# Urban Spatiotemporal Data Synthesis via Neural Disaggregation

Bin Han<EMAIL_ADDRESS>University of WashingtonSeattleUSA and  Bill Howe
<EMAIL_ADDRESS>University of WashingtonSeattleUSA

###### Abstract.

The level of granularity of open data often conflicts the benefits it can
provide. Less granular data can protect individual privacy, but to certain
degrees, sabotage the promise of open data to promote transparency and assist
research. Similar in the urban setting, aggregated urban data at high-level
geographic units can mask out the underline particularities of city dynamics
that may vary at lower areal levels. In this work, we aim to synthesize fine-
grained, high resolution urban data, by breaking down aggregated urban data at
coarse, low resolution geographic units. The goal is to increase the usability
and realize the values as much as possible of highly aggregated urban data. To
address the issue of simplicity of some traditional disaggregation methods –
1) we experimented with numerous neural-based models that are capable of
modeling intricate non-linear relationships among features. Neural methods can
also leverage both spatial and temporal information concurrently. We showed
that all neural methods perform better than traditional disaggregation
methods. Incorporating the temporal information further enhances the results.
2) We proposed a training approach for disaggregation task, Chain-of-Training
(COT), that can be incorporated into any of the training-based models. COT
adds transitional disaggregation steps by incorporating intermediate
geographic dimensions, which enhances the predictions at low geographic level
and boosts the results at higher levels. 3) We adapted the idea of
reconstruction (REC) from super-resolution domain in our disaggregation case —
after disaggregating from low to high geographic level, we then re-aggregate
back to the low level from our generated high level values. Both strategies
improved disaggregation results on three datasets and two cities we tested on.

urban computing, spatial disaggregation

††ccs: General and reference Empirical studies††ccs: Computing methodologies
Computer vision††ccs: Applied computing

##  1\. Introduction

High-quality, longitudinal, and freely available urban data, coupled with
advances in machine learning, improve our understanding and management of
urban environments (Han and Howe, 2023). Over the last two decades, cities
have increasingly released datasets publicly on the web, proactively, in
response to transparency regulation. For example, in the US, all 50 states and
the District of Columbia have passed some version of the federal Freedom of
Information (FOI) Act. While this first wave of open data was driven by FOI
laws and made national government data available primarily to journalists,
lawyers, and activists, a second wave of open data, enabled by the advent of
open source and web 2.0 technologies, was characterized by an attempt to make
data “open by default” to civic technologists, government agencies, and
corporations (Verhulst et al., 2020).

While making data publicly available possesses numerous benefits, such as
enabling extensive analyses of urban dynamics or assisting policymakers in
making urban development decisions (Vogel et al., 2011; Yu et al., 2017),
however, the open data might contain sensitive information about individuals.
Consequently, sharing such data at the individual level imposes potential
risks to individual privacy. For example, starting in 2017, NYC open data
portal no longer released longitudes and latitudes of taxi trips. Instead,
they released the central point of the geographic regions where the taxi trips
started and ended.

The level of granularity of open data often conflicts the benefits it can
provide. As stated in (Green et al., 2017), less granular data can protect
individual privacy, but to certain degrees, sabotage the promise of open data
to promote transparency and assist research. For instance, in population
disaggregation studies, highly aggregated population counts at large, coarse
areal units can hide critical local hotspots and trends, by smoothing out the
spatial variations (Monteiro et al., 2019a). Similar in the urban setting,
aggregated urban data at high-level geographic units can mask out the
underline particularities of city dynamics that may vary at lower areal
levels. Additionally, the predefined geographic units could often mismatch
with the units that users would like to work with for certain type of
analyses, not to mention that the boundaries of those pre-defined units could
also change overtime.

In this paper, we aim to synthesize fine-grained, high resolution urban data,
by breaking down aggregated urban data at coarse, low resolution geographic
units. The goal is to increase the usability and realize the values as much as
possible of highly aggregated urban data. Traditional spatial disaggregation
methods, such as areal weighting and dasymetric mapping, are frequently used
in the task. Areal weighting is a simple method that requires no auxiliary
information. It is operated under relatively simple assumptions, thus
hindering its capacities to achieve great disaggreagtion performances.
Dasymetric mapping methods are popular and leverage auxiliary information to
conduct weighted disaggregation. Machine learning and deep learning approaches
could be incorporated within to enhance the performances. However, dasymetric
mapping methods are highly reliant on auxiliary data, which are often not
available in urban setting. The quality of results are also highly dependent
on the relevance between auxiliary data and the source data.

To address the issue of simplicity of some traditional disaggregation methods,
we experimented with numerous neural-based models that are capable of modeling
intricate non-linear relationships among features. Neural methods can also
leverage both spatial and temporal information concurrently. We showed that
all neural methods perform better than traditional disaggregation methods. To
enhance the disaggregation results of neural methods, we proposed a training
strategies that can be adopted by any training-based methods — COT-REC: chain-
of-training with reconstruction. COT adds transitional disaggregation steps by
incorporating intermediate geographic dimensions, which enhances the
predictions at low geographic level and boosts the results at higher levels.
We adapted the idea of reconstruction (REC) from super-resolution domain in
our disaggregation case — after disaggregating from low to high geographic
level, we then re-aggregate back to the low level from our generated high
level values. Both strategies improved disaggregation results almost all
disaggregation tasks we tested.

In summary, we make the following contributions:

  * •

We leveraged neural methods to break down aggregated urban data, which
outperformed traditional, simple disaggregation methods that are performed
under simple assumptions. We tested neural methods on four different datasets
covering different domains and grids.

  * •

We proposed a training strategy — COT-REC. COT-REC adds transitional steps in
disaggregation steps, which enforces better results at lower geographic levels
thus enhancing higher lever disaggregation results. COT-REC provides better
results on almost all disaggregation tasks we experimented on.

##  2\. Related Work

Our work is in align with the domain of spatial disaggregation, which is a
process to transform values from a spatial scale at low resolution into higher
resolution. It is widely used in population studies (Qiu et al., 2019;
Wardropa et al., 2018), as well as in other areas, such as disease mapping
(Arambepola et al., 2020) and vaccination coverage (Utazi et al., 2018).

The most basic approach for spatial disaggregation is areal weighting (AW),
which breaks down the source value uniformly over the total number of target
regions. No auxiliary information is needed for this method, but the
assumption of homogeneity is implied — the values are evenly distributed among
the target regions (Goodchild et al., 1993). Even though this method is quite
simple, in the absence of auxiliary information to help with the
disaggregation task, it remains to be a valid and valuable approach.
Pycnophylactic interpolation (PI), which was first introduced by Tobler in
1979, works similar as areal weighting, but with slight refinement and
operates under different assumption. PI distributes the values from source
regions onto target regions in an iterative manner, aiming to avoid sharp
discontinuity between the target regions while to still preserve the total
counts in the source regions. Each iteration will adjust the value for each
target zone by considering the weighted average of its nearest neighbors,
which ensures the smooth boundaries.

Dasymetric mapping/interpolation/weighting (DM) approach is highly popular in
the domain of spatial disaggregation. Unlike areal weighting scheme,
dasymetric mapping uses auxiliary information to generate a weighted
distribution of source values onto the target regions. Recent methods
leveraged machine learning approaches to model the relationships between
auxiliary data and source values and determine the weights for disaggregation
(Stevens et al., 2015; Qiu et al., 2019; Monteiro et al., 2018, 2019b). Some
previously used auxiliary information include satellite images (Stevens et
al., 2015), 3D building information (Qiu et al., 2019), mobile phone usage
data (Deville et al., 2014), terrain elevation and human settlement (Monteiro
et al., 2019b) etc.

Despite the popularity of dasymetric mapping methods in spatial
disaggregation, there are several potential limitations of them (Comber and
Zeng, 2019). They are highly dependent on the availability of auxiliary
variables, which are not always available(e.g., remote sensing images or land
type data in population disaggregation tasks). Additionally, the quality of
the auxiliary information and the relevance between the auxiliary data and
source values have great impacts on the disaggregation performances.

##  3\. Datasets

We worked with four datasets: NYC taxi data, NYC bikeshare data, NYC 911 call
data, and Chicago taxi data. Each dataset contains records at the individual
level (e.g., individual taxi/bikeshare trip; individual 911-call location).
Those four datasets cover various domains and city grids.

  * •

NYC Taxi Data: NYC taxi trip data were collected from NYC Open Data
portal111https://opendata.cityofnewyork.us/data/ from 01/01/2016 to
06/30/2016. The raw data are presented in tabular format. Each record
summarizes the information for one single taxi trip, which contains the
longitude and latitude of the location where the taxi took off.

  * •

NYC Bikeshare Data: NYC bikeshare data were collected from NYC DOT
222https://citibikenyc.com/system-datafrom 01/01/2021 to 06/30/2021. Similar
to the taxi data, the raw data are presented in tabular format. Each data
point summarizes the information for one single bike trip, including the
longitude and latitude of the location where the bike was unlocked.

  * •

NYC 911 Call Data: NYC 911 call data were collected from NYC Open Data
portal333https://data.cityofnewyork.us/Public-Safety/NYPD-Calls-for-Service-
Year-to-Date-/n2zq-pubd from 01/01/2021 to 06/29/2021. Similar to the taxi
data, the raw data are presented in tabular format. Each data point summarizes
the call information, including the longitude and latitude of the location
where the call was made.

  * •

Chicago Taxi Data Data: Chicago taxi data were collected from Chicago Data
portal 444https://data.cityofchicago.org/Transportation/Taxi-
Trips-2022/npd7-ywjz from 01/01/2022 to 12/31/2022. Similar to NYC datasets,
the raw data are presented in tabular format. Each data point summarizes each
taxi trip information, including the longitude and latitude of the location
where the passenger was picked up.

The average counts for each geographic level and the corresponding standard
deviations are reported in Table 1. We noticed that the standard deviations
are rather large. This is because the uneven distribution of data points. Take
taxi data for example, upper Manhattan regions (e.g., Inwood) have way fewer
taxi rides than central Manhattan.

Data |  PUMA |  NTA |  TRACT |  BLOCK |  EXTREME
---|---|---|---|---|---
Taxi |  1443.01 (1776.03) |  450.94 (689.15) |  50.99 (73.26) |  3.85 (8.02) |  1.27 (3.59)
Bikeshare |  189.53 (279.24) |  59.23 (97.86) |  6.7 (13.06) |  0.5 (2.53) |  0.17 (1.41)
911 Calls |  23.25 (14.22) |  7.27 (7.05) |  0.82 (1.34) |  0.06 (0.32) |  0.02 (0.19)
Data |  Community |  TRACT |  BLOCK |  EXTREME |  -
Chicago Taxi |  27.71 (64.61) |  2.39 (10.91) |  0.06 (1.7) |  0.04 (1.35) |  -
Table 1. Descriptive statistics of four datasets. The reported numbers are the
average counts per geographic region. The standard deviation is in the
parenthesis.

For NYC, we select four predefined geographic levels, covering lower to finer
geospatial resolutions — Public Use Microdata Area (PUMA), Neighborhood
Tabulation Areas (NTA), Census Tracts (Tract), and Census Blocks (Block).
Their geographic boundaries in 2010 are collected from NYC open data portal.
We generated an geographic resolution level — Extreme, which contains areal
units that are smaller than Census Block. This geographic resolution is to
prepare for the synthesis of individual data records. For Chicago, which has
different predefined geographic structures than NYC, we select geographic
levels as close as possible to those of NYC — Community Areas (COM), Census
Tracts (Tract), and Census Blocks (Block). We also generated an geographic
resolution level — Extreme, which contains areal units that are smaller than
Census Block. Figure 1 shows the resolutions of five geographic levels in NYC.

Figure 1. Visualizations of five different geographic levels. PUMA has the
most coarse resolution, while EXTREME has the finest resolution.

We construct two types of input data:

  * •

Vector Inputs: We construct the aggregated hourly count data at the five
geographic levels, using the individual records from the datasets. For each
hour, we count how many records are located within each areal unit at each
geographic level. The vector data is represented as
$X_{vec}\in\mathbb{R}^{N\times d}$, where $N$ is the total number of hours,
and $d$ is the number of areal units in each geographic level (e.g. $d$ = 10
for PUMA; $d$=32 for NTA).

  * •

Image Inputs: to disaggregate urban data, we need to model the spatial
correlations among the units between coarse and fine geographic level, as well
as within each level. Convolutional Neural Networks (CNN) are good at modeling
spatial connections. Therefore, we transform each vector input into an image.
We plot units at each geographic level. The pixels in each unit takes the
value of $\frac{Count\;Value}{\\#of\;pixels\;in\;unit}$

For all three NYC datasets, we use the month of June as the test split, the
month of May as the validation split, and the rest as training data. For
chicago taxi data, we use the month of December as the test split, November as
the validation split, and the rest as training data. The split information is
presented in Table 2.

Data |  Train |  Val |  Test
---|---|---|---
Taxi |  2,904 |  744 |  720
Bikeshare |  2,904 |  744 |  720
911 Calls |  2,880 |  744 |  720
Chicago Taxi |  7,296 |  720 |  744
Table 2. Count of hourly data records in each split.

##  4\. Models

###  4.1. Baselines Models

As our baseline, we tested several neural models as well as simple,
traditional disaggregation methods:

  * •

Constant Weighting (CW): a simple method that disaggregates data uniformly
over the total number of regions at the finer resolution.

  * •

Areal Weighting (AW): a simple method that disaggregates data proportionally
to the areas of target regions at the finer resolution. The larger the region,
the larger the value it gets.

  * •

Historical Ratios (HR): a simple method that disaggregates data based on
historical distribution ratios. Unlike AW that disaggregates uniformly, HR
calculates the average disaggregation ratios from the source regions to the
target regions based on historical data (e.g., training data). The ratios are
then applied on unseen data.

  * •

Feedforward Neural Network (FNN): a multi-layer feedforward neural network,
which models the non-linear spatial connections among the areal units between
coarse and fine geographic levels. We name it spatial NN to distinguish it
from spatiotemporal NN, which incorporates both spatial and temporal
information.

  * •

Convolutional Neural Network (CNN): a model with UNet architecture, which
takes in image inputs and models the spatial correlations among pixel values.

  * •

LSTM: Long Short Term Memory network is a well-known network architecture
which is powerful in capturing sequential dependency. We chose T=5 as the
temporal sequence length based on the study (Han and Howe, 2023).

###  4.2. Proposed Methods

####  4.2.1. Chain of Training (COT)

Based on preliminary experimental results, we noticed that as we disaggregate
into finer geographic regions (e.g., from puma to block compared with fromp
puma to nta), the task gets harder thus yielding worse results. We hypothesize
that if we can disaggregate in a hierarchical style, the results could be
boosted. Therefore, we propose a training approach for disaggregation task,
Chain-of-Training (COT), that can be incorporated into any of the training-
based models. The idea is simple — when we disaggregate from low to high
geographic resolution, we add transitional disaggregation steps by
incorporating intermediate geographic dimensions. See Figure 2 for detailed
illustration.

Figure 2. The visualizations show the model architectures to disaggregate from
PUMA level to BLOCK level. Left: architecture of a regular feedforward neural
network model with two hidden layers. The hidden dimensions could be of any
values. Right: The two hidden layers have the dimension sizes that are equal
to the count of NTA and TRACT regions.

The advantage of adding intermediate geographic dimensions is that it makes
the model layers interpretable. Additionally, when we have data at the high
geographic level, we automatically have data at the intermediate levels, which
can be utilized for training purposes. In regular training (e.g., FNN), the
objective function is the $\ell_{1}$ loss at the highest geographic level:
$\ell_{high}=\frac{1}{N}|\sum\hat{X_{high}}-X_{high}|$. With COT, we also
calculate the loses at the intermediate levels and back-propagate them
together with the loss at the last layer:

$\ell_{total}=\ell_{high}+\ell_{intermedite}$
$\ell_{intermedite}=\frac{1}{N}|\sum\hat{X_{intermedite}}-X_{intermedite}|$

We hypothesize that this would be particularly helpful when the disaggregation
range is wide (e.g. going from PUMA to BLOCK). Traing on those hidden layers
could potentially help with the disaggregation results by making improvements
step by step.

####  4.2.2. Reconstruction (REC) Loss

Inspired by (Yuan et al., 2018) in the work of super-resolution, where they
generated high-resolution images from low-resolution, and restored the high-
resolution images backward to low-resolution. Then the models are jointly
trained on the loss calculated from both inputs and outputs. We adapted
similar idea in our disaggregation case — together with COT training
procedure, we first disaggregate from low to high geographic level, and then
re-aggregate back to the low level from our generated high level values. We
calculate disaggregation losses at both high and intermediate levels, as well
as reconstruction losses. We tested Full-reconstruction as shown in Figure 3.
For each high geographic level, we reconstruct all possible lower levels
beneath it, and take the average at each lower level. The objective function
is then:

$\ell_{total}=\alpha_{1}*\ell_{PUMA}\;+\;\alpha_{2}*\ell_{NTA}\;+\;\alpha_{3}\ell_{TRACT}\;+\;\alpha_{4}\ell_{BLOCK}\;+\;\alpha_{5}\ell_{EXTREME}$

Figure 3. Reconstruction regimes.

For NYC data, the models disaggregate from PUMA level data, into NTA, TRACT,
BLOCK, and EXTREME levels. Therefore, we have four disaggregation tasks.
Likewise, we have three disaggregation tasks for Chicago taxi data, which all
start from COM level. We evaluate the results using Mean Absolute Error (MAE).
For neural methods, the batch size is 8 and learning rate is 1e-4. We use
early stop setting to prevent over-fitting the training data.

##  5\. Experimental Results

In this section, we present the experimental results of all the models as well
as our proposed methods on four datasets.

###  5.1. Neural Methods Outperform Traditional Methods

For each dataset, the models are trained on the its own training set, and the
results are reported on the corresponding test set. The errors are normalized
by the area. Consequently, we could compare the results across different
disaggregation resolutions. Table 3 presents the quantitative disaggregation
results. For the convenience of comparison, we visualize the errors in Figure
4.

Figure 4. High-regime disaggregation results on three datasets. X-axis shows the disaggregation resolutions. Y-axis shows the error per squared meter. Different colors indicate different models. Dataset | Resolutions | CW | AW | HR | FNN | CNN | LSTM
---|---|---|---|---|---|---|---
Taxi |  PUMA $\rightarrow$ NTA | 1.820705 | 1.400443 | 0.463015 | 0.364603 | 0.227565 | 0.209696
PUMA $\rightarrow$ TRACT | 1.850812 | 2.055297 | 0.960405 | 0.700117 | 0.592701 | 0.562141
PUMA $\rightarrow$ BLOCK | 3.088336 | 2.963414 | 1.757388 | 1.500080 | 1.509036 | 1.421459
|  PUMA $\rightarrow$ EXTREME | 4.282211 | 3.907982 | 2.314584 | 2.661453 | 2.242518 | -
Bikeshare |  PUMA $\rightarrow$ NTA | 0.296892 | 0.201911 | 0.107852 | 0.101145 | 0.086823 | 0.089066
PUMA $\rightarrow$ TRACT | 0.518658 | 0.490639 | 0.265565 | 0.255558 | 0.241655 | 0.241166
PUMA $\rightarrow$ BLOCK | 1.412735 | 1.354402 | 0.398009 | 0.390442 | 0.386120 | 0.357188
|  PUMA $\rightarrow$ EXTREME | 1.559778 | 1.523974 | 0.406618 | 0.688281 | 0.445166 | -
911 Call |  PUMA $\rightarrow$ NTA | 0.030705 | 0.023857 | 0.015683 | 0.016084 | 0.015639 | 0.016175
PUMA $\rightarrow$ TRACT | 0.067976 | 0.068798 | 0.054865 | 0.050578 | 0.050630 | 0.050546
PUMA $\rightarrow$ BLOCK | 0.123104 | 0.120838 | 0.101465 | 0.063181 | 0.064917 | 0.062418
|  PUMA $\rightarrow$ EXTREME | 0.128736 | 0.127147 | 0.105850 | 0.064858 | 0.067793 | -
Table 3. Disaggregation results traditional and neural-based methods. The unit
of the error is count/block/hour.

We have several observations from the visualizations: 1) As the target
disaggregation resolution gets finer, the task gets harder, which is supported
by the observation that the errors are larger for finer high resolutions. 2)
Simple disaggregation methods, such CW and AW, do not perform well across all
resolutions in all three datasets. HR, though without any training, improves
the performances a lot over the simple methods. 3) Neural methods overall
outperform simple methods. However, models that utilize temporal information,
in addition to the spatial information, have better performances than those
models that only use spatial information. LSTM appears to be the best model
out of all.

###  5.2. COT+Reconstruction Improves Results

We tested the proposed COT-REC method on two models — FNN and LSTM, across all
three datasets. The results are presented in Table 4. We noticed that — 1)
when the plain models are trained together with COT or both COT and REC, the
performances are better than the plain results for most of the disaggregation
tasks. With Taxi data, training with both COT and REC improves the most, while
for the rest two datasets, COT alone generates better results. 2) For the
cases where the plain models outperform COT and COT-REC, three out of four are
disaggregation from PUMA to NTA, which is the easiest task. Additionally, the
differences are trivial and statistically insignificant.

Dataset | Model | Resolutions | Plain | +COT | +COT, +REC-Full
---|---|---|---|---|---
Taxi | FNN |  PUMA $\rightarrow$ NTA | 0.2276 | 0.2302 | 0.2328
PUMA $\rightarrow$ TRACT | 0.5927 | 0.5752 | 0.5695
PUMA $\rightarrow$ BLOCK | 1.5090 | 1.5023 | 1.4890
PUMA $\rightarrow$ EXTREME | 2.2425 | 2.2328 | 2.2025
LSTM |  PUMA $\rightarrow$ NTA | 0.2097 | 0.2101 | 0.2149
PUMA $\rightarrow$ TRACT | 0.5621 | 0.5448 | 0.5429
PUMA $\rightarrow$ BLOCK | 1.4215 | 1.4136 | 1.3926
Bike | FNN |  PUMA $\rightarrow$ NTA | 0.0868 | 0.0806 | 0.0815
PUMA $\rightarrow$ TRACT | 0.2417 | 0.2314 | 0.2321
PUMA $\rightarrow$ BLOCK | 0.3861 | 0.3675 | 0.3913
PUMA $\rightarrow$ EXTREME | 0.4452 | 0.4224 | 0.4456
LSTM |  PUMA $\rightarrow$ NTA | 0.0891 | 0.0830 | 0.0829
PUMA $\rightarrow$ TRACT | 0.2412 | 0.2335 | 0.2316
PUMA $\rightarrow$ BLOCK | 0.3572 | 0.3447 | 0.3771
911-Call | FNN |  PUMA $\rightarrow$ NTA | 0.0156 | 0.0156 | 0.0157
PUMA $\rightarrow$ TRACT | 0.0506 | 0.0502 | 0.0531
PUMA $\rightarrow$ BLOCK | 0.0649 | 0.0638 | 0.0884
PUMA $\rightarrow$ EXTREME | 0.0678 | 0.0667 | 0.0952
LSTM |  PUMA $\rightarrow$ NTA | 0.0162 | 0.0156 | 0.0156
PUMA $\rightarrow$ TRACT | 0.0505 | 0.0502 | 0.0527
PUMA $\rightarrow$ BLOCK | 0.0624 | 0.0625 | 0.0946
Table 4. Disaggregation results of neural-based methods and our proposed COT-
REC method. The unit of the error is count/block/hour.

##  6\. Ablation Study

In this section, we present two ablation studies about moddel weighting and
different reconstruction schemes.

###  6.1. Weighted v.s. Unweighted Models

Since we calculate errors at all geographic levels and train the models with
all the errors jointly, we need to weight each term in the objective function
properly. We observed that the disaggregating from PUMA to EXTREME is a much
harder task than from PUMA to NTA. Therefore, the loss term at the EXTREME
level would be larger than that at the NTA level. Consequently, the weights
for each term in the objective function is determined by the dimension of each
geographic level, which up-weight the NTA loss more. To show the effects of
proper weighting, we trained models without the weighting and report the
results in Table 5.

Dataset | Model | Resolutions | Plain | +COT | +COT, +REC-Full
---|---|---|---|---|---
Taxi | Unweighted FNN |  PUMA $\rightarrow$ NTA | 0.2276 | 0.2313 | 0.2308
PUMA $\rightarrow$ TRACT | 0.5927 | 0.5773 | 0.5715
PUMA $\rightarrow$ BLOCK | 1.5090 | 1.5157 | 1.5884
PUMA $\rightarrow$ EXTREME | 2.2045 | 2.2328 | 2.3131
Weighted FNN |  PUMA $\rightarrow$ NTA | 0.2276 | 0.2302 | 0.2328
PUMA $\rightarrow$ TRACT | 0.5927 | 0.5752 | 0.5695
PUMA $\rightarrow$ BLOCK | 1.5090 | 1.5023 | 1.4890
|  PUMA $\rightarrow$ EXTREME | 2.2425 | 2.2328 | 2.2025
Table 5. Disaggregation results of weighted and unweighted models. The unit of
the error is count/block/hour.

We noticed that when disaggregating from PUMA to NTA, weighting does not
provide much benefits, though the differences are still insignificant. For the
other two disaggregation tasks, we observed larger improvement with weighted
models. The reason is that NTA loss is much smaller than EXTREME loss. Without
the weighting, EXTREME loss will dominate the learning process, which counters
the idea of enforcing better results at low levels.

###  6.2. Reconstruction Schemes

In the main text, we reported the results of Full reconstruction. Here we
explored two more reconstruction options, namely — Bridge reconstruction and
BottomUp reconstruction. Bridge reconstruction only reaggregates lower level
values from the adjacent higher level, such as from NTA to PUMA and from BLOCK
to TRACT. BottomUp reconstruction reaggregates lower lever values only from
the highest geographic level in the task. We trained the models in the same
was described above. The results are provided in Table 6. Full and BottomUp
reconstruction both provide promising results, though BottomUp reconstruction
sometimes generates way worse results than the plain model (e.g. PUMA to
TRACT). Therefore, Full reconstruction is relatively more stable. Bridge
reconstruction improves over the plain model results, but not as good as the
other two methods.

Dataset | Model | Resolutions | Plain | +COT |  +COT, +REC-BottomUp |  +COT, +REC-Bridge |  +COT, +REC-Full
---|---|---|---|---|---|---|---
Taxi | FNN |  PUMA $\rightarrow$ NTA | 0.2276 | 0.2302 |  0.2328 |  0.2328 |  0.2328
PUMA $\rightarrow$ TRACT | 0.5927 | 0.5752 |  0.6197 |  0.5780 |  0.5695
PUMA $\rightarrow$ BLOCK | 1.5090 | 1.5023 |  1.4908 |  1.5203 |  1.4890
PUMA $\rightarrow$ EXTREME | 2.2425 | 2.2328 |  2.1683 |  2.2911 |  2.2025
LSTM |  PUMA $\rightarrow$ NTA | 0.2097 | 0.2101 |  0.2149 |  0.2149 |  0.2149
PUMA $\rightarrow$ TRACT | 0.5621 | 0.5448 |  0.5405 |  0.5412 |  0.5429
PUMA $\rightarrow$ BLOCK | 1.4215 | 1.4136 |  1.3926 |  1.4033 |  1.3926
Table 6. Disaggregation results of different reconstruction schemes. The unit
of the error is count/block/hour.

##  7\. Discussion

In this work, we aim to synthesize fine-grained, high resolution urban data,
by breaking down aggregated urban data at coarse, low resolution geographic
units. The goal is to increase the usability and realize the values as much as
possible of highly aggregated urban data. To address the issue of simplicity
of some traditional disaggregation methods – 1) we experimented with numerous
neural-based models that are capable of modeling intricate non-linear
relationships among features. Neural methods can also leverage both spatial
and temporal information concurrently. We showed that all neural methods
perform better than traditional disaggregation methods. Incorporating the
temporal information further enhances the results. 2) We proposed a training
approach for disaggregation task, Chain-of-Training (COT), that can be
incorporated into any of the training-based models. COT adds transitional
disaggregation steps by incorporating intermediate geographic dimensions,
which enhances the predictions at low geographic level and boosts the results
at higher levels. 3) We adapted the idea of reconstruction (REC) from super-
resolution domain in our disaggregation case — after disaggregating from low
to high geographic level, we then re-aggregate back to the low level from our
generated high level values. Both strategies improved disaggregation results
on three datasets and two cities we tested on.

## References

  * (1)
  * Arambepola et al. (2020) Rohan Arambepola, Tim C. D. Lucas, Anita K. Nandi, Peter W. Gething, and Ewan Cameron. 2020\.  A simulation study of disaggregation regression for spatial disease mapping.  _Statistics in Medicine_ 41 (2020), 1 – 16.
  * Comber and Zeng (2019) Alexis J. Comber and Wen Zeng. 2019.  Spatial interpolation using areal features: A review of methods and opportunities using new forms of data with coded illustrations.  _Geography Compass_ (2019).
  * Deville et al. (2014) Pierre Deville, Catherine Linard, Samuel Martin, Marius Gilbert, Forrest R. Stevens, Andrea E. Gaughan, Vincent D. Blondel, and Andrew J. Tatem. 2014.  Dynamic population mapping using mobile phone data.  _Proceedings of the National Academy of Sciences of the United States of America_ 111, 45 (Sept. 2014), 15888–15893.  https://doi.org/10.1073/pnas.1408439111
  * Goodchild et al. (1993) M F Goodchild, Luc Anselin, and Uwe Deichmann. 1993\.  A Framework for the Areal Interpolation of Socioeconomic Data.  _Environment and Planning A_ 25 (1993), 383 – 397.
  * Green et al. (2017) Ben Green, Gabe Cunningham, Ariel Ekblaw, Paul M. Kominers, Andrew Linzer, and Susan P. Crawford. 2017.  Open Data Privacy: A risk-benefit, process-oriented approach to sharing and protecting municipal data.
  * Han and Howe (2023) Bin Han and Bill Howe. 2023\.  Adapting to Skew: Imputing Spatiotemporal Urban Data with 3D Partial Convolutions and Biased Masking.  arXiv:2301.04233 [cs.CV]
  * Monteiro et al. (2019a) João Monteiro, Bruno Martins, Patricia Murrieta-Flores, and João M. Pires. 2019a.  Spatial Disaggregation of Historical Census Data Leveraging Multiple Sources of Ancillary Information.  _ISPRS International Journal of Geo-Information_ 8, 8 (2019).  https://doi.org/10.3390/ijgi8080327
  * Monteiro et al. (2019b) João Monteiro, Bruno Martins, Patricia Murrieta-Flores, and João M. Pires. 2019b.  Spatial Disaggregation of Historical Census Data Leveraging Multiple Sources of Ancillary Information.  _ISPRS International Journal of Geo-Information_ 8, 8 (2019).  https://doi.org/10.3390/ijgi8080327
  * Monteiro et al. (2018) João Monteiro, Bruno Martins, and João Pires. 2018\.  A hybrid approach for the spatial disaggregation of socio-economic indicators.  _International Journal of Data Science and Analytics_ 5 (03 2018).  https://doi.org/10.1007/s41060-017-0080-z
  * Qiu et al. (2019) Yue Qiu, Xuesheng Zhao, Deqin Fan, and Songnian Li. 2019\.  Geospatial Disaggregation of Population Data in Supporting SDG Assessments: A Case Study from Deqing County, China.  _ISPRS Int. J. Geo Inf._ 8 (2019), 356.
  * Stevens et al. (2015) Forrest R. Stevens, Andrea E. Gaughan, Catherine Linard, and Andrew J. Tatem. 2015.  Disaggregating Census Data for Population Mapping Using Random Forests with Remotely-Sensed and Ancillary Data.  _PLOS ONE_ 10, 2 (02 2015), 1–22.  https://doi.org/10.1371/journal.pone.0107042
  * Utazi et al. (2018) CE Utazi, Julia Thorley, V. Alegana, Mjgs Ferrari, Kristine Nilsen, Saki Takahashi, C. Jessica E. Metcalf, Justin Lessler, and AJ Tatem. 2018.  A spatial regression model for the disaggregation of areal unit based data to high-resolution grids with application to vaccination coverage mapping.  _Statistical Methods in Medical Research_ 28 (2018), 3226 – 3241.
  * Verhulst et al. (2020) Stefaan Verhulst, Andrew Young, Andrew Zahuranec, Susan Ariel Aaronson, Ania Calderon, and Matt Gee. 2020.  The emergence of a third wave of open data.  __, (2020), .
  * Vogel et al. (2011) Patrick Vogel, Torsten Greiser, and Dirk Christian Mattfeld. 2011\.  Understanding bike-sharing systems using data mining: Exploring activity patterns.  _Procedia-Social and Behavioral Sciences_ 20 (2011), 514–523.
  * Wardropa et al. (2018) N. A. Wardropa, W. C. Jochema, T. J. Birda, H. R. Chamberlaina, David J. Clarkea, D. Kerra, Lars Bengtssona, S. Juranc, V. Seamand, and A. J. Tatema. 2018\.  Spatially disaggregated population estimates in the absence of national population and housing census data.
  * Yu et al. (2017) Haiyang Yu, Zhihai Wu, Shuqin Wang, Yunpeng Wang, and Xiaolei Ma. 2017.  Spatiotemporal recurrent convolutional networks for traffic prediction in transportation networks.  _Sensors_ 17, 7 (2017), 1501.
  * Yuan et al. (2018) Yuan Yuan, Siyuan Liu, Jiawei Zhang, Yongbing Zhang, Chao Dong, and Liang Lin. 2018\.  Unsupervised Image Super-Resolution Using Cycle-in-Cycle Generative Adversarial Networks. In _2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW)_. 814–81409.  https://doi.org/10.1109/CVPRW.2018.00113