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CPS1196 Song X. et al.
Where is computed as
(( ), ( ))
2
1
= { (( ), )
1
2
( , ( ))
1
2

The research uses the annual macroeconomic data of 35 Chinese cities
from year 2007 to year 2016, which are publicly available on the website of
The National Bureau of Statistics. The 35 cities are in top 3 tiers in China's
administrative level classifications:
1. Direct-controlled municipalities (4): Beijing, Tianjin, Shanghai,
Chongqing;
2. Provincial capitals (26): Taiyuan, Guangzhou, Haikou, Nanjing,
Hangzhou, Hefei, Fuzhou, Nanchang, Jinan, Zhengzhou, Wuhan,
Changsha, Shenyang, Changchun, Harbin, Hohhot, Shijiazhuang,
Yinchuan, Xi’an, Lanzhou, Xining, Urumqi, Chengdu, Guiyang,
Kunming, Lhasa, Nanning;
3. Cities specifically listed in economic plans (5): Shenzhen, Ningbo,
1
Ningbo, Qingdao, Dalian.
The metrics we selected as input features are those closely reflect a city's
economic growth patterns. In particular, the weights of secondary and tertiary
sectors in the economy are considered. In the cluster analysis, the values are
2
standardized to z-scores by year.

3. Results
The DTW time series clustering with the standardized industry
composition data results in five city groups as shown in Table 1.

Table 1: Five city groups are identified by cluster analysis.
Group Number of Cities Cities
A 7 Beijing, Guangzhou, Haikou, Harbin, Hohhot, Shanghai,
Urumqi
B 9 Guiyang, Hangzhou, Jinan, Lanzhou, Nanjing, Shenzhen,
Taiyuan, Xi'an, Xiamen
C 6 Chengdu, Fuzhou, Kunming, Nanning, Qingdao, Wuhan
D 4 Changchun, Chongqing, Dalian, Shijiazhuang
E 9 Changsha, Hefei, Nanchang, Ningbo, Shenyang, Tianjin,
Xining, Yinchuan, Zhengzhou

1 Chinese: 计划单列市.
2 The first sector was excluded, for the obvious reason that its values are perfectly linear
combination of the other two
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