Revisiting the Modiﬁable Areal Unit Problem in Deep Trafﬁc
Prediction with Visual Analytics
Wei Zeng, Chengqiao Lin, Juncong Lin, Jincheng Jiang, Jiazhi Xia, Cagatay Turkay, Wei Chen
(a) 50x25
region 1
region 2
region 2
scale up
scale up
(b) 100x50
(c) 200x100
(d) Multi-scale Attribution View of uncertainty coefficients
0
1
region 1
Fig. 1. Diagnosing deep trafﬁc predictions across multiple scales. We design Bivariate Maps (a-c) to depict trafﬁc volumes and
prediction errors simultaneously across space, and Multi-scale Attribution View (d) to compare scale-independent metrics across
scales. One interesting observation here is that the volume of region 2 is mainly coming from a particular sub-region on the western
end of the region at scale 200×100. This discrepancy is also highlighted in the 50×25 attribution view where region 2 shows a higher
level of uncertainty as can be seen by the blue coloured dot.
Abstract— Deep learning methods are being increasingly used for urban trafﬁc prediction where spatiotemporal trafﬁc data is ag-
gregated into sequentially organized matrices that are then fed into convolution-based residual neural networks. However, the widely
known modiﬁable areal unit problem within such aggregation processes can lead to perturbations in the network inputs. This issue
can signiﬁcantly destabilize the feature embeddings and the predictions – rendering deep networks much less useful for the experts.
This paper approaches this challenge by leveraging unit visualization techniques that enable the investigation of many-to-many rela-
tionships between dynamically varied multi-scalar aggregations of urban trafﬁc data and neural network predictions. Through regular
exchanges with a domain expert, we design and develop a visual analytics solution that integrates 1) a Bivariate Map equipped with
an advanced bivariate colormap to simultaneously depict input trafﬁc and prediction errors across space, 2) a Moran’s I Scatterplot
that provides local indicators of spatial association analysis, and 3) a Multi-scale Attribution View that arranges non-linear dot plots in
a tree layout to promote model analysis and comparison across scales. We evaluate our approach through a series of case studies
involving a real-world dataset of Shenzhen taxi trips, and through interviews with domain experts. We observe that geographical
scale variations have important impact on prediction performances, and interactive visual exploration of dynamically varying inputs
and outputs beneﬁt experts in the development of deep trafﬁc prediction models.
Index Terms—MAUP, trafﬁc prediction, deep learning, model diagnostic, visual analytics
1
INTRODUCTION
• Wei Zeng and Jincheng Jiang are with Shenzhen Institutes of Advanced
Technology, Chinese Academy of Sciences, China. E-mail: {wei.zeng,
jc.jiang}@siat.ac.cn.
• Chengqiao Lin and Juncong Lin are with Xiamen University, China.
E-mail: {linchengqiao, jclin}@xmu.edu.cn. Juncong Lin is the
corresponding author.
• Jiazhi Xia is with Central South University, China. E-mail:
xiajiazhi@csu.edu.cn.
• Cagatay Turkay is with University of Warwick, UK. E-mail:
cagatay.turkay@warwick.ac.uk.
• Wei Chen is with the State Key Lab of CAD&CG, Zhejiang University,
China. E-mail: chenwei@cad.zju.edu.cn.
Trafﬁc prediction is a key tool for urban transportation and urban plan-
ning helping analysts and planners in improving trafﬁc management
and control [39]. As a result, numerous trafﬁc prediction algorithms
have been developed within the last few decades, such as the auto re-
gressive integrated moving average (ARIMA) [23, 44] that takes ad-
vantage of repeating occurrences in temporal historical data. How-
Manuscript received xx xxx. 201x; accepted xx xxx. 201x. Date of Publication
xx xxx. 201x; date of current version xx xxx. 201x. For information on
obtaining reprints of this article, please send e-mail to: reprints@ieee.org.
Digital Object Identiﬁer: xx.xxxx/TVCG.201x.xxxxxxx
arXiv:2007.15486v3  [cs.CV]  7 Sep 2020

ever, such conventional methods are usually limited when it comes to
modeling the complex non-linear spatial and temporal properties of
urban trafﬁc. Recently, deep neural networks (DNNs) showed supe-
rior performance in trafﬁc prediction. DNN approaches (e.g., [51, 15])
typically partition an underlying territory into grids, aggregate in- and
out-ﬂows in each grid, and model the spatio-temporal ﬂows as a se-
quence of raster images. In this way, urban trafﬁc can be modeled and
predicted using a convolution-based residual neural network [12].
The ﬂow aggregation step is highly crucial in this aforementioned
process, which however, is subject to the modiﬁable areal unit prob-
lem (MAUP) [9, 27]: aggregations are inﬂuenced by both partition
shapes (e.g., grids vs. administrative units) and scales (e.g., coarse
vs. ﬁne granularity) of the spatial partition units (see Fig. 3). The
differences in ﬂow aggregations, which are consumed as network in-
puts, can cause signiﬁcant distortions to network outputs, since DNNs
generally suffer from adversarial perturbation problem [24, 54]. This
is counter-productive for transportation experts who expect stable and
reliable outputs from predictive models [46]. Therefore, it is critical to
incorporate approaches that consider the impact of MAUP within the
diagnosis of deep trafﬁc predictions.
This work seeks to address this need with a visual analytics ap-
proach. This is nevertheless a non-trivial task. First, urban trafﬁc
exhibits dynamic spatial variances. Domain experts would like to an-
alyze spatial associations of prediction accuracies vs. localized trafﬁc
aggregations. However, conventional side-by-side choropleth maps
have limitations in presenting such information simultaneously in a
way that effectively supports comparison [29]. Second, existing meth-
ods [51, 15] measure prediction accuracy using a single numeric statis-
tic, i.e., root mean square error (RMSE), which neglects the unique-
ness of individual region and is not comparable over scales. Consid-
ering how critical it is to understand how perturbations in inputs af-
fect the outputs in improving machine learning models [42], effective
model building requires methods that can support the exploration of
individual regions in relation to scale-independent metrics [7].
To address these challenges, we present a visual analytics solu-
tion with three main visualization modules: (i) A Bivariate Map en-
codes trafﬁc volumes and prediction errors simultaneously on a bi-
variate map. Here we employ a value-suppressing uncertainty palette
(VSUP) [5] to encourage more cautious inspections of error-high re-
gions. (ii) A Moran’s I Scatterplot depicts local indicators of spatial
association (LISA) [2] indices of urban trafﬁc at each region and at a
local tract that corresponds to the size of convolution matrix adopted
by the DNN model. (iii) A Multi-scale Attribution View adopts the idea
of nonlinear dot plot [31] to encode each region as a dot. All modules
leverage unit visualization techniques, i.e., visualizations where each
visual element correspond to a single data point rather than depict-
ing an aggregate [28], in order to enable the investigation of models
over individual data points. We evaluate our system on a real-world
dataset of Shenzhen taxi movements, and demonstrate its effectiveness
through case studies and interviews with domain experts.
The main contributions of this work include:
• A visual analytics system that incorporates various unit visual-
ization techniques, including bivariate choropleth map, scatter-
plot, and nonlinear dot plot, for diagnosing impacts of the MAUP
on deep trafﬁc prediction.
• A new layout strategy for nonlinear dot plot that positions all
dots in a compact manner, and supports ﬂexible arrangement of
multiple dot plots in a tree layout.
• Illuminating insights revealed from case studies, such as im-
pacts of spatial variations on prediction accuracy, which provides
promising directions for improving deep trafﬁc prediction.
2
RELATED WORK
Geographical Partition: Partitioning geographical space into appro-
priate regions is a necessary step in many applications, e.g., urban form
studies [34] and movement visualization [49]. In its simplest form, a
territory can be partitioned into equal-sized grids, yielding a w×h ma-
trix. Many prior studies adopted this approach when visualizing move-
ment data, e.g., [41, 6]. Besides grid-based division, another popular
partition method is by administrative units, which are typically in ir-
regular shapes. Examples include municipalities, districts, and census
tracts. In many circumstances, it is also desirable to construct multi-
ple scales of partitions, which are internally homogeneous and occupy
contiguous regions in space.
The two dimensional properties of partition units, i.e., shaping ef-
fect referring to changes in the shape, and scalar effect referring to
changes in the size, can cause the MAUP, which states that aggre-
gations by different partitions may present different (or even wrong)
patterns [9, 27]. Recent works of utilizing DNNs for trafﬁc predic-
tion [51, 15] partitioned the space by grids, generating ﬁxed-size ma-
trices for network consumption. Nevertheless, effects of the MAUP
on network inputs and prediction performances were neglected. This
work supplements the gap with a visual analytics approach.
MAUP Analysis and Visualization:
Understanding shaping and
scalar effects of the MAUP requires a spatial analytical approach. On
one hand, attributes of spatial data exhibit similarities in nearby spatial
units, as stated by the ﬁrst law of geography −“everything is related to
everything else, but near things are more related than distant things”;
on the other hand, experiments also revealed that values for a partic-
ular measure vary across all spatial units [3]. These characteristics
derive the development of spatial autocorrelation analysis, including
Geary’s C [8], Moran’s I [25], etc. In addition to numerical indica-
tors, researchers also exploited exploratory data analysis approaches
to investigate the effects of the MAUP. Among them, attribute signa-
tures [36] utilized small multiple charts to provide visual summaries
of different statistical variables under the varying levels of aggrega-
tion. Goodwin et al. [10] modeled MAUP as a geo-visual parameter
space analysis [32] problem, and designed a set of glyphs to encode
correlations of a given variable at different scales. Zhang et al. [50]
coupled spatial lens with glyph-based designs to maintain the context
of the spatial clusters at different spatial scales.
Those studies focused on understanding the MAUP across an en-
tire or a subset of dataset, while some other exploratory data analyt-
ics explored the MAUP by examining individual data points. Nelson
and Brewer [26] depicted correlations between a variable and itself
across multiple scales. Zhang et al. [52] interactively explored and
compared the impact of geographical variations for multivariate clus-
tering. Huang et al. [14] recently explored choropleth classiﬁcation
results upon data uncertainty. These works in like manner adopt choro-
pleth maps and scatterplots to depict spatial information and numerical
variables, respectively.
Our work enables investigation of individual regions.
A distin-
guishing feature of our system is that we design Multi-scale Attribu-
tion View, allowing users to compare changes caused by the scalar
effect and corresponding model performances across multiple scales.
Visual Interpretation for Deep Learning: Deep learning (DL) has
advanced ﬁelds such as image and natural language processing. How-
ever, DL models are regarded as a ‘black box’, hindering their usabil-
ity in many domains such as trafﬁc prediction, which requires stable
prediction outputs. An example for stability issues is the adversar-
ial perturbation problem, i.e., marginal input differences may cause
signiﬁcant effects on the output [24, 54]. Cao et al. [4] analyzed the
robustness of DL models against adversarial examples by depicting
the internal datapaths of how adversarial and normal examples diverge
and merge in the prediction process. Many visualizations have been
developed to unveil internal working mechanism, especially the hid-
den layer behaviors, of DL models. Examples for convolutional neural
networks (CNNs) include [48, 18, 30, 17], and recurrent neural net-
works (RNNs) include [21, 35, 16, 33]. Interested readers are referred
to [19, 13, 47] for comprehensive surveys.
Other than depicting internals of DL models, some other methods
focus on understanding the relationships between input features and
output predictions. These methods usually assign each feature an im-
portance score to indicate how it impacts the ﬁnal prediction. For

time
Input
Output
....
Conv. 1
Conv. 2
ResUnit 1
ResUnit L
.......
.....
Fusion
....
Conv. 1
Conv. 2
ResUnit 1
ResUnit L
....
Conv. 1
Conv. 2
ResUnit 1
ResUnit L
closeness
period
trend
Fig. 2. Simpliﬁed architecture of ST-ResNet adopted in our work.
instance, SHAP [20]−Shapley values from game theory−measured
feature attribution from a local perspective, and calculated the feature
contribution of a data point by comparing it with a set of reference data
points. The method is more consistent and locally accurate, in com-
parison with global solutions. A recent work −the What-If Tool [42]
−supports both analysis of decision on a single data point, and under-
standing of model behavior across an entire dataset. Users are allowed
to explore how general changes to data points affect predictions. An
important feature of the tool is ﬂexible sorting, which is crucial for
user-centric explainable AI [38].
Speciﬁcally, this work seeks to understand the relationships be-
tween network input of trafﬁc aggregations that are affected by the
MAUP, and output predictions suffering from the adversarial pertur-
bation problem. We leverage various unit visualization techniques to
enable unit-level investigation.
3
BACKGROUND, TASK, AND SYSTEM OVERVIEW
Table 1. Meanings of all notations.
Notation
Description
T ; t
Set of all time slots; a time slot.
M; m
Set of all movements; a movement.
R; r
Set of all regions at a partition shape and scale; a region.
G; g
Set of all grids for network input; a grid.
xr,t or xg,t
Aggregated trafﬁc in time slot t and region r or grid g.
yr,t or yg,t
Predicted trafﬁc in time slot t and region r or grid g.
The section introduces the research background (Sec. 3.1), followed
by the analytical tasks (Sec. 3.2) and system overview (Sec. 3.3). To
facilitate the discussion, we list down common notations adopted in
this work as in Table 1.
3.1
Background
The interest in the research efforts on trafﬁc prediction have recently
shifted towards DNNs. ST-ResNet [51] as a pioneering work, models
urban trafﬁc as temporal-varying matrices, and employs ResNet [12]
to encapsulate the spatio-temporal dynamics. Fig. 2 presents a sim-
pliﬁed architecture of ST-ResNet adopted in this work. As a ﬁrst step,
the method partitions the entire area into non-overlapping grids at time
slot t, and aggregates trafﬁc in each grid g as xg,t. In this way, a ﬂat-
tened matrix Xt ∈Rw×h representing aggregated trafﬁc in all grids
of size w × h is constructed. Next, ST-ResNet consumes a series
of {Xt|t ∈{t0, · · · , tn}} as network input, and learns the periodic
patterns in the historical trafﬁc. Speciﬁcally, ST-ResNet models the
temporal dependency as: i) trend for weekly trend, ii) period for daily
periodicity, and iii) closeness for recent time dependence. Finally, ST-
RestNet fuses the three learned periodic patterns, and produces a ma-
trix Ytn+1 ∈Rw×h as trafﬁc prediction for time slot tn+1.
However, trafﬁc aggregations are subject to shapes and scales of the
spatial partition units, i.e., the MAUP [9, 27]. As shown in Fig. 3, we
can aggregate urban trafﬁc by different shapes, such as grids (top) or
trafﬁc analysis zones (TAZs) (bottom), and by different scales, such as
2 × 2 (middle) or 4 × 4 (right) grids. Notice that TAZs are in irregular
shapes, we need to further rasterize the results into grids to feed the
neural network. For example, we can rasterize the TAZs into 4 × 4
grids, as the same size with 4 × 4 Grid partition. Though grid sizes
are the same, grid values by griding and TAZ partitions are different,
e.g., x1 ̸= ˜x1. The differences may be marginal, but it may cause
signiﬁcant effects on the output, because DNNs generally suffer from
adversarial perturbation problem [24, 54].
Get-on position
TAZ
Grid
Aggregation by 2x2 grids
Aggregation by TAZs
Rasterization into 2x2 grids
Rasterization into 4x4 grids
Aggregation by 4x4 grids
x1
~
x1
Fig. 3. Aggregations of urban trafﬁc are subject to shapes (e.g., grid vs.
TAZ) and scales (e.g., 2×2 vs. 4×4) of partition units.
In the past eight months, we closely worked with a collaborating re-
searcher (CR) specialized in the ﬁeld of geography and trafﬁc analysis.
CR is interested in applying deep learning techniques in trafﬁc predic-
tion. In the beginning, we divided the studying area into 50 × 25 grids
that is close to the setting adopted in [51], and employed ST-ResNet
for trafﬁc prediction. We showed CR the prediction results in terms
of RMSE, which is a typical metric for evaluating prediction accuracy.
However, CR questioned the choice for 50 × 25 grids, and introduced
the MAUP to us. CR expected a visual analytics to diagnose the pre-
dictions upon different partition shapes and scales.
3.2
Analytical Tasks
To better understand the problem domain, we conducted several
rounds of semi-structured interviews with CR. Rather than attempting
to examine the internal mechanisms of ST-ResNet, CR is more inter-
ested in investigating correlations between input features and output
predictions, such that he can manipulate data processing to ﬁne-tune
the results. In consultation with CR, we distilled three research goals:
G1: understand the MAUP effect on trafﬁc aggregations; G2: under-
stand the output predictions upon variances in input features; and G3:
support the exploration of an individual region. To this end, we com-
pile a set of analytical tasks:
T.1: Spatial Variation Exploration. Urban trafﬁc exhibit dynamic
spatial variance. The experts would like to explore trafﬁc dis-
tributions upon shaping and scaling effects over space (G1 &
G3), and how the output predictions vary accordingly (G2 &
G3). This task requires the solution to present spatially varying
bivariate variables simultaneously.
T.2: Spatial Association Analysis. Furthermore, ST-ResNet applies
2D convolutional operations on the ﬂattened matrix of trafﬁc
aggregations. A 2D convolution applies an element-wise mul-
tiplication of neighborhood matrix indices and a small matrix
of weights, and sums up the results into a single cell. Hence,
it is necessary to support the exploration of spatial associations
among input trafﬁc at individual regions and at local tracts that
are the surrounding regions of a region under investigation (G1),
and explore the effects on output predictions (G2).
T.3: Scale-independent Comparison. Diagnosing the scaling effect
needs to consider feature variances upon scales. The comparison
shall remove the scaling effect of different attribution ranges. Be-
sides, the criteria are measured upon each region, rather than a
summary statistic on the entire area (G3). The visual analytics
should incorporate unit visualization that provides ﬂexibility for
investigating a single data point.
3.3
System Overview
The system mainly consists of three modules: 1) data preprocessing,
2) prediction & analysis, and 3) interactive visualization. In data pre-
processing stage, we process the raw data of two-month (59 days) taxi
movements into network consumable matrices (Sec. 4.2). We select
two types of partition shapes, i.e., grid and TAZ; and three levels of
scales, i.e., 50×25, 100×50, and 200×100. We also experimented
with scale 400×200, but the network failed to converge, probably be-
cause there are too many zero values in the input matrix. For TAZ

24:00
18:00
12:00
06:00
00:00
Weekday
Weekend
2K
4K
6K
8K
10K
border to HK
airport
Fig. 4. Distribution of taxi movements in space (left) and time (right).
shapes, the scales refer to matrix size after rasterization. After pre-
processing, we generate six sequences (two shapes × three scales) of
ﬂattened matrices representing the two-month taxi movements.
In prediction & analysis stage, we select the ﬂattened matrices for
the ﬁrst 52-days from each matrix sequence as training data, gener-
ating in total six ST-ResNet models. Each model is used to predict
trafﬁc for the remaining 7-day testing data. Last, we evaluate the pre-
diction accuracy using scale-independent metrics (Sec. 4.3). Both data
preprocessing and prediction & analysis stages are conducted ofﬂine
on a workstation with 8 core 3.2 GHz AMD Ryzen 7 2700 CPU and
a NVIDIA GeForce RTX 2080Ti graphics card. The training takes
about 20 hours for the scale 50×25, and up to two days for the scale
200×100.
The processed matrices and analysis results are passed to the in-
teractive visualization module. The interface mainly integrates three
coordinated views of a Bivariate Map, a Moran’s I Scatterplot, and a
Multi-scale Attribution View (Sec. 5). The interface is implemented
in LWJGL, with the map, scatterplot, and dot plot rendered with
OpenGL, and overlaid buttons and text realized in NanoVG. The sys-
tem currently runs on an Intel Core i7 2 2.8GHz MacBook Pro with
16GB memory and an AMD Radeon R9 M370X graphics board.
4
DATA PROCESSING AND MODEL EVALUATION
4.1
Input Dataset
The input dataset consists of the following data in Shenzhen, China.
Taxi Transaction Records: The data record taxi transactions made
by over 20k taxis during the period from 1 Jan. 2019 to 28 Feb. 2019
(59 days). There are about 800k transactions recorded per day, sum-
ming up to over 47 million transactions in total. Each taxi transaction
is regarded as an individual movement. For each movement m, the
following attributes are recorded: taxi ID, price, operating mileage,
get-on position (denoted as mp0) and time (mt0), and get-off position
(mp1) and time (mt1). The raw data contains various corrupt or in-
accurate records, such as locations outside Shenzhen, or missing get-
on/-off times, etc. We cleaned up the data to alleviate the effects on
the following experiments. After data cleaning, there remain about 45
million valid transaction records.
Trafﬁc Analysis Zones: A TAZ is a geography unit constructed by
census block information for tabulating trafﬁc-related data. The spa-
tial extent of TAZs varies, which are typically large areas in the exurb
and small blocks in central business districts. In this way, the number
of people in each zone is balanced, such that to better couple with con-
ventional trafﬁc planning and demand analysis. This work leverages
TAZs of 1066 zones delineated by Shenzhen transportation ofﬁcials.
An illustration of the TAZs is presented in Fig. 4 (left). Notice that the
zones are typically small where trafﬁc volumes are high.
Fig. 4 presents spatial (left) and temporal (right) distributions of
journey origin locations and times averaged over every 30 minutes.
Fig. 4 (left) depicts that the taxi movements are concentrated in south-
ern parts of the city, which are central business districts on border
with Hong Kong. There is also a high-volume zone in the west where
the airport is located. Less taxi movements are found in other places.
Fig. 4 (right) show averaged trafﬁc on weekdays (red) and weekends
(blue), respectively. The distributions show dramatic drops of taxi
movements after midnight, whilst the drop delays about one hour on
weekends. A morning peak hour can be found at around 9:00 on week-
days. Some other peaks can be found at around 15:00, 18:00, and
22:00 on both weekdays and weekends. The dramatic spatial and tem-
poral variances bring challenges for trafﬁc predictions.
4.2
Data Preprocessing
ST-ResNet is designed to consume a sequence of ﬁxed-sized matrices.
Before training, we need to process the raw taxi movements to ﬁt the
network inputs. The preprocessing takes the following steps:
• Geographical partition: To explore the shaping effect, two par-
tition shapes are tested: grids and TAZs. The studying area has
been divided into 1066 partitions in TAZ, yet we need to deter-
mine the size for Grid partition. We check ranges of the studying
area, which are [113.775, 114.629] in longitude, and [22.443,
22.855] in latitude. That is, the range of longitude is roughly
two times of latitude. To accommodate the matrix size adopted
in ST-ResNet [51], that is 32×32, we choose a similar size of
50×25 as the coarsest scale. Next, to diagnose the scalar effect,
we would like to compare multiple partition scales. CR noted
that smaller matrix size will make each grid cover a too large un-
derlying area, which is useless for trafﬁc prediction. Therefore
we choose ﬁner scales of 100×50 and 200×100.
• Aggregation: We split each day into 48 time slots, with each
slot covering 30 minutes. There are in total 2832 (59 × 48) time
slots, i.e., |T | = 2832. Next, we assign taxi movements into
each time slot t based on their getting-on times, which can be
represented as Mt = {m ∈M|mt0 ∈t}. Next, we separate
Mt into regions based on their get-on positions. The regions of a
particular partition shape and scale are denoted as R = {ri}n
i=1,
where n = 1066 for TAZ partition, and n = 1250 for scale
50 × 25, n = 5000 for scale 100 × 50, and n = 20000 for scale
200×100 under Grid partition. The regions are non-overlapping
and ﬁll up the studying area. Thus, we can ﬁnd unique region r
for a movement m that meets the condition mp0 ∈r.
In this way, we derive a nonnegative integer xr,t counting the
number of movements in a region r and time slot t.
Aggregations for Grid partition are naturally in a matrix format that
can be directly consumed by ST-ResNet. On the other hand, TAZ
partitions are in arbitrary shapes, and possess only one scale. In order
to be used as network inputs and enable multi-scale comparison, we
further adopt the following steps for TAZ partitions.
• Rasterization: The process is to convert TAZ-based trafﬁc ag-
gregations Xr
t into a raster matrix Xg
t ∈Rw×h. Each grid g
could intersect with arbitrary number of TAZ regions {ri}k
i=1.
We calculate the value for each grid xg,t as:
xg,t =
k
X
i=1
xri,t × S(ri ∩g)
S(ri)
(1)
where S(·) stands for the area of a region, and ri ∩g indicates
the intersection between ri and g.
By this, we generate a sequence of raster matrices {Xt|Xt ∈
Rw×h} as network inputs for both Grid and TAZ partitions. Note that
the rasterization of TAZ partition is employed to ﬁt in ST-ResNet in-
puts only. One can easily compute predicted ﬂow volume for each
TAZ partition from predicted ﬂow volumes of grid partitions by ST-
ResNet. Nevertheless, the rasterization operation obliterates neighbor-
hood relationships among original TAZ partitions, which may cause
negative effects on trafﬁc predictions. This is regarded as a limitation
of deep trafﬁc prediction with 2D convolutions [15].
4.3
Scale-Independent Evaluation Metrics
To support multi-scale comparison (T.3), the comparison metrics
should be scale-independent to remove the scaling effect of different
value ranges. We select three metrics satisfying this requirement [7]:
percentage RMSE (PRMSE), uncertainty coefﬁcient (U), and corre-
lation coefﬁcient (CORR). The coefﬁcients are useful for comparing
different forecast models, e.g., whether a sophisticated model is, in
fact, any better than a simple one that repeats the last observed value.
We measure the metrics for each grid, such that to support the goal
of exploring a region (G3). This is possible because each grid g pos-
sesses a sequence of predictions {yg,t} and observations {xg,t}, for
t ∈{t1, · · · , tn}. The metrics can be measured as follows:

• PRMSE measures variances between the predictions and obser-
vations, which is calculated as:
PRMSEg = 1
xg
r
1
n
Xtn
t=t1 (yg,t −xg,t)2
(2)
where xg is the mean value of observations in g.
Value of
PRMSE is positive, and is preferred to be close to 0.
• Uncertainty coefﬁcient (U) measures how well a time series of
predictions match with a time series of observations.
Ug =
q
1
n
Ptn
t=t1 (yg,t −xg,t)2
q
1
n
Ptn
t=t1 y2
g,t +
q
1
n
Ptn
t=t1 x2
g,t
(3)
Value of U ranges from [0, 1], and is preferred to be close to 0.
• Correlation coefﬁcient (CORR) measures how strong is the rela-
tionship between the predictions and observations.
CORRg =
Ptn
t=t1
 yg,t −yg

(xg,t −xg)
qPtn
t=t1(xg,t −xg)2
qPtn
t=t1(yg,t −yg)2
(4)
Value of CORR ranges in [-1, 1], where 0 indicates no relation-
ship and +/-1 indicate perfect positive/negative correlations.
5
VISUALIZATION DESIGN
To address the analytical tasks (Sec. 3.2), we follow the following ra-
tionales in designing the interface:
R.1: Coordinated Views: Various input features could cause predic-
tion errors, e.g., spatial heterogeneity, local autocorrelation, etc.
To comprehensively reveal the correlations between input fea-
tures and output predictions, coordinated multiple views (CMV)
that support visual analytics from multiple joint-perspectives
would fulﬁll the requirement.
R.2: Overview + Details: The visual analytics should provide an
overview of data attributions over space and across multiple
scales, and allow users to explore details on demand. Efﬁcient
selection operations shall be incorporated to support examina-
tion of a single or a subset of data points.
R.3: Unit Visualization:
Aggregated statistics and visualization
would support the analytical tasks, such as to explore trafﬁc
variance over space (T.1). Instead, unit visualization can main-
tain the identity of each visual mark and its relation to a data
item [28]. Unit visualization needs to also support sorting by
particular criteria of importance, which is encouraged for user-
centric explainable AI [38].
Based on these rationales, we design a CMV system that primar-
ily incorporates three unit visualization modules of a Bivariate Map
(Sec. 5.1), a Moran’s I Scatterplot (Sec. 5.2), and a Multi-scale Attri-
bution View (Sec. 5.3). We also integrate a set of interactions (Sec. 5.4)
to facilitate system exploration.
5.1
Bivariate Map
We design Bivariate Map to support spatial variation exploration (T.1).
The view is essentially a bivariate choropleth map that simultane-
ously depicts trafﬁc volume and prediction error at each grid. The
bivariate map is constructed as follows: For each grid g, we com-
pute the mean value of observed trafﬁc xg in the testing data as the
ﬁrst dimension, then compute the mean value of absolute prediction
errors Ptn
t=t1(|yg,t −xg,t|)/n as the second dimension. We divide
the ﬁrst dimensional values into eight ranges, while the second di-
mensional values are divided into four ranges. Then, we encode the
two-dimensional values using a value-suppressing uncertainty palette
(VSUP) [5]. As shown in Fig. 5(a), the VSUP is in wedge shape, in-
stead of a conventional bivariate colormap in square shape. By this
adaption, VSUP emphasizes those grids with higher prediction errors,
high volume,
high error
low volume,
high error
low error
(b) Temporal
View
(a) VSUP
Fig. 5. Bivariate Map adopts a value-suppressing uncertainty palette
(VSUP) (a) to simultaneously present trafﬁc volumes and prediction er-
rors over space. Temporal View (b) is shown for a selected partition,
presenting temporal variations over all time stamps.
Prediction
Observation
Fig. 6. Arranging choropleth maps side-by-side is an alternative design
choice for the bivariate map.
i.e., colors towards outbound of the wedge. From Fig. 5, we can no-
tice that grids with high prediction errors are mostly concentrated in
the south, which also exhibit high trafﬁc volumes.
The view allows users to select speciﬁc grids for in-depth investi-
gation. Upon selection, variations of trafﬁc volumes and prediction
errors over all testing time slots (7 days×48 slots/day) are presented
as a heatmap (Fig. 5(b)).
The heatmap adopts the same color en-
codings as the VSUP. Multiple grids can be selected for comparison,
and heatmaps can be dragged around to mitigate occlusion. Fig. 5(b)
presents temporal view of a grid in central business district, which
produces the highest prediction errors under Grid partition at scale
50×25. We can observe that the grid exhibit high trafﬁc volumes and
high prediction errors throughout all the time slots.
Alternative design. Besides the bivariate map, an alternative design
choice is to arrange two choropleth maps side-by-side. An example is
shown in Fig. 6. Here, the left one presents observed trafﬁc volumes,
while the right one presents predicted trafﬁc volumes. The views ef-
fectively depict dynamic spatial variations, and reveal strong corre-
lations between observations and predictions. However, prediction
errors are not obvious, as grids on both sides show almost the same
colors; see insets for an example. Alternatively, we can also directly
present prediction errors in the right-side choropleth map. Though
the design can better depict prediction errors, users need more efforts
to link the grids in side-by-side views. Therefore, the design cannot
compete with the bivariate map.
5.2
Moran’s I Scatterplot
The Moran’s I Scatterplot is designed to reveal the spatial autocor-
relation of trafﬁc volumes in each grid-based partition and local tract
(T.2). There exist many indicators for spatial association analysis, e.g.,
Geary’s C [8], Moran’s I [25], etc. Among them, Moran’s I is perhaps
the most widely used metric, which can be measured as:
I =
n
P
i
P
j wij
P
i
P
j wij(xi
g −xij
g )(xj
g −xij
g )
P
i(xig −xij
g )2
(5)
where xi
g indicates trafﬁc volume of grid i surrounding grid g, xij
g is
the mean volume of all surrounding grids, n is the number of spatial
grids indexed by i and j, and wij is an element of spatial weights.
Here, we opt to the ﬁrst-order queen contiguity spatial weight matrix,
which is a common choice in the literature [53, 26]. We choose 3 × 3
for the matrix size, corresponding to the setting of convolution kernel
size adopted by ST-ResNet.

Regression line
color by
standardized error
error increases
Fig. 7. Moran’s I Scatterplot depicts local autocorrelation of spatial as-
sociation between trafﬁc volume in regions and in local tracts.
To support the investigation of each region, we decompose the
global Moran’s I into local indicators of spatial association (LISA) [2]
indices. In this way, each region can be represented as a point in the
scatterplot as shown in Fig. 7. The point position corresponds to traf-
ﬁc volume of region along x-axis, and trafﬁc volume of local tract
along y-axis. The point color indicates prediction error. To couple
with multi-scale comparison, we standardize trafﬁc volumes and pre-
diction errors with a mean of 0 and variance of 1. The mean of all
LISA indices is proportion to the global Moran’s I, which is repre-
sented as a regression line. The correlation and conﬁdence are also
presented. Selected points will be highlighted in blue and the point
sizes are enlarged; see an example in Fig. 7.
Fig. 7 presents the corresponding scatterplot for the bivariate map
in Fig. 5. Most points are positioned around the regression line. A
correlation value of 0.793 and conﬁdence p < 0.01 indicate a strong
positive correlation. The point colors gradually change from light yel-
low (low prediction error) to dark yellow (high prediction error) from
left to right, whilst marginal changes are observed in y-dimension.
This indicates that the prediction accuracy is more dependent on traf-
ﬁc volume of region, rather than trafﬁc volume of local tract.
5.3
Multi-scale Attribution View
We design Multi-scale Attribution View to support scale-independent
comparison (T.3). To enable the comparison of individual regions, we
opt to unit visualization techniques rather than an aggregated visual-
ization presenting a summary statistic. This is nevertheless a nontriv-
ial task, because there are huge amounts of regions to display and the
data attributions exhibit dynamic variances. To this end we choose
dot plots [43], which encodes each data point as a dot. However,
conventional dot plots using constant dot size cannot effectively ad-
dress scalability and dynamic variance issues. Inspired by nonlinear
dot plots [31], we employ adaptive dot sizes and propose a new layout
algorithm to address these issues.
The plot is constructed through the following procedures:
1. Sorting: We ﬁrst put all region into a list, which is the simplest
and most common way to construct explanation [38]. The list is
then sorted in ascending order by absolute prediction error, such
that the region with high prediction errors will be emphasized.
2. Layout: Next, we place the regions in the display space, as il-
lustrated in Fig. 8 (top). The layout algorithm takes input of an
ordered list of data points D := {D1, · · · , Dk} where Di in-
dicates a region, together with an enclosing rectangle (W, H)
where W & H indicate the width and height, respectively.
The layout problem is essentially to divide D into n columns
C := {C1, · · · , Cn}, where each column Ci contains a set of
data points {Di,1, · · · , Di,ci} ⊆D.
For each Di,j, we calculate its diameter in proportion to traf-
ﬁc volume of the region, denoted as di,j; and for each Ci, we
can derive the width Wi as Wi = max(di,1, · · · , di,ci), and
the height Hi = Pci
j di,j. We formalize the problem as a con-
strained optimization problem, with an objective to ﬁnd the op-
timal column number n and row number ci of each column Ci,
0
PRMSE:
50
{
{
H1
W1
W2
W3
Wn
∑Wi
d1,1
d1,2
d1,3
d1,c1
size by
traffic volume
position by
prediction error 
color by
scale-independent metric
Fig. 8. Multi-scale Attribution View: illustration of the layout algorithm for
positioning dots in an enclosing rectangle (top); arrangement of three-
scale dot plots in a hierarchy structure to facilitate comparison over mul-
tiple scales (bottom). Highlighting a region at a coarse scale will also
highlight its sub-regions at ﬁner scales.
such that the height of each column approximates the average
height of all columns H = Pn
i=1 Hi/n, and the aspect ratio is
as close as possible to that of the enclosing rectangle:
arg min
n,ci
X
i
|
ci
X
j=1
di,j −H| + |
P
i Wi
H
−W
H |
(6)
constrained to Pn
i=1 ci = k , 0 < n, ci < k. We solve the
problem by ﬁrstly initializing n with an estimated value n =
q
k × W
H , and ci to satisfy Pci
j=1 di,j ≈Pk
i=1
di
n . The optimal
variable values are achieved through some turbulence.
3. Color coding: We color code each dot according to a scale-
independent metric (see Sec. 4.3) speciﬁed by users. For ex-
ample, dots in Fig. 8 (bottom) are colored by PRMSE.
Arrangement: To facilitate multi-scale comparison, we organize three-
scale dot plots under the same partition shape in a hierarchical struc-
ture, as seen in Fig. 8 (bottom). Speciﬁcally, we divide the data points
into four subsets at scale 100×50, where each subset posses around
one-fourth of all trafﬁc volumes; then we generate one dot plot for
each subset, and arrange the four dot plots side-by-side. Similarly, we
generate 16 dot plots at scale 200×100. This arrangement reminds
users that a partition at scale 50×25 corresponds to four partitions at
scale 100×50, and 16 partitions at scale 200×100.
In summary, the Multi-scale Attribution View utilizes the following
visual channels to represent data attributions.
• Position encodes absolute prediction error. At each scale, dots
are positioned from left to right in ascending order of prediction
errors; within each column, the dots are positioned from top to
bottom in ascending order of prediction errors.
• Size encodes trafﬁc volume. Since total trafﬁc volumes at all
three scales are the same, dot sizes are comparable across scales.
• Color encodes one of the scale-independent evaluation metrics.
The three-scale dot plots share the same colormap, thus the dot
colors are also comparable across scales.
Alternative design.
An alternative design here is nonlinear dot
plots [31].
The paper proposed many strategies for adapting dot
sizes, such as making the column height following logarithmic scale
(Fig. 9(a)) or constant height (Fig. 9(b)). In comparison to the plot by
our algorithm (Fig. 9(c)), those size adaption strategies produce differ-
ent visual representations of data attributions, as follows:
• Position: In Fig. 9(a&b), each stack is positioned horizontally
based on prediction error of the dot in the bottom. The other

(a) Nonlinear dot plot in logarithmic scale
(b) Nonlinear dot plot in constant height
(c) Nonlinear unit plot by our algorithm
Fig. 9. Alternative designs: nonlinear dot plots in logarithmic scale (a)
and constant height (b) by [31], and by our algorithm (c).
dots in the stack are those data points nearby. In this sense, posi-
tions of most dots infer only relative ordering, as the same with
ours. However, the stacking strategy will leave many paddings
in-between stacks, causing space usage deﬁciency.
• Size: Dot sizes in Fig. 9(a&b) are adjusted based on the num-
ber of dots in each stack, which is essentially the frequency of
data distribution. In contrast, our algorithm determines dot size
according to explicit trafﬁc volume, which promotes correlation
analysis between input trafﬁc and output prediction. As shown
in Fig. 9(c), dot size generally grows from left to right.
• Color: All plots encode scale-independent metrics using color.
However, their algorithm may cause misleading correlation anal-
ysis, and spoil multi-scale comparison because dot sizes reﬂect
data distributions instead of explicit trafﬁc volume. As shown
in Fig. 9(a&b), the left part exhibits obvious plum colors. Users
may perceive high PRMSE values, however these regions count
up to insigniﬁcant trafﬁc volume as in Fig. 9(c).
5.4
User Interactions
In addition to basic map navigations, our system also integrates vari-
ous interactions that enable:
• Exploration: First, the interface includes widgets to explore par-
tition scales (50×25, 100×50, and 200×100) and shapes (grid
and TAZ). Second, Multi-scale Attribution View allows users to
select one out of the three scale-independent metrics (PRMSE,
U, and CORR). The metric range is determined by the minimum
and maximum values across all scales.
• Selection & Filtering: Users can select a speciﬁc data point of
interest with Point selection tool, or ﬁlter a subset of data points
with Rect or Lasso tools. The tools apply to all views, i.e., bi-
variate map, scatterplot, and attribution view. Selected/ﬁltered
data points are highlighted in blue color. Speciﬁcally for data
points selected by Point tool, heatmaps (see Fig. 5(b)) are shown
on the map view, presenting detailed variations of ﬂow volumes
and prediction errors in each time slot over seven days.
• Linking. Automatic linking among the three visualization mod-
ules is supported for coordination across multiple views. Fig. 10
presents an example. Here, we ﬁlter points of high prediction
errors in the scatterplot with Lasso tool, and corresponding re-
gions will be highlighted in the map. The regions are located in
the southern part of Shenzhen, which borders on Hong Kong and
is more developed than other regions.
6
EVALUATION
The inline ﬁgure presents RMSEs generated by the six ST-ResNet
models. The statistic varies upon both partition shapes and scales.
For both Grid and TAZ partition, the coarsest scale 50×25 yields the
highest RMSE, and RMSE drops to similar values at scale 100×50.
The decline could be due to either improvement in network predic-
tions, or simply the increase in number of partitions. Interestingly in
the ﬁnest scale 200×100, RMSE continues to drop for TAZ partition,
but increases for Grid partition.
Linking
lasso
filtering
flitered partitions
on the map
Fig. 10. The views are linked: ﬁltering points in the scatterplot (left)
highlights corresponding grids on the map view (right).
To unveil the underlying mechanism, we
conduct three case studies in diagnosing pre-
dictions across multiple scales (Sec. 6.1) and
by different partition shapes (Sec. 6.2), and
exploring individual unit (Sec. 6.3). In the
end we present expert reviews (Sec. 6.4).
6.1
Study 1: Diagnostics of Multiple-
scale Predictions
From the above analysis, we observe that the RMSE varies upon par-
tition scales. To eliminate the confounding factor of partition num-
ber, this study compares predictions across multiple scales using scale-
independent metrics. Here, we select Grid partition and compare pre-
dictions of scales 50×25, 100×50, and 200 ×100. Fig. 1 presents the
bivariate maps on the top, and the attribution view in the bottom.
All the bivariate maps present dynamic spatial variations: dark
colors (i.e., high prediction errors) are concentrated in the south-
ern regions of the city, which are more developed areas and most
taxi movements are there; in contrast, the regions towards the north
show light colors (i.e., low prediction errors). Moreover, we can no-
tice that Fig. 1(a)&(b) share similar maximum prediction errors, but
Fig. 1(b) presents less dark colors than Fig. 1(a). This indicates that
scale 100×50 improves network predictions for many grids than scale
50×25. Instead, the maximum prediction error in Fig. 1(c) is two
times of that in Fig. 1(b), whilst the two maps exhibit similar color dis-
tributions. Hence the predictions are not improved from scale 100×50
to scale 200×100, which explains the increase of RMSE.
Fig. 1(d) compares uncertainty coefﬁcient (U) across multiple
scales. We notice that dots at scales 50×25 and 100×50 are mostly in
green or lemon (low uncertainties), whilst those at scale 200×100 are
mostly in plum (high uncertainties). Speciﬁcally, we select two par-
titions from dot plot of scale 50×25: partition 1 presents the highest
prediction error but low uncertainty, while partition 2 shows a lower
prediction error but high uncertainty. The dots of their sub-partitions
are also highlighted in the dot plots of scales 100×50 and 200×100.
We can observe that most sub-partitions of partition 1 have high pre-
diction errors and low uncertainties, whilst most sub-partitions of par-
tition 2 show low prediction errors and high uncertainties.
6.2
Study 2: Comparison of Different Partition Shapes
Grid and TAZ partitions share similar RMSEs at scale 100×50. Nev-
ertheless, RMSE is a summary statistic that can not reveal uniqueness
of individual unit. To overcome this limitation, this study compares
predictions of individual units over different partition shapes.
Fig. 11 presents the results by Grid partition (a) and TAZ parti-
tion (b), both at scale 100×50. Overall the views present largely the
same results, yet minor differences exist. In the map views, neigh-
boring regions share more similar predictions in Fig. 11(b) than those
in Fig. 11(a). This is expectable because rasterization in TAZ parti-
tion eventually smoothen trafﬁc volumes in neighboring regions. The
scatterplots prove the argument, as the points are more concentrated
nearby the regression line in Fig. 11(b). From the attribution views,
we can observe that Fig. 11(b) present more lemon dots in PRMSE,
especially for those dots on the left side. That is, TAZ partition gener-
ates more accurate predictions than Grid partition in terms of PRMSE
at scale 100×50, though their RMSEs are similar.

(a) Grid partition
(b) TAZ partition
PRMSE
CORR
U
airport
airport
airport
airport
airport
airport
station
station
station
station
station
station
Fig. 11. Comparing predictions by Grid partition (a) and TAZ partition (b) of the same scale 100×50. Though the two partitions produce similar
RMSEs, our system reveals that TAZ partition performs better in terms of PRMSE, U, and CORR.
airport
airport
(a) Grid partition, 200x100 scale
(b) TAZ partition, 200x100 scale
station
airport
station
station
station
airport
Fig. 12. Investigating prediction variations over time of individual re-
gions. The airport shows great differences in Grid partition (a) and TAZ
partition (b), while the difference is minor for the station.
In addition, individual units present rather different outputs. Here
we select two units with highest prediction errors in Grid partition: one
locates the airport, while the other one locates a high-speed railway
station. Both have high trafﬁc volumes. As shown in Fig. 11(a), they
are salient in the map view, and are far away from the regression line in
the scatterplot. On the other hand, the units are much less noticeable in
Fig. 11(b), especially the airport. The collaborating expert CR found
a possible reason: the airport is located in a remote area where the
TAZ is large −trafﬁc is shared with neighboring regions; in contrast,
the station is in the city center where the TAZ is small −trafﬁc is not
shared with neighboring regions.
6.3
Study 3: Investigation of Individual Units
To understand why RMSE of TAZ partition at scale 200×100 contin-
ues to decline while that of Grid partition increases, this study con-
ducts in-depth investigation of prediction variations over time of indi-
vidual units. Fig. 12 presents temporal views of the airport and sta-
tion by Grid partition (a) and TAZ partition (b) at scale 200×100. By
comparing the scatterplots in Fig. 12 with those in Fig. 11, we can ob-
serve that the points in Fig. 12(a) (Moran’s I 0.834) are more sparse
than those in Fig. 11(a) (Moran’s I 0.828) −spatial heterogeneity in-
creases when Grid partition scales up. On the other hand, the points
in Fig. 12(b) (Moran’s I 0.922) are more concentrated that those in
Fig. 12(b) (Moran’s I 0.891) −spatial heterogeneity remains when
TAZ partition scales up.
In Fig. 12(a), the airport and station are far away from the regression
line, and the points are in dark orange colors. Their partition/tract
volume ratios are bigger, indicating more granularity in Grid partition
enlarges trafﬁc volume differences between neighboring partitions. By
referring to their temporal views, we can notice that the airport exhibits
high trafﬁc volumes and high prediction errors throughout the whole
day, whilst the station shows low prediction errors between midnight
to six o’clock in the early morning. The difference is likely due to
the fact that high-speed railway service are terminated before dawn,
while the ﬂight service operates all day. From the comparison, we
can observe that the airport and station points are much closer to the
regression line in Fig. 12(b). The station point in Fig. 12(b) is still in
orange, but lighter than that in Fig. 12(a). The airport point changes
to light orange, indicating a lower prediction error. The differences
are more visible in the temporal views, where the airport unit exhibits
mostly light colors.
6.4
Expert Review
We conducted interviews with two independent experts (denoted as EA
and EB) other than our collaborating researcher CR. Both experts are
specialized in transportation, and have been actively working on trafﬁc
management for several years. Each interview lasted for around one
hour. In the ﬁrst thirty minutes, we explained visual designs adopted
in the system, demonstrated how the system works, and presented case
studies. Next, we allowed them to explore the system for about twenty
minutes. In the end, we collected their feedbacks.
Methodology.
Both experts have experimented with deep learning
models, but “most often the outcomes are suspicious”. EB pointed out
“interpretable outcomes will make deep learning more useful in trafﬁc
management”. In this sense, both experts appreciated the efforts on
developing a visual analytics to diagnose the predictions. They also
agreed with CR to start with the MAUP, which is a hot topic in trans-
portation and geography. They especially appreciated the capability of
investigating an individual region, which was not supported by most
works they followed up.
Interactive Visual Design. Both experts conﬁrmed that the interface is
nicely designed in accordance with the analytical tasks. They agreed
with the choice of multiple views to depict information from multiple
perspectives, and they appreciated the linking among views. EA high-
lighted “it is important that I can select a partition in the scatterplot or
attribute view, and see where it is on the map”. All experts (including
CR) were not aware of the term ‘unit visualization’, though they have
utilized choropleth map and scatterplot before. They easily adapted

to the concept and felt “deﬁnitely better than summary statistics (e.g.,
the RMSE ﬁgure) that omit details”. EA and EB were familiar with
conventional bivariate colormaps provided in GIS software such as
Esri ArcGIS, but not with the VSUP [5]. After understanding the
visual encodings, they acknowledged that VSUP is more suitable in
this work, as VSUP leverages fewer colors and emphasizes partitions
with higher prediction errors. In addition, all experts (including CR)
agreed that the bivariate map using VSUP surpasses the performance
of side-by-side maps. From Fig. 5, “we know which partitions should
be examined”, EA commented.
The experts felt some difﬁculty in understanding the multi-scale at-
tribution view. They fully comprehended the visual encodings only
after we illustrated how the view is constructed (Fig. 8) and showed
the comparison with non-linear dot plots (Fig. 9). At ﬁrst EA showed
his preference of the non-linear dot plot in constant height (Fig. 9(b)),
which “is easy to understand”. He nevertheless agreed that our design
“is more accurate and useful”, after we explained that over-sized dots
of low-volume partitions could cause misleading correlation analysis.
Both experts liked the arrangement of multiple dot plots in an hierar-
chical structure, which “facilitates the multi-scale analysis of spatial
heterogeneity”, EA pointed out.
Applicability. The experts were intrigued to ﬁnd out how the MAUP
affects deep trafﬁc prediction. As depicted in the Moran’s I scatterplot
(Fig. 7), prediction errors increase in line with ﬂow volumes in parti-
tion, but not with those in local tract. The difference is proved in study
2 that compares predictions of the airport and the highway station.
Here peak ﬂow volumes of the airport are distributed to the neigh-
boring partitions under TAZ partition, and the prediction error drops
dramatically. The studies demonstrated that TAZ partition better sup-
ports deep trafﬁc prediction, coinciding with many empirical studies in
trafﬁc analysis relying on spatial partition. Transportation researchers
have gained much experience in ﬁnding proper spatial partitions, and
the studies illustrate how the experience could be applied to improve
deep learning models. Based on the insights, the experts can “focus on
generating reasonable input features, rather than tuning parameters of
complex neural networks that we are not familiar with”, EA suggested.
7
DISCUSSION
The studies provide several illuminating insights: Study 1 shows that
ﬁner grained partition scales may generate worse scale-independent
metrics. The result is opposite with that derived from RMSE (the in-
line ﬁgure in Sec. 6) −a performance metric widely adopted for deep
trafﬁc prediction. Taking Grid partition for an example, RMSE sug-
gests that scale 100 × 50 achieves better performance than the other
two scales, but Fig. 8 reveals that the coarsest scale 50 × 20 produces
lowest PRMSE as most dots in the scale are in lemon color. A pos-
sible cause for this phenomena is that prediction errors are linearly
correlated with ﬂow volumes, and scale-independent metrics can cope
with the correlations but not RMSE. Hereby, we suggest that scale-
independent metrics should be used in future studies for fair compar-
ison across different scales. Besides, a promising direction for im-
proving the prediction performance is to introduce attention mecha-
nism [37] that emphasizes regions with high ﬂow volumes.
Study 2 reveals that TAZ partition is more suitable than Grid parti-
tion for deep trafﬁc prediction. And study 3 depicts a probable reason
−TAZ partition reduces the number of outliers by averaging peak traf-
ﬁc into neighboring regions. From average values of PRMSE, CORR,
and U, we notice that PRMSE and uncertainty increase while cor-
relation drops, indicating prediction performance drops, when scal-
ing up for Grid partition. In contrast, PRMSE and uncertainty de-
crease while correlation increases, indicating prediction performance
improves, when scaling up for TAZ partition. This is probably be-
cause spatial heterogeneity decreases when scaling up for TAZ par-
tition, while that increases when scaling up for Grid partition, and
deep learning models can better predict trafﬁc of regions with low spa-
tial heterogeneity. The ﬁnding leads to promising directions on how
to improve trafﬁc prediction without tedious hyperparameter tuning
in neural networks. For instance, in addition to Grid and TAZ, geo-
graphical partitions can also be formulated based on human activities
through spatial clustering [1, 45], or graph partitioning [11, 40]. Be-
sides, gradual partition [22] could generate more balanced trafﬁc par-
titions, which could also bring a positive effect on trafﬁc prediction.
The insights are disclosed with unit visualization techniques, which
are in high demand by GIS and transportation colleagues [26]. These
visualizations however also face signiﬁcant scalability issue. For ex-
ample, the scatterplots (Fig. 12) of scale 200×100 suffer from some
amount of overplotting. If ﬁner partitions are employed (e.g., scale
400×200), the occlusion would be even worse, and dots in the non-
linear dot plot become tiny. Proper aggregations (e.g., [10, 50]) can be
incorporated to mitigate such issues.
Limitation and Future Work. The current system exhibits some limi-
tations. First, this work only examined grid and TAZ partition shapes,
whilst many other partition units are available. For instance, segment-
ing the territory based on road network could reﬂect urban trafﬁc bet-
ter. The experts expected the road-based partition could produce more
accurate trafﬁc predictions. We would like to examine these partition
methods in the future work. Second, the system employs inconsis-
tent colormaps among the three visualization modules. For example,
the sequential colormap in the scatterplot is different with the 4-class
OrRd colormap in the bivariate map, even though both colors encode
prediction errors. In fact, we experimented with the settings, but unsat-
isfactory visualizations were generated. In addition, prediction errors
in the scatterplot are standardized, while those in the bivariate map
are absolute values −they are not the same. Hence, we opt to dif-
ferent colormaps in the end. Nevertheless, it is worthwhile to strive
for consistency in the visual encodings across the different views to
support the visual analysis further. Finally, ST-ResNet model adopted
in this work applies 2D convolution operations on temporal-varying
matrices. The model requires to partition the entire region into non-
overlapping grids, which however casts away neighborhood relation-
ships between TAZs and may cause negative effect on prediction per-
formance. The deﬁciency can be overcome using graph convolutional
networks (GCN) with graph convolution operations. We would like to
employ GCN that can encapsulate both spatial and temporal attributes
at the same time to model trafﬁc predictions.
8
CONCLUSION
This paper presents a visual analytics approach for diagnosing the
MAUP in deep trafﬁc prediction. Through discussions with a collabo-
rating expert, we identify various analysis criteria and formulate a set
of analytical tasks. To cope with the analytics tasks, we (i) train six
ST-ResNet [51] models by applying Grid and TAZ partition shapes,
and three partition scales of 50×25, 100×50, and 200×100, to the un-
derlying studying area; (ii) employ scale-independent metrics, instead
of the conventional RMSE, to evaluate network predictions; and (iii)
develop a visual analytics system integrating three visualization mod-
ules, namely Bivariate Map, Moran’s I Scatterplot, and Multiscale
Attribution View. All the views adopt unit visualization techniques
that support investigation on a single data point. Speciﬁcally, we em-
ploy a value-suppressing uncertainty palette [5] in the bivariate map,
and we design a new layout strategy for nonlinear dot plots, which
is more space efﬁcient and trustworthy than existing layout methods,
in the multiscale attribution view. The designs are well recognized
by transportation experts. In the end, we conduct three case studies
on a real-world taxi data in Shenzhen, which reveal several insightful
ﬁndings. For example, predictions can be improved by more evenly
distributed trafﬁc aggregations. Feedbacks from independent experts
also conﬁrm the effectiveness of our system.
ACKNOWLEDGMENTS
The authors wish to thank the independent experts and the anony-
mous reviewers for their valuable comments. This work is supported
in part by National Natural Science Foundation of China (61802388,
61702433, 61872389, 41701452). Wei Chen is supported by National
Natural Science Foundation of China (61772456, U1609217).

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