GeoAI中的位置编码策略：深度学习模型的关键驱动力

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本文是一篇针对地理人工智能（GeoAI）领域中位置编码方法及其应用的综合评述文章，标题为《GeoAI定位编码方法及应用综述》。作者Gengchen Ma等人来自多个知名机构，包括UC Santa Barbara、Stanford University和University at Buffalo等，他们在文章中探讨了在地质科学和深度学习相结合的背景下，如何有效地处理和编码不同类型的空间数据，如兴趣点（points）、轨迹（polylines）、行政区划（polygons）、交通网络（graphs）以及遥感图像（rasters）。地理位置的数据在地理信息系统（GIS）和人工智能模型中扮演着核心角色，特别是在地理空间分析和预测任务中。为了使这些数据能够无缝融入深度学习模型，关键在于开发和优化位置编码技术。位置编码的目标是将复杂的地理位置信息转换成低维的、连续的向量表示，这种表示既保留了原始数据的地理含义，又能适应神经网络的学习过程。文章详细介绍了几种常见的位置编码方法，包括： 1. **经纬度编码**：最直接的方法是使用经度和纬度坐标，但这种方式在高维度数据中容易造成稀疏性和冗余性问题。 2. **坐标编码**：通过将地理位置映射到一个连续的二维或三维空间，例如Mercator投影或其他正交投影，使得距离在欧几里得空间内有直观的解释。 3. **网格编码**：将地理区域划分为均匀的格子，每个位置用其所在的网格坐标来代表，适用于较小范围的地理数据。 4. **几何编码**：利用位置与地理特征的几何关系，如圆周率编码、球面三角函数等，可以更好地捕捉空间结构。 5. **编码网络**：如自编码器（Autoencoders）和变分自编码器（Variational Autoencoders），用于学习位置数据的潜在分布，提供更高效的压缩和解析。 6. **多模态编码**：结合文本描述、图像或语义信息，生成联合表示，增强位置编码的表达能力。 7. **Transformer架构**：基于注意力机制的编码方式，如PointNet++和Geoformer，能够捕获空间数据的局部和全局特征。 8. **地理编码**：将位置信息与地图坐标系统进行转换，如Google Maps或OpenStreetMap的编码，便于处理大规模地理位置数据。文章还讨论了这些编码方法在实际应用中的优势和局限性，如地理精度、计算效率、模型泛化能力等，并且探讨了未来的研究方向，比如更高效的位置编码算法、多尺度位置编码以及在城市规划、环境保护、灾害预警等领域中的潜力。《GeoAI定位编码方法及应用综述》为GeoAI研究人员和开发者提供了一个全面的框架，帮助他们选择和设计适合特定场景的位置编码策略，以提升地理数据在深度学习模型中的表现和效果。

location encoder deliberately.

Besides the above two spatial information preservation properties, Location Encoder

Enc

pP,θq

should also satisfy the following two properties to ensure its generalizability.

Property 2.3

(Inductive Learning Method)

Location Encoder

Enc

pP,θq

is an

inductive learning method, i.e., the pretrained location encoder can be utilized to

encode any location without retraining even if it does not appear in the training set.

Property 2.3 makes

Enc

pP,θq

diﬀer from many existing transductive-learning-based

location representation learning methods such as Location2Vec (Zhu

et al.

2019a),

POI2Vec (Feng

et al.

2017), and Kejriwal and Szekely (2017). For example, Kejriwal

and Szekely (2017) converted a set of GeoNames locations into a k-th nearest neighbor

graph in which locations (i.e., nodes) are linked to nearby locations by distance-weighted

edges. A random-walk-based graph embedding method is used to learn an embedding

for each location. This method is essentially a transductive learning model: when new

locations are added to the training set, the graph is modiﬁed and the whole model has

to be retrained to obtain the embeddings of new locations.

Property 2.4

(Task Independence)

Location Encoder

Enc

pP,θq

should be task-

independent or so called task-agnostic, i.e., the same model architecture can be used in

diﬀerent downstream tasks without any modiﬁcation.

Property 2.4 also diﬀerentiate

Enc

pP,θq

from some existing task-dependent location

representation approaches. For instance, both Location2Vec (Zhu

et al.

2019a) and

POI2Vec (Feng

et al.

2017) learned the embeddings of locations (e.g., cell stations,

POIs) based on trajectories by adopting a Word2Vec-style training objective. This kind

of location representation cannot be easily transferred to other tasks beyond human

mobility. Similarly, Gao

et al.

(2020) discretized the study area into

N ˆ N

lattice and

learned the embedding of each location by letting a Long Short Term Memory (LSTM)

based artiﬁcial agent navigate through the study area. The learned location embeddings

are used for simulation purpose but not for other geospatial tasks.

Property 2.5

(Parametric Model)

parametric model

is a learning model with a

ﬁnite set of parameters θ.

A parametric model is not very ﬂexible, but the model complexity is bounded. In

contrast, a

non-parametric model

assumes that the data distribution cannot be deﬁned

with a ﬁnite set of parameters

and the size of parameters

can grow as the amount

of data grows

(Russell and Norvig 2015)

. So a non-parametric model is more ﬂexible

while the model complexity is unbounded.

Although Property 2.1, 2.2, and 2.5 are expected for location encoders, not all

models we will discuss in Section 4 have these properties. See Table 1 for the detailed

comparison. However, all location encoders discussed in Section 4 satisfy Property 2.3

and 2.4. So we will not discuss these two properties separately for each model.

For simplicity, we will use Encpq and Enc

pPq

pq to indicate Enc

pθq

pq and Enc

pP,θq

pq.

3. The necessity of location encoding for GeoAI

In this section we motivate the need to embed a location

x P R

(

L “ 2, 3

) into a high

dimensional vector

Enc

pP,θq

pxq P R

, which may seem counter-intuitive at ﬁrst. We

mainly address this issue from a machine learning perspective.

A key concept in statistical machine learning is bias-variance trade-oﬀ (Hastie

et al.

2009). On the one hand, when a learning system is required to pick one hypothesis out

of a large hypothesis space (e.g., deciding the parameters of a large 24 layer neural

networks), it is ﬂexible enough to approximate almost any non-linear distribution (low

bias). However, it needs a lot of training data to prevent overﬁtting. This is called

the low bias high variance situation. On the other hand, when the hypothesis space is

restricted (e.g., linear regression or single layer neural nets) the system has little chance

to over ﬁt, but might be ill-suited to model the underlying distribution and result in low

performance in both training and testing sets (high bias). This situation is called low

variance high bias. For many applications the data distribution is complex and highly

non-linear. We may not have enough domain knowledge to design good models with low

variance (the eﬀective model complexity) and low bias (the model data mismatch) at

the same time. Moreover, we might want to avoid adopting too much domain knowledge

into the model design which will make the resulting model task speciﬁc. For example,

the distribution of plant species (such as

P py|xq

in Figure 1) may be highly irregular

inﬂuenced by several geospatial factors and interactions among species (Mac Aodha

et al.

2019). Kernel (smoothing) methods (e.g., Radial Basis Function (RBF)) and

neural networks (e.g., feed-forward nets) are two types of most successful models which

require very little domain knowledge for model design. They both have well established

ways of controlling the eﬀective model complexity. The kernel methods are more suited

to low dimensional input data – modeling highly non-linear distributions with little

model complexity. However, they need to store the kernels during inference time which

is not memory eﬃcient. Neural networks have more representation power which means

a deep network can approximate very complex functions with no bias, while requiring

more domain knowledge for model design to achieve lower variance and bias.

From a statistical machine learning perspective, the main purposes of location

encoding is to produce

learning friendly representations of geographic locations

for

downstream models such as SVM and neural networks. By learning friendly we mean

that the downstream model does not need to be very complex and require large

training samples. For example, the location encoding process may perform a feature

decomposition (

x P R

Ñ Enc

pP,θq

pxq P R

, where

L ă d

) so that the distribution we

want to model such as

P py|xq

in Figure 1 becomes linear in the decomposed feature

space, and a simple linear model can be applied. Figure 3 illustrates this idea by using

a simple binary classiﬁcation task. If we use the original geographic coordinates

the input features to train the binary classiﬁer, the resulting classiﬁer

will be a

complex and nonlinear function which is prone to overﬁtting as shown in the left of

Figure 3. After the location encoding process, the geographic coordinates feature is

decomposed so that a simple linear model M

can be used as the binary classiﬁer

4. A review of the current landscape of location encoding

In this section, we provide a comprehensive review of the existing location encoding

techniques. Instead of enumerating every existing location encoding approach we

organize our discussion in a top-down manner. We ﬁrst classify location encoding

models into diﬀerent groups according to the input of location encoders and how they

manipulate the spatial features. Firstly, according to the input, we can classify the

existing location encoders into two categories:

single point location encoder Encpxq

The dimensionality of the location embedding space will be larger (e.g., 32 or 128); we use 3D here for ease of

illustration.

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