Human activity intensity prediction method based on generalized spatial heterogeneity learning

Abstract

The present application proposes a human activity intensity prediction method based on generalized spatial heterogeneity learning, including node-to-node propagation learning and node-to-partition propagation learning, using a mobility-guided graph learning module, combining a mobility model modeling spatial interaction with graph information propagation; a radiation model is introduced to calculate the movement probability matrix between nodes to capture the random process of local liquidity decisions; the migration amount of inflow and outflow is introduced to optimize the fitting of movement possibility; the local heterogeneity problem is solved from the perspective of mobility cost; a spectrum attention module is used to dynamically group nodes based on node attributes, and to adaptively adjust according to the time evolution mode; a linearized transformer attention is used to establish dynamic interaction between nodes and partitions, and the spatial partition features are used as additional channel parameters; the present application improves the prediction accuracy, can more effectively capture and simulate the real human movement rules, and makes the prediction results more realistic 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. Through spectral attention, a linearized transformer attention is used to establish dynamic interaction between nodes and partitions, 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. By introducing a neural network tensor to improve the end-to-end formula of the radiation model, it simulates 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 suppress 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 movement cost from one node in N nodes to another at time point T, and is used to encode prior knowledge of travel costs between units; Step S12: Input data; given past data Human activity and movement data at each time step, namely:

[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 is the feature dimension; Step S13: Transmit the data from step S12 into the spatiotemporal embedding module.

[0045] Step S2 includes the following steps;

[0046] 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:

[0047]

[0048]

[0049]

[0050] These are learnable parameters;

[0051]

[0052] The feature dimension is a hyperparameter.

[0053] 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:

[0054]

[0055] 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;

[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 to optimize 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, a 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] where 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 includes the following steps.

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

[0078]

[0079] is a learnable parameter in the transformer layer;

[0080] where 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] where is a tanh activation function; is a ReLU activation function; is a linear transformation operation,

[0084] , ​is a learnable adaptive node vector for obtaining an adaptive adjacency matrix;

[0085] 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 achieved 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:

[0086]

[0087] wherein is a learnable parameter in the graph pooling layer; is a Softmax activation function for tensor normalization;

[0088] 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:

[0089]

[0090] O T is an output feature tensor capturing time dependence; R T is an input tensor in time feature calculation, used for interaction with the query Q and the key K;

[0091] Step S45: in combination with steps S44 and S43, based on the obtained spatio-temporal feature, we use the concept of channel attention for weighted fusion, and finally, we perform channel dimension mapping to obtain the output feature of N2PPL, and the calculation expression is as follows:

[0092]

[0093] wherein is a channel parameter for spatio-temporal data fusion; is a learnable parameter of the mapping layer; represents a deep convolution for assisting better gradient flow.

[0094] 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 spatial feature channel weight, which are used for channel-level adaptive fusion of the output time feature and the spatial feature; is an intermediate feature fused with time and space attention information, is the final output feature of the module.

[0095] Step S5 comprises the following steps:

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

[0097]

[0098] wherein represents the GLU-FFN; represents a GELU activation function, represents a learnable parameter in the FFN;

[0099] Step S6 includes the following steps.

[0100] Step S61: residual skip connection is performed on the data output by each layer of the Propformer, and the calculation expression is as follows:

[0101]

[0102] wherein is a learnable parameter of the (l-1) layer of the residual skip connection, is an output result of the l layer of the Propformer;

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

[0104] Step S62: the features are decoded by using a multilayer perceptron (MLP) head, and a memory bank method is used before the MLP head to enhance the ability to process spatial and temporal uncertainty, to obtain a final prediction; the calculation expression is as follows:

[0105]

[0106] wherein , is a learnable parameter of the decoder final prediction, M s , M t is a spatial / temporal memory module for enhancing the input features; M s captures spatial uncertainty / heterogeneity, M t captures temporal uncertainty / event influence;

[0107] Finally, the L1 loss is selected as a loss function to train the model, and the formula is as follows:

[0108]

[0109] wherein a ground truth of human activity intensity, a Hermes prediction result;

[0110] n represents the total number of samples, i is the sample index, a ground truth of the ith sample, a prediction result of the ith sample. a prediction result of the ith sample.

[0111] The prediction method uses information data of historical human activity intensity, inflow and outflow based on large-scale mobile phone data, and is used for predicting the crowd gathering scale and activity level of a space unit in a census block within two hours in the future with a time granularity of 30 minutes.

[0112] In the present application, a node-to-node propagation learning is proposed, which is a mobility-guided graph learning module that combines a mobility model modeling spatial interaction with graph information propagation; existing methods usually choose nearby places to meet their activity needs, resulting in local heterogeneity in spatial interaction. Therefore, the present proposal introduces a radiation model to calculate the movement probability matrix between nodes, capturing the stochastic process of local mobility decisions; inspired by the gravity model, the inflow and outflow migration amount is introduced to optimize the fitting of movement possibility; the local heterogeneity problem is solved from the perspective of mobility cost. Experiments show that the spatial interaction relationship learned by the module has high interpretability. The inter-node interaction matrix generated by the module presents sparsity, which is highly consistent with human mobility behavior in the real world - that is, people's activities are usually concentrated in a few functional core areas, and there is less interaction between most areas. In addition, the interaction relationship shows a clear "distance decay" effect, that is, the interaction intensity decreases with increasing geographic distance, which is consistent with the first law of geography. More importantly, the interaction scale learned by the module is highly consistent with the observed human community scale travel distance in sociological research, proving that the module not only improves prediction accuracy, but also effectively captures and simulates real human mobility rules, making its prediction results more realistic and reliable.

[0113] In the present application, a node-to-partition propagation learning is proposed, which is a spectrum attention module that dynamically groups nodes based on node attributes and adaptively adjusts according to time evolution patterns; existing methods rely only on pre-existing static partitions for human activity prediction, and they cannot capture temporal dynamics and require additional external data, thereby increasing data collection costs. Therefore, the present proposal proposes a spectral attention, which is not a direct attention of nodes to other nodes, but a dynamic interaction between nodes and partitions using linearized transformer attention. Unlike traditional linear, the spatial partition features are used as additional channel parameters to achieve dynamic and adaptive adjustment of node-partition membership.

[0114] The present application has the advantages of:

[0115] (1) The generalized spatial heterogeneity is cooperatively modeled, and the technical effect is better and stable. The present application simultaneously considers the spatial local heterogeneity and the spatial hierarchical heterogeneity through the N2NPL and the N2PPL mentioned above, and through the ablation experiment, it is proved that the two modules are indispensable for improving the model performance, and are better than the traditional attention mechanism or the simple graph convolution. This double modeling mechanism makes the model have better prediction stability, especially when predicting the activity intensity of the peak and the trough.

[0116] (2) The effective fusion of physical mechanism and deep learning is realized without relying on additional data. Compared with the existing technologies considering the transfer mode (for example, STDEN and ST-PEFs), the present application introduces the method according to the gravity model and the importance parameter for graph propagation , while ensuring to consider the transfer cost, successfully injects the mobile physical priori knowledge into the graph neural network without relying on any additional and expensive fine-grained OD flow data, solves the problem of “paradox” of such methods, and has high application flexibility and practical value. BRIEF DESCRIPTION OF DRAWINGS

[0117] The present application will be further described in detail below in combination with the drawings and specific embodiments:

[0118] The accompanying drawings are attached Figure 1 is the principle framework schematic diagram of the human activity intensity prediction model in the embodiments of the present application. DETAILED DESCRIPTION

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

[0120] In the node-to-node propagation learning, a mobility-guided graph learning module is used to combine the mobility model of spatial interaction modeling and the graph information propagation; a radiation model is introduced to calculate the mobility probability matrix between nodes, to capture the random process of local mobility decision; inspired by the gravity model, the inflow and outflow transfer amount is introduced to optimize the fitting of the movement possibility; the local heterogeneity problem is solved 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 time evolution mode; through spectral attention, a linearized transformer attention is used to establish dynamic interaction between nodes and partitions, and the spatial partition features are taken as additional channel parameters to realize dynamic and adaptive adjustment of the node-partition membership.

[0122] 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;

[0123] Node-to-node propagation learning (N2NPL) uses a node-to-node propagation learning module, specifically: the module is an N2NPL submodule, which models the different contributions of the interaction between individual nodes 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.

[0124] 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 they belong to to address spatial hierarchical heterogeneity, 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, 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.

[0126] The N2NPL submodule is responsible for combining the mobility model that models spatial interaction 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 geographic / attractive information between input data nodes and pass it into a graph convolution component; a graph convolution (Graph Propagate) component for graph network propagation, which aggregates messages for the current node features and adjacency relationships; a replacement component for weighted fusion of the adjacency relationships in the IRM component and the graph convolution.

[0127] The N2PPL sub-module mainly captures the interaction mode between nodes and partitions through learning dynamic partitioning, including a spectrum attention module; its internal components include: a projection layer (K / Q / V Projection) responsible for transforming original features into a representation suitable for attention calculation; a temporal region (Temporal Region) representing the division of the node's historical sequence into several time periods with similar dynamic characteristics in the time dimension; a spatial region (Spatial Region) representing the division of nodes into several regions with similar functions or interaction modes in the spatial dimension; a temporal region attention mechanism (TR Attention) representing the learning of the dependency relationship between different time slices in the time dimension, strengthening the modeling of temporal patterns; a spatial region attention mechanism (SR Attention) representing the learning of the interaction relationship and dependency strength between different spatial regions in the spatial dimension (i.e., the node dimension), strengthening the modeling of spatial patterns; and a linear feature mapping (Projection) that converts 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 a part of neurons control the output of another part", which adjusts the information flow through the "gate" to help selectively activate or inhibit features, improve the nonlinear expression ability and operation performance of the model.

[0129] In the human activity intensity prediction model, the value output by the Propformer is processed through the multi-layer perceptron with memory enhancement (MA-MLP), which converts the stacked high-level spatio-temporal representation into the final prediction, and introduces the "memory" mechanism to retain long-term or global patterns (the overall framework diagram is as follows Figure 1 ).

[0130] The human activity intensity prediction method comprises the following steps:

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

[0132] Step S2: In the spatio-temporal embedding phase, perform spatio-temporal feature coding on the input data ;

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

[0134] Step S4: In the N2PPL phase, dynamically group nodes based on node attributes, and adaptively adjust these groups according to the time evolution pattern;

[0135] Step S5: In the GLU-FNN and hierarchical normalization phase, perform high-performance prediction;

[0136] Step S6: In the MA-MLP stage, residual skip connection and memory enhancement are performed on the data output by the Propformer to enhance the ability to deal with spatial and temporal uncertainty, and then MLP decoding is performed for the final spatio-temporal 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 , where the edge takes distance as weight; 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 , where denotes the T-th time step, and the signal feature tensor of all nodes;

[0139] For each time snapshot, there is also a dynamic spatial division , is the dynamic spatial division result of all nodes at the T-th time step; it provides a soft assignment of N nodes to M partitions at each time step, and gives a movement cost matrix , which represents the movement cost from one node to another node in N nodes at time point T, and is used to encode the travel cost prior knowledge between units; Step S12, input data; given the human activity and flow data in the past time steps, that is:

[0140] human activity intensity ,

[0141] inflow ,

[0142] outflow ; Step S13, pass the data in step S12 into the space-time embedding module.

[0143] Step S2 includes the following steps:

[0144] Step S21, generate a spatial relationship embedding representation; encode the spatial attributes of the node (the area to which it belongs, the geographic coordinates, and the learnable node vector) into a vector, and its calculation expression is as follows:

[0145]

[0146]

[0147]

[0148] are learnable parameters for learning partition and meta-learning;

[0149]

[0150] where C is the original feature dimension of input data X, is an intermediate feature dimension designed for the model;

[0151] Step S22, generating a time relationship embedding representation; encoding time periodicity and holiday information into a vector, whose calculation expression is as follows:

[0152]

[0153] are learnable parameters for learning partition and meta-learning; represents a channel-level connection, is a meta timestamp, which is input for time sequence 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, connecting all embedding features, and applying a Hadamard mapper to effectively convert the features into a linear space while reducing noise, thereby obtaining a complete space-time representation as the input of Propformer, whose calculation expression is as follows:

[0156]

[0157] where is a learnable parameter for changing the feature dimension, is a learnable parameter in Harmard projection;

[0158] H0 is initially 1.

[0159] Step S3 includes the following steps:

[0160] 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 movement possibility, whose calculation expression is as follows:

[0161]

[0162] where is the data of step S12, representing the migration amount flowing into and out of each place; 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; Indicated by 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 calculated by a series of activation functions, the calculation expression is as follows:

[0177]

[0178] Wherein is a tanh activation function; is a ReLU activation function; is a linear transformation operation,

[0179] , is a learnable adaptive node vector used to obtain an adaptive adjacency matrix;

[0180] Step S43: In combination with steps S21, S41 and S42, the formula defines a 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:

[0181]

[0182] Wherein is a learnable parameter in the graph pooling layer; is a Softmax activation function used for tensor normalization;

[0183] Step S44: In combination with step S22, according to the method of obtaining the spatial partition feature, the time feature is calculated, and the calculation expression is as follows:

[0184]

[0185] Step S45: In combination with steps S44 and S43, based on the obtained space-time feature, we use the concept of channel attention for weighted fusion, and finally, we perform Channel dimension mapping to obtain the output feature of N2PPL, and the calculation expression is as follows:

[0186]

[0187] Wherein is a channel parameter used for space-time data fusion; is a learnable parameter of the mapping layer; represents a deep convolution used to assist better gradient flow.

[0188] , respectively represent the time feature channel weight and the spatial feature channel weight. representing fusion features inside the module, representing the final output of the module;

[0189] Step S5 comprises the following steps;

[0190] Step S51: high-performance prediction is achieved by using a feedforward network (FFN) and layer normalization (LayerNorm), and on this basis, effective information filtering is carried out by using a gated linear unit feedforward network (GLU-FFN); the calculation expression is as follows:

[0191]

[0192] wherein represents the GLU-FFN; represents a GELU activation function, represents a learnable parameter in the FFN; r is a dimensional scaling factor for controlling the degree of dimensional expansion of the features inside the model, is a dimensional hyperparameter;

[0193] Step S6 comprises the following steps;

[0194] Step S61: residual skip connection is performed on the data output by each layer of the Propformer, and the calculation expression is as follows:

[0195]

[0196] wherein is a learnable parameter of the (l-1) layer of the residual skip connection, is an output result of the l layer Propformer;

[0197] is a dimensional hyperparameter;

[0198] Step S62: the features are decoded by a multilayer perceptron (MLP) head, and a memory bank method is used before the MLP head to enhance the ability to process spatial and temporal uncertainty, to obtain a final prediction; the calculation expression is as follows:

[0199]

[0200] wherein , is a learnable parameter of the final prediction of the decoder, M s , M t is a spatial / temporal memory module for enhancing the input features; M s captures spatial uncertainty / heterogeneity, M t captures temporal uncertainty / event influence;

[0201] Finally, the L1 loss is chosen as the loss function to train the model, which is expressed in the formula as:

[0202]

[0203] where is the ground truth of human activity intensity, is the prediction result of Hermes.

[0204] n is the total number of samples, is the ground truth of the ith sample, is the prediction result of the ith sample. is the prediction result of the ith sample.

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

[0206] Embodiments:

[0207] In this example, multiple baseline methods including STAEformer, PatchSTG and Gravityformer are selected from the classic to the most advanced time series and spatio-temporal prediction methods for comparison. These methods can be divided into the following four categories: ① classic time series prediction methods, including HA, FC-LSTM and TCN; ② the latest time series prediction methods, including Dlinear and iTransformer; ③ graph-based spatio-temporal prediction methods, including STGCN, GraphWaveNet, AGCRN, DSTAGNN, MegaCRN, ST-Wave, HyGCN, STID, BigST, HimNet and STG-Mamba; ④ Transformer-based spatio-temporal prediction methods, including ASTGNN, STAEformer, STGformer, PatchSTG and Gravityformer.

[0208] To verify the effectiveness of the proposed framework, we conduct experiments on six complex human activity forecasting tasks in major US metropolitan areas (Minneapolis, Atlanta, Boston, San Francisco, Chicago, and Los Angeles). The tasks utilize historical human activity intensity, inflow, and outflow information derived from large-scale mobile phone data to predict the population aggregation scale and activity level within the next 2 hours at a 30-minute time granularity and a census block, a fine spatial unit. The experimental datasets cover different city sizes and spatial structures, aiming to comprehensively evaluate the actual effect of the proposed method in real and diverse urban scenarios, improving prediction accuracy, stability, and generalization ability through modeling of generalized spatial heterogeneity. The specific results are shown in Table 2.

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

[0210]

[0211] Table 2 Continued

[0212]

[0213] The relevant performance evaluation shows that the proposed Hermes framework is superior to all baseline models in most cases. For example, the maximum reduction in RMSE in the core error indicator is about 10%, and MAE and MAPE are also significantly improved. Further analysis by two-sided t-test shows that the above effect improvement has clear statistical significance (p < 0.025), effectively excluding the accidental effects of purely random disturbances. It is worth mentioning that the proposed scheme is particularly outstanding in the smooth control of RMSE, showing lower error and more stable prediction results in all datasets and time periods. Especially in the peak period of high population activity, the error suppression effect of the proposed scheme is more significant, indicating that the framework has strong generalization ability and robustness.

Claims

1. A method for predicting the intensity of human activities based on generalized spatial heterogeneity learning, characterized in that: The prediction method includes node-to-node propagation learning and node-to-partition propagation learning. 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 to capture the stochastic process of local mobility decisions; 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. In the propagation learning from node to partition, a spectrum attention module is used to dynamically group nodes based on node attributes and adaptively adjust according to the time evolution pattern. 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 membership. 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. 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 component for physical inspiration, which calculates a prior propagation weight matrix based on the geographical or attraction information between input data nodes and feeds it into the graph convolution component; a graph convolution component for graph network propagation, which aggregates the current node features and adjacency relationships; and a fusion representation that performs weighted fusion of the adjacency relationships in the IRM component and the graph convolution component. The N2PPL submodule captures the interaction patterns between nodes and partitions through learned dynamic partitioning, including a spectrum attention module. Its internal components include: a projection layer that transforms the original features into a representation suitable for attention computation; a temporal region representation that divides the historical sequence of nodes into several time periods with similar dynamic features in the temporal dimension; a spatial region representation that divides nodes into several regions with similar functions or interaction patterns in the spatial dimension; a temporal region attention mechanism that learns the dependencies between different time slices in the temporal dimension, strengthening temporal pattern modeling; a spatial region attention mechanism that learns the interaction relationships and dependency strengths between different spatial regions in the spatial dimension, strengthening spatial pattern modeling; and a linear feature map that transforms the input features into a new feature space to facilitate data transmission. In the human activity intensity prediction model, the forward propagation of GLU selectively activates or suppresses features, improving the model's nonlinear expressive power and computational performance; In the human activity intensity prediction model, the output value of Propformer is processed by a multilayer perceptron with memory enhancement, and the stacked high-level spatiotemporal representation is transformed into the final prediction. A "memory" mechanism is introduced to retain long-term or global patterns. The method for predicting the intensity of human activities includes the following steps; Step S1: During the data transmission phase, prepare the data required for subsequent processes; Step S2: In the spatiotemporal embedding stage, the input data... Perform spatiotemporal feature encoding; Step S3: In the N2NPL phase, the mobility model of spatial interaction modeling is combined with graph information propagation; 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. Step S5: Perform predictions during the GLU-FNN and hierarchical normalization stages; Step S6: In the MA-MLP stage, by enhancing the ability to handle spatial and temporal uncertainties, residual skip connections and memory enhancement are performed on the entire Propformer output data, and then MLP decoding is performed for the final spatiotemporal prediction. 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 and a fine spatial unit scale.

2. The method for predicting human activity intensity based on generalized spatial heterogeneity learning according to claim 1, characterized in that: 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. The node-to-node propagation learning uses the node-to-node propagation learning module, which is an N2NPL submodule. 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 human movement costs guide information propagation between locations. The node-to-partition propagation learning uses the node-to-partition propagation learning module, which is an N2PPL submodule. 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.

3. The method for predicting human activity intensity based on generalized spatial heterogeneity learning according to claim 1, characterized in that: Step S1 includes the following steps; 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 represents the signal characteristic components of all nodes at the T-th time step; For each time snapshot, there is also a corresponding dynamic space partitioning. ;in This indicates that each time step provides a soft allocation from N nodes to M partitions, where T represents the total number of time steps, and a movement cost matrix is ​​given. This 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: Human activity intensity , Inflow , Outflow ; Where t represents the current time index and C is the original feature dimension of the input data X; Step S13: Pass the data from step S12 into the spatiotemporal embedding module.

4. The method for predicting human activity intensity based on generalized spatial heterogeneity learning according to claim 3, characterized in that: Step S2 includes the following steps; Step S21: Generate spatial relation embedding representation; encode the spatial attributes of nodes into vectors, the calculation expression of which is as follows: These 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, The weight matrix is ​​a learnable matrix. It is a learnable bias vector; in, This represents the original feature encoding after fusion, with dimension . , in This is a spatial soft-assignment matrix used to represent the correspondence between N nodes and M partitions, i.e., geospatial features, with dimensions of [missing information]. ; in This represents the feature representation aggregated through spatial relationships, with a dimension of [dimensionality]. ; The feature dimension is a hyperparameter. The bias vector representing the feature encoding; This represents the bias vector of the spatial soft-assignment intermediate layer; This represents the bias vector of the spatially soft-assigned output layer; A bias vector representing the aggregation of spatial relationships; 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: 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; Where T is the number of time steps and w is the number of time partitions; ; : Time partition matrix, which is the dynamic time partition allocation result obtained by meta-learning; : Basic temporal feature embedding, including the timestamp encoding vector; The final time-partition embedding vector integrates dynamic partitioning information and basic temporal features; 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: in For learnable parameters used to change the feature dimension, These are learnable parameters in the Harmard projection; It is a hyperparameter representing the dimension of the input features; These represent the embedding of daily, weekly, hourly, and spatial features, respectively. , , , Both represent feature dimensions and are hyperparameters; Z in It is a temporal embedding feature tensor, which is obtained by concatenating and linearly mapping meta-features of multiple time dimensions, and is used to encode the temporal periodicity and dynamic patterns of human activities. H p It is a recursively constructed Hadamard transformation matrix used to perform linear transformation and noise reduction on the fused temporal features, and optimize the feature space distribution. yes Transpose of a matrix.

5. The method for predicting human activity intensity based on generalized spatial heterogeneity learning according to claim 4, characterized in that: Step S3 includes the following steps; Step S31, the inflow 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: 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; It is a learnable bias vector; Two power-law learning parameters are used to achieve flexible scaling of some quality terms; and These represent the inflow and outflow migration tensors, respectively. 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: in Indicates position Population size or attractiveness; Indicates position Population size or attractiveness; Indicates With the center of the circle, Within a circular area on the circumference, all locations present opportunities and uncertainties. It is the probability of moving from node i to node j; Step S33: Combining steps S31 and S32, use graph information propagation to transmit the motion pattern back to the tensor of each location, and simulate the impact of the corresponding movement behavior on the activity. Add learnable importance parameters during graph propagation. To achieve differentiated scaling across nodes, the tensor calculation expression is as follows: in This represents the Softmax activation function used to normalize the moving cost matrix; This represents a nonlinear mapping function from graph to graph, used to map the input tensor Z and the shift probability. Transform into an intermediate feature tensor between nodes. , It is an intermediate feature tensor representing the mutual influence between nodes; Step S34: Normalize each feature of the sample through the LayerNorm layer.

6. The method for predicting human activity intensity based on generalized spatial heterogeneity learning according to claim 5, characterized in that: Step S4 includes the following steps; Step S41: Pre-calculate the query, key, and value tensors of the transformer Propformer, with the following calculation expressions: K represents the query tensor, K represents the key tensor, and V represents the value tensor. These are learnable parameters in the Propformer layer of the transformer. Where h represents the number of attention heads. Represents the feature dimensions of each attention head; Step S42: The adaptive spectral adjacency matrix is ​​calculated through a series of activation functions, and its calculation expression is as follows: in The tanh activation function; It is the ReLU activation function; For linear transformation operations, , These are learnable adaptive node vectors used to obtain the adaptive adjacency matrix; A s C represents an adaptive adjacency matrix, used to describe the dynamic connection relationships between nodes; e It is the feature dimension of node embedding; Step S43: Combining steps S21, S41, and S42, define the graph information propagation function in the spectral attention layer. That is, feature diffusion across nodes is achieved through the spectral adjacency matrix As and the geospatial feature Sspatial. Calculate the spatial partitioning features of each layer. The calculation expression is as follows: in, This represents the feature propagation function based on the attention mechanism, used for fusing tensors. Adaptive adjacency matrix A s and geospatial features , This represents the feature tensor obtained after spatial partitioning feature diffusion; in Learnable parameters in graph pooling layers; It is the Softmax activation function used for tensor normalization; O s It is the output feature tensor that captures spatial dependencies; b s1 b s2 It is a learnable bias vector used in spatial feature calculation; 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: 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; Step S45: Combining steps S44 and S43, based on the obtained spatiotemporal features, weighted fusion is performed using the concept of channel interest, and finally, [the process is as follows]. Channel dimension mapping yields the output features of N2PPL, and its calculation expression is as follows: in It is the final output feature tensor after channel dimension mapping; in These are channel parameters used for spatiotemporal data fusion; These are the learnable parameters of the mapping layer; Indicates used for Depth convolutions that facilitate better gradient flow; 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.

7. The method for predicting human activity intensity based on generalized spatial heterogeneity learning according to claim 6, characterized in that: Step S5 includes the following steps; Step S51: High-performance prediction is achieved using a feedforward network and layer normalization, and effective information filtering is performed using a gated linear unit feedforward network; its calculation expression is as follows: in This indicates a gated feedforward network (GLU-FFN) used for further feature processing. Represents the GELU activation function. This represents the learnable parameters in FFN; This indicates a gated feedforward network used for further feature processing. This indicates that the output of the previous layer is normalized. It is a feature transformation function that fuses node features with dynamic spatial partitioning features and models spatial hierarchical heterogeneity. The input is the feature tensor Z of the previous layer, and the output is the feature tensor after fusing heterogeneous information. Step S6 includes the following steps; Step S61: Perform residual skip joins on the data output from each layer of the Propformer. The calculation expression is as follows: 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; It is a dimensional hyperparameter representing the feature dimension in the residual skip connection; Step S62: Decode the features through the multilayer perceptron head and use a memory bank method before the MLP head to enhance the ability to handle spatial and temporal uncertainties and obtain the final prediction; Its calculation expression is as follows: This represents the Lth layer of enhanced features that incorporates spatial and temporal memory information; Represents a non-linear activation function; in , M is the learnable parameter that the decoder ultimately predicts. s M t It is a spatial or temporal memory module that enhances the input features; M s M captures spatial uncertainty or heterogeneity t Capture the impact of time uncertainties or events; Finally, L1 loss was chosen as the loss function to train the model, expressed by the following formula: in This represents the actual ground-level value of human activity intensity. For Hermes prediction results; n represents the total number of samples, and i is the sample index. Let i be the true value of the i-th sample. Let be the predicted value for the i-th sample.

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