependency strengths between different spatial regions in the spatial dimension (i.e., node dimension), strengthening spatial pattern modeling; and a linear feature mapping (Projection) that transforms the input features into a new feature space for data transmission.

[0128] In the human activity intensity prediction model, the forward propagation of GLU (GLU-FFN) is equivalent to "letting one part of the neurons control the output of another part". By regulating the information flow through "gates", it helps to selectively activate or suppress features, thereby improving the model's nonlinear expressive power and computational performance.

[0129] In the human activity intensity prediction model, the Propformer output is processed by a multilayer perceptron with memory enhancement (MA-MLP) to transform the stacked high-level spatiotemporal representation into the final prediction. A "memory" mechanism is introduced to retain long-term or global patterns (overall framework diagram as shown). Figure 1 ).

[0130] The method for predicting the intensity of human activities includes the following steps;

[0131] Step S1: During the data transmission phase, prepare the data required for subsequent processes;

[0132] Step S2: In the spatiotemporal embedding stage, the input data... Perform spatiotemporal feature encoding;

[0133] Step S3: In the N2NPL phase, the mobility model of spatial interaction modeling is combined with graph information propagation;

[0134] Step S4: In the N2PPL stage, nodes are dynamically grouped based on node attributes, and these groups are adaptively adjusted according to the time evolution pattern.

[0135] Step S5: Perform high-performance predictions in the GLU-FNN and hierarchical normalization stages;

[0136] Step S6: In the MA-MLP stage, by enhancing the ability to handle spatial and temporal uncertainties, residual jump connections and memory enhancement are performed on the entire Propformer output data, and then MLP decoding is performed for the final spatiotemporal prediction.

[0137] Step S1 includes the following steps;

[0138] Step S11, Data Definition; Define the overall structure of the built-up area as a graph. The edges are weighted by distance; based on the constructed graph structure, human activities over time... The strength of can be viewed as a signal acting on each node, denoted as . ,in This refers to the signal feature tensor of all nodes at the T-th time step;

[0139] For each time snapshot, there is also a corresponding dynamic space partitioning. , This represents the dynamic spatial partitioning result for all nodes at time step T; it provides a soft allocation of N nodes to M partitions at each time step and gives a movement cost matrix. , representing the movement cost from one node in N nodes to another at time point T, is used to encode prior knowledge of travel costs between units; Step S12, Input data; given past Human activity and movement data at each time step, namely:

[0140] Human activity intensity ,

[0141] Inflow ,

[0142] Outflow Step S13: Transmit the data from step S12 into the spatiotemporal embedding module.

[0143] Step S2 includes the following steps;

[0144] Step S21: Generate spatial relationship embedding representation; encode the spatial attributes of nodes (region, geographic coordinates, learnable node vectors) into vectors, the calculation expression of which is as follows:

[0145]

[0146]

[0147]

[0148] These are learnable parameters;

[0149]

[0150] Where C is the original feature dimension of the input data X. An intermediate feature dimension designed for the model;

[0151] Step S22: Generate a temporal relationship embedding representation; encode the time periodicity and holiday information into a vector, the calculation expression of which is as follows:

[0152]

[0153] These are learnable parameters in learning partitions and meta-learning; Indicates a channel-level connection. The meta-timestamp is used as the input for time-series meta-learning;

[0154] Where T is the number of time steps and w is the number of time partitions; ;;

[0155] Step S23: Combining steps S21 and S22, all embedded features are concatenated, and the Hadamard mapper is applied to effectively transform the features into a linear space while reducing noise, thus obtaining a complete spatiotemporal representation. As input to the Propformer, its computation expression is as follows:

[0156]

[0157] in For learnable parameters used to change the feature dimension, These are learnable parameters in the Harmard projection;

[0158] The initial value of H0 is 1.

[0159] Step S3 includes the following steps;

[0160] Step S31, inspired by the gravity model, will flow into and outflow The migration tensor and mobility tensor Z are combined to optimize the fitting of motion possibilities, and its calculation expression is as follows:

[0161]

[0162] in The data for step S12 represents the inflow and outflow of migration at each location; To transform the transfer parameters into learning parameters of a high-dimensional tensor, The Softplus activation function is used to ensure nonlinear fitting of the quality parameters;

[0163] Two power-law learning parameters are used to achieve flexible scaling of some quality terms;

[0164] Step S32: After passing through the IRM component, the flow allocation process calculated according to the radiation model is an inherently uncertain process, and its expression is as follows:

[0165]

[0166] in , Representing positions respectively and Population size or attractiveness; Indicates With the center of the circle, Within the circular area on the circumference (excluding) (Itself), all opportunities and uncertainties in all positions;

[0167] Step S33: Combining steps S31 and S32, graph information propagation is used to transmit motion patterns back to the tensors at each location, simulating the impact of corresponding movement behaviors on the activity; and a simple but learnable importance parameter is added during the graph propagation process. To achieve differentiated scaling across nodes, the final tensor calculation expression is as follows:

[0168]

[0169] in This represents the Softmax activation function used to normalize the moving cost matrix;

[0170] Step S34: Normalize each feature of the sample through the LayerNorm layer.

[0171] Step S4 includes the following steps;

[0172] Step S41: Pre-compute the query, key, and value tensors of Propformer, with the following computation expressions:

[0173]

[0174] These are learnable parameters in the transformer layer;

[0175] h represents the number of attention heads. The feature dimension of each attention head

[0176] Step S42: The adaptive spectral adjacency matrix is ​​calculated through a series of activation functions, and its calculation expression is as follows:

[0177]

[0178] in The tanh activation function; It is the ReLU activation function; For linear transformation operations,

[0179] , These are learnable adaptive node vectors used to obtain the adaptive adjacency matrix;

[0180] Step S43: Combining steps S21, S41, and S42, this formula defines the graph information propagation function in the spectral attention layer. That is, it realizes cross-node feature diffusion through the spectral adjacency matrix As and the geospatial feature Sspatial, and calculates the spatial partitioning features of each layer. Its calculation expression is as follows:

[0181]

[0182] in These are the learnable parameters in the graph pooling layer; It is the Softmax activation function used for tensor normalization;

[0183] Step S44: Combining with step S22, calculate the temporal features according to the method for obtaining spatial partitioning features. The calculation expression is as follows:

[0184]

[0185] Step S45: Combining steps S44 and S43, based on the obtained spatiotemporal features, we use the concept of channel focus for weighted fusion, and finally, we perform... Channel dimension mapping yields the output features of N2PPL, and its calculation expression is as follows:

[0186]

[0187] in These are channel parameters used for spatiotemporal data fusion; These are the learnable parameters of the mapping layer; This represents a depthwise convolution used to assist in a better gradient flow.

[0188] , These represent the weights of the time feature channel and the weights of the spatial feature channel, respectively. This indicates the fusion characteristics within the module. This indicates the module's final output;

[0189] Step S5 includes the following steps;

[0190] Step S51: High-performance prediction is achieved using a feedforward network (FFN) and layer normalization (LayerNorm), and effective information filtering is performed using a gated linear unit feedforward network (GLU-FFN) based on this; its calculation expression is as follows:

[0191]

[0192] in Indicates GLU-FFN; Represents the GELU activation function. This represents the learnable parameters in FFN; r is a dimensionality scaling factor used to control the degree of dimensionality expansion of features within the model. It is a one-dimensional hyperparameter;

[0193] Step S6 includes the following steps;

[0194] Step S61: Perform residual skip joins on the data output from each layer of the Propformer. The calculation expression is as follows:

[0195]

[0196] in These are the learnable parameters of the (l-1) layer of the residual skip connection. It is the output of the l-level Propformer;

[0197] It is a one-dimensional hyperparameter;

[0198] Step S62: Decode these features using a multilayer perceptron (MLP) head and employ a memory bank method before the MLP head to enhance the ability to handle spatial and temporal uncertainties, obtaining the final prediction; its calculation expression is as follows:

[0199]

[0200] in , M is the learnable parameter that the decoder ultimately predicts. s M t It is a spatial / temporal memory module that enhances the input features; M s Capturing spatial uncertainty / heterogeneity, M t Capture the uncertainty of time / the impact of events;

[0201] Finally, L1 loss was chosen as the loss function to train the model, expressed by the following formula:

[0202]

[0203] in This represents the actual ground-level value of human activity intensity. This is the Hermes prediction result.

[0204] n is the total number of samples. The true value of the i-th sample. for The predicted value of the i-th sample.

[0205] The prediction method uses historical human activity intensity, inflow and outflow information based on large-scale mobile phone data to predict the scale and activity level of the population in a census tract within the next two hours, with a preset time granularity of 30 minutes.

[0206] Example:

[0207] In this example, several baseline methods, including STAEformer, PatchSTG, and Gravityformer, are selected from classic to state-of-the-art time series and spatiotemporal prediction methods for comparison. These methods can be categorized into four types: ① Classical time series prediction methods, including HA, FC-LSTM, and TCN; ② Recent time series prediction methods, including Dlinear and iTransformer; ③ Graph-based spatiotemporal prediction methods, including STGCN, GraphWaveNet, AGCRN, DSTAGNN, MegaCRN, ST-Wave, HyGCN, STID, BigST, HimNet, and STG-Mamba; ④ Transformer-based spatiotemporal prediction methods, including ASTGNN, STAEformer, STGformer, PatchSTG, and Gravityformer.

[0208] To verify the effectiveness of this invention framework, we implemented a complex human activity prediction task in six major U.S. metropolitan areas (Minneapolis, Atlanta, Boston, San Francisco, Chicago, and Los Angeles). This task utilizes historical human activity intensity, inflow, and outflow information derived from large-scale mobile phone data, using a 30-minute time granularity, to predict the size and activity level of crowds within the next two hours at a fine spatial unit—the census block. The experimental dataset covers different city sizes and spatial structures, aiming to comprehensively evaluate the practical effect of the proposed method in real-world, diverse urban scenarios, improving prediction accuracy, stability, and generalization ability through modeling generalized spatial heterogeneity. Specific results are shown in Table 2 below.

[0209] Table 2. Performance of different models on six human activity datasets

[0210]

[0211] Table 2 (continued)

[0212]

[0213] Performance evaluations show that the Hermes framework proposed in this invention outperforms all baseline models in the vast majority of cases. For example, the RMSE, a core error metric, is reduced by up to approximately 10%, with significant improvements in MAE and MAPE as well. Further analysis using a two-tailed t-test demonstrates that these improvements are statistically significant (p < 0.025), effectively eliminating the random effects of purely stochastic disturbances. Notably, this scheme exhibits particularly strong stationary control over RMSE, demonstrating lower errors and more stable predictions across all datasets and time periods. Especially during peak periods of high population activity, the error suppression effect is even more pronounced, indicating the framework's strong generalization ability and robustness.

Claims

1. A human activity intensity prediction method based on generalized spatial heterogeneity learning, characterized in that: The prediction method comprises node-to-node propagation learning and node-to-partition propagation learning, In the node-to-node propagation learning, a mobility-guided graph learning module is used to combine a mobility model modeling spatial interaction with graph information propagation; a radiation model is introduced to calculate a mobility probability matrix between nodes, to capture the stochastic process of local liquidity decisions; a migration amount of inflow and outflow is introduced to optimize the fitting of movement possibility; a local heterogeneity problem is solved from the perspective of mobility cost; In the node-to-partition propagation learning, a spectral attention module is used to dynamically group nodes based on node attributes, and to adaptively adjust according to time evolution patterns; Through spectral attention, a linearized transformer attention is used to establish dynamic interaction between nodes and partitions, and spatial partition features are taken as additional channel parameters to realize dynamic and adaptive adjustment of node-partition membership. 2.The human activity intensity prediction method based on generalized spatial heterogeneity learning according to claim 1, characterized in that: The prediction method further comprises a spatio-temporal embedding module, which is an initial module for encoding spatio-temporal features from input data, and is used to generate preliminary dynamic spatial and temporal partitions, as a basis for modeling spatial hierarchical heterogeneity; The node-to-node propagation learning uses a node-to-node propagation learning module, specifically: the module is an N2NPL submodule, which models different contributions of interactions between individual nodes to capture spatial local heterogeneity, and improves an end-to-end formula of a radiation model by introducing a neural network tensor, to simulate how human mobility cost guides information propagation between locations; The node-to-partition propagation learning uses a node-to-partition propagation learning module, specifically: the module is an N2PPL submodule, which learns dynamic relationships between individual nodes and the broader internal homogeneous partitions to which they belong, to solve spatial hierarchical heterogeneity, and utilizes spectral attention to explicitly model these node-to-partition associations. 3.The human activity intensity prediction method based on generalized spatial heterogeneity learning according to claim 2, characterized in that: The human activity intensity prediction method uses a human activity intensity prediction model, the main body of which is Proformer, which is used to learn complex relationships between space and time, and each layer of which contains two main submodules, namely a node-to-node propagation learning module N2NPL and a node-to-partition propagation learning module N2PPL; The N2NPL submodule is responsible for combining a mobility model modeling spatial interaction with graph information propagation, including a mobility-guided graph learning module; Its internal components include: an improved radiation model component for physical inspiration, which is used to calculate a prior propagation weight matrix based on geographic / attractive force information between input data nodes and input into a graph convolution component; a graph convolution component for graph network propagation, which aggregates messages of current node features and adjacency relationships; a fusion representation for weighted fusion of the IRM component and the adjacency relationships in the graph convolution; The N2PPL sub-module captures the interaction patterns between nodes and partitions through learning dynamic partitioning, including a spectrum attention module; the internal components include: a projection layer responsible for transforming the original features into a representation suitable for attention calculation; a time region representation that divides the historical sequence of nodes into several time periods with similar dynamic characteristics in the time dimension; a spatial region representation that divides nodes into several regions with similar functions or interaction patterns in the spatial dimension; a time region attention mechanism that learns the dependency between different time slices in the time dimension, strengthening time pattern modeling; a spatial region attention mechanism that learns the interaction relationship and dependency strength between different spatial regions in the spatial dimension, strengthening spatial pattern modeling; a linear feature mapping that converts input features into a new feature space for data transmission; In the human activity intensity prediction model, the forward propagation of GLU selectively activates or suppresses features, improving the model's nonlinear expression ability and computational performance; In the human activity intensity prediction model, the value output by the Propformer is processed through a multi-layer perceptron with memory enhancement, converting the stacked high-level spatio-temporal representation into the final prediction, and introducing a "memory" mechanism to retain long-term or global patterns. 4.The human activity intensity prediction method based on generalized spatial heterogeneity learning according to claim 3, characterized in that: The human activity intensity prediction method comprises the following steps: Step S1: In the data transmission phase, prepare the data required for the subsequent process; Step S2: in the spatio-temporal embedding stage, spatio-temporal feature encoding is performed on the input data ; Step S3: In the N2NPL phase, combine the mobility model of spatial interaction modeling with graph information propagation; Step S4: In the N2PPL phase, dynamically group nodes based on node attributes, and adaptively adjust these groups according to the time evolution pattern; Step S5: In the GLU-FNN and hierarchical normalization phase, perform prediction; Step S6: In the MA-MLP phase, enhance the ability to handle spatial and temporal uncertainty by performing residual jump connection and memory enhancement on the data output by the entire Propformer, and then performing MLP decoding for the final spatio-temporal prediction. 5.The human activity intensity prediction method based on generalized spatial heterogeneity learning according to claim 4, characterized in that: Step S1 comprises the following steps: Step S11, data definition; define the overall structure of the built-up area as a graph where edges are weighted by distance; Based on the constructed graph structure, the intensity of human activities over time can be regarded as a signal acting on each node, denoted as ; where represents the Tthtime step, the signal feature component of all nodes. For each time snapshot, there also corresponds a dynamic spatial partitioning ; wherein N nodes to M partitions at each time step, T denotes the total number of time steps, and gives a mobility cost matrix , which encodes the prior knowledge of travel cost between cells; step S12, input data; given past time steps of human activity and flow data, i.e.: Human activity intensity , Inflow , outflow ; Where t represents the current time index, C is the original feature dimension of the input data X; Step S13, the data in step S12 is transmitted into the spatio-temporal embedding module. 6.The human activity intensity prediction method based on generalized spatial heterogeneity learning according to claim 5, characterized in that: Step S2 comprises the following steps: Step S21, generate spatial relationship embedding representation; encode the spatial attributes of nodes into vectors, whose calculation expression is as follows: are learnable parameters; where C is the original feature dimension of the input data X, an intermediate feature dimension designed for the model; In this step, is a learnable weight matrix, is a learnable bias vector. wherein, denotes the fused original feature encoding, with dimension , wherein is a spatial soft assignment matrix, used to represent the correspondence between N nodes and M partitions, i.e. the geographical spatial feature, with dimension ; wherein denotes the feature representation aggregated by the spatial relationship, with dimension ; represents the feature dimension, which is a hyperparameter; bias vector representing feature encoding; bias vector representing spatial soft assignment middle layer; bias vector representing spatial soft assignment output layer; bias vector representing spatial relationship aggregation; Step S22, generate time relationship embedding representation; encode the time periodicity and holiday information into vectors, whose calculation expression is as follows: are learnable parameters in learning partitions and meta-learning; represent channel-wise connections, are meta-timestamps, which are inputs for temporal meta-learning. where T is the number of time steps, and w is the number of time partitions; ; : a time partition matrix, i.e., a dynamic time partition allocation result obtained by meta-learning; : base timing feature embedding, including an encoded vector of timestamps; : final temporal partition embedding vector, fusing dynamic partition information and base timing features; Step S23, in combination with steps S21, S22, all embedded features are connected and a Hadamard mapper is applied to effectively convert the features into a linear space while reducing noise, thus obtaining a complete spatio-temporal representation As the input of Propformer, its computational expression is as follows: wherein is a learnable parameter for changing the feature dimensionality, is a learnable parameter in Harmard projection; is a hyperparameter representing the input feature dimension; The initial value of H0 is 1; denote day, week, hour, spatial feature embeddings, respectively; , , , all represent feature dimensions, all are hyperparameters; Z in is a time embedding feature tensor, which is obtained by concatenating and linearly mapping multiple time dimension meta-features, and is used to encode the time periodicity and dynamic rules of human activities; H p is a recursively constructed Hadamard transform matrix for linear transformation and noise reduction of the fused time features, optimizing the feature space distribution; is the transpose of the matrix.

7. The human activity intensity prediction method based on generalized spatial heterogeneity learning according to claim 6, characterized in that: Step S3 comprises the following steps: Step S31, combine the migration tensor and mobility tensor Z of the inflow and outflow and optimize the fit of the motion possibility, whose calculation expression is as follows: For the data of step S12, the amount of migration flowing in and out of each place is indicated; to convert the migration amount into a high-dimensional tensor of learning parameters, to ensure a quality parameter non-linear fitting of a Softplus activation function; a learnable bias vector; The two power-law learning parameters enable flexible scale adjustment of the partial mass terms. and and respectively represent the inflow and outflow migration tensors, Step S32, pass through the IRM component; the calculation of the radiation model is a flow distribution process with inherent uncertainty, whose expression is as follows: wherein , respectively represent the location and population size or attractiveness; represent a circular area with as the center, on the circumference, all the opportunities and uncertainty factors of the location; is the probability of moving from node i to node j; Step S33, combine steps S31 and S32, use graph information propagation to transmit the movement patterns back to the tensor of each place, simulating the impact of corresponding movement behavior on activity; and add learnable importance parameters during graph propagation and achieve differentiated scaling across nodes, the tensor computation expression is as follows: wherein denotes a Softmax activation function for normalizing the mobile cost matrix; denotes a graph-to-graph non-linear mapping function for transforming the input tensor Z and the movement probability into a node-to-node intermediate feature tensor , is an intermediate feature tensor representing the inter-node influence; Step S34, normalize each feature of the sample through the LayerNorm layer.

8. The human activity intensity prediction method based on generalized spatial heterogeneity learning according to claim 7, characterized in that: Step S4 comprises the following steps: Step S41: The query, key and value tensors of the transformer Propformer are calculated in advance, and the calculation expression is as follows: denotes the query tensor, K denotes the key tensor, and V denotes the value tensor; are the learnable parameters in the transformer Propformer layer; where h denotes the number of attention heads, denotes the feature dimension of each attention head; Step S42: The adaptive spectral adjacency matrix calculated by a series of activation functions is as follows: wherein is a tanh activation function; is a ReLU activation function; is a linear transformation operation, , is a learnable adaptive node vector used to obtain an adaptive adjacency matrix; A s denotes an adaptive adjacency matrix, which is used to describe the dynamic connection relationship between nodes; C e is the feature dimension of node embedding; Step S43: In combination with steps S21, S41 and S42, the formula defines the graph information propagation function in the spectral attention layer, that is, the feature diffusion across nodes is realized through the spectral adjacency matrix As and the geographical spatial feature Sspatial, and the spatial partition feature of each layer is calculated, and the calculation expression is as follows: wherein, denotes a feature propagation function based on attention mechanism for fusing tensors , an adaptive adjacency matrix A s and geospatial features , denotes a feature tensor obtained after spatial partitioned feature diffusion; wherein are learnable parameters in the graph pooling layer; is a Softmax activation function for tensor normalization; O s is the output feature tensor capturing the spatial dependency; b s1 , b s2 is a learnable bias vector used in the spatial feature computation; Step S44: In combination with step S22, the time feature is calculated according to the method of obtaining the spatial partition feature, and the calculation expression is as follows: O T is an output feature tensor that captures time dependence; R T is an input tensor in time feature computation, used to interact with query Q and key K; Step S45: In combination with steps S44 and S43, based on the obtained spatio-temporal features, we use the concept of channel attention for weighted fusion, and finally, we perform Channel dimension mapping, obtaining the output features of N2PPL, whose calculation expression is as follows: wherein is the final output feature tensor after channel-wise mapping; wherein is a channel parameter for spatio-temporal data fusion; is a learnable parameter of the mapping layer; denotes a function for Deep convolution for better auxiliary gradient flow; r is a dimension scaling factor for controlling the degree of dimension expansion of the features inside the model; and respectively represent the time feature channel weight and the space feature channel weight, which are used for adaptive fusion of the output time features and space features at the channel level; is the intermediate feature fused with time and space attention information, is the final output feature of the module.

9. The human activity intensity prediction method based on generalized spatial heterogeneity learning according to claim 8, characterized in that: Step S5 includes the following steps. Step S51: High-performance prediction is realized by using a feedforward network and layer normalization, and effective information filtering is realized by using a gated linear unit feedforward network on this basis; and the calculation expression is as follows: wherein denotes a gating feed-forward network GLU-FFN for further feature processing; stands for a GELU activation function, denotes learnable parameters in the FFN; denotes a gating feed-forward network for further feature processing; denotes layer normalization on the output of the previous layer; is a feature transformation function that fuses node features with dynamic spatial partition features, models spatial hierarchical heterogeneity, takes the feature tensor Z of the previous layer as input, and outputs the feature tensor after fusing the heterogeneity information; Step S6 includes the following steps. Step S61: The data output by each layer of the Propformer is subjected to residual skip connection, and the calculation expression is as follows: wherein is a learnable parameter of the (l-1)th layer of the residual skip connection, is an output result of the lth layer of the Propformer. is a dimension hyper-parameter representing the feature dimension in the residual skip connection; Step S62: The features are decoded by a multilayer perceptron head, and a memory bank method is used before the MLP head to enhance the ability to process spatial and temporal uncertainty, and finally the prediction is obtained; The calculation expression is as follows: represents the Lth layer enhanced features that fuse spatial and temporal memory information; represents a nonlinear activation function; wherein , are learnable parameters of the decoder final prediction, M s , M t is a spatial / temporal memory module that enhances the input features; M s Capture spatial uncertainty / heterogeneity, M t Capture temporal uncertainty / events impact; Finally, the L1 loss function is selected to train the model, and the formula is as follows: wherein is the ground truth value of human activity intensity, is the Hermes prediction result; n denotes the total number of samples, i is the sample index, is the true value for the i-th sample, is the predicted value for the i-th sample. 10.The human activity intensity prediction method based on generalized spatial heterogeneity learning according to claim 4, characterized in that: The prediction method uses information data of historical human activity intensity, inflow and outflow based on large-scale mobile phone data, and is used to predict the population gathering scale and activity level of the spatial unit within two hours in the future at the fine spatial unit scale of the population census block with a preset time length as the time granularity.

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