Computers, Environment and Urban Systems 60 (2016) 79–88 Contents lists available at ScienceDirect Computers, Environment and Urban Systems journal homepage: www.elsevier.com/locate/ceus Understanding operation behaviors of taxicabs in cities by matrix factorization Chaogui Kang a,⁎, Kun Qin a,b,⁎⁎ a School of Remote Sensing and Information Engineering, Wuhan University, 129 Luoyu Road, Wuhan, Hubei 430079, China b Collaborative Innovation Center of Geospatial Technology, 129 Luoyu Road, Wuhan, Hubei 430079, China article info abstract Article history: Taxicabs play significant roles in public transport systems in large cities. To meet repetitive demands of daily Received 4 February 2016 intra-urban travels, cabdrivers acquire self-organized habitual operation behaviors in space and time, largely Received in revised form 2 August 2016 with assistance of their longitudinal operating experience. Recognizing those collective operation behavior pat- Accepted 4 August 2016 terns of taxicabs will enable us to better design and implement public transport services and urban development Available online 21 August 2016 plan. In this paper, we systematically study patterns of the spatial supply of 6000+ taxicabs in Wuhan, China based on a monthly collection of their digital traces and the non-negative matrix factorization method. We suc- Keywords: Taxicab mobility cessfully identify a set of high-level statistical features of the spatial operation behaviors of taxicabs in Wuhan, Travel demand-supply providing valuable insights to our knowledge of the demand and supply of taxicabs in (similar) large cities. Habitual operation behavior First, we decouple several spatially cohesive regions with intensive internal taxicab travels (termed as demand Digital trace regions), which intuitively reveal the well-known multi-sectored urban configuration of Wuhan. Second, by ap- Matrix factorization plying the non-negative matrix factorization to taxicab's longitudinal traces, we uncover remarkably self- organized operation patterns of cabdrivers in space (termed as supply regions) as reactions to the sectored distri- bution of daily travel behaviors. We find that a large proportion of cabdrivers frequently operate within single specific service area and a small proportion of taxicabs works as shifting tools between different service areas. Last, we focus on performances of taxicabs with distinct spatial operation behaviors and unveil their statistical characteristics in terms of frequency, duration and distance with passenger on board. Our work demonstrates the great potential to understand and improve urban mobility and public transport system from cabdrivers' col- lective intelligence. © 2016 Elsevier Ltd. All rights reserved. 1. Introduction and provide a promising tool for inspecting empirically the spatio- temporal patterns of movement behaviors of a massive volume of taxi- Taxicabs play significant roles in public transport systems in large cabs in various city settings . cities. It has been intensively reported worldwide that intra-city travels In this paper, we systematically study the spatial patterns of labor- carried by taxicabs can account to N10% of total daily travels in a large supply behaviors of 6000+ taxicabs in Wuhan, China based on a city. To meet intensive and repetitive demands of daily intra-urban monthly collection of their digital traces and the non-negative matrix travels (Huff & Hanson, 1986; Eagle & Pentland, 2009), cabdrivers factorization method. Our primary research questions are as follows: might acquire self-organized habitual operation behaviors in space (1) Whether (and how) do taxicabs' habitual operation behaviors rely and time, with assistance of their longitudinal operating experience on the spatial distribution of intra-urban travel demands? (2) What and their cognition map of urban built environment. Recognizing are the differences between the performances of taxicabs with distinct those collective and habitual operation behaviors of taxicabs will enable spatial habitual behaviors? In solving these problems, we identify a set us to rationally design and implement public transport services and of high-level statistical features of the spatial operation behaviors of urban configuration (Castro, Zhang, Chen, Li, & Pan, 2013). In recent taxicabs in the case study city, which provide valuable insights to our years, the prevalent deployment of vehicle-embedded GPS devices in knowledge of the demand and supply of taxicabs in (similar) cities. taxi service and the easy accessibility of relevant data for the public First, we decouple several spatially cohesive regions with intensive in- (Farber, 2015) lead to a burst of studies on taxi/passenger mobility, ternal taxicab travels, which intutively reveals the well-known multi- sectored urban configuration of Wuhan. Second, by applying the non- negative matrix factorization to taxicab's longitudinal digital traces, ⁎ Corresponding author. we uncover that cabdrivers' operation patterns are remarkably self- ⁎⁎ Correspondence to: K. Qin, Collaborative Innovation Center of Geospatial Technology, 129 Luoyu Road, Wuhan, Hubei 430079, China. organized in space as reactions to the sectored distribution of daily E-mail addresses: [email protected] (C. Kang), [email protected] (K. Qin). intra-urban travel behaviors. We find that a large proportion of http://dx.doi.org/10.1016/j.compenvurbsys.2016.08.002 0198-9715/© 2016 Elsevier Ltd. All rights reserved. 80 C. Kang, K. Qin / Computers, Environment and Urban Systems 60 (2016) 79–88 cabdrivers frequently operate within a single specific service area boost city dwellers' traveling; (3) The regularity of activity-venue and (i.e., supply region) and a small proportion of taxicabs works as shifting travel-route selections. It implements statistical quantities, such as cy- travel tools between (two) different supply regions. Last, we focus on clical rhythm (Liu et al., 2012b) and spatio-temporal entropy (Peng, performances of taxicabs with distinct spatial operation behaviors and Jin, Wong, Shi, & Liò, 2012), to describe the high predictability of deter- reveal their statistical characteristics in terms of frequency, duration mining taxi trip origins and destinations in cities. Strong evidences exist and distance with passenger on board. to demonstrate that the number of frequent visitation venues and The major contribution of our work lies in the following: (1) We un- routes of individual dwellers' traveling is astonishingly small, e.g. with veil the relationship between longitudinal intra-urban travel demands an average of four venues and two routes. These studies shed bright and taxicabs' self-organized habitual behaviors; (2) We develop a ma- light on the repetitious daily routines and the highly limited activity trix factorization based analytical framework to quantify, visualize and budgets of city dwellers. evaluate taxicabs' operation behavior patterns in space. Our work also demonstrates the great potential to understand and improve urban mo- 2.2. Cabdrivers' mobility patterns bility and public transport system from cabdrivers' collective intelligence. For the sake of improving taxi service efficiency, another strand of studies heavily emphasize on cabdrivers' operation strategy for gaining 2. Related work optimal (e.g., minimal and maximal) profit(Liu, Andris, & Ratti, 2010). For most cabdrivers, there are three key decisions they have to make The continued development of urban computing and human mobil- during working as follows: (1) Where to search for the next passenger ity studies has been accumulating a rich body of evidences of the de- by cruising? (i.e., hunting behavior). Previous literature have reported scriptive characteristics of intra-urban travel activities. Taxi driving several well-received searching strategies based on hotspot detection trajectories, as a prevailing data source of related works, contain at (Chang, Tai, & Hsu, 2009), cabdrivers' historical performances (Li et al., least three major facets of human travel behaviors as being summarized 2011), and time-series-based prediction (Moreira-Matias, Gama, as: (1) General mobility patterns of city dwellers represented by pas- Ferreira, & Damas, 2012) of travel demands. The hunting behavior sengers' daily usages of taxicabs (Section 2.1); (2) Operation behavior should also take the cost of energy (as a proxy of cruising distance) patterns of cabdrivers represented by hunting, waiting and shifting for and time (as an indicator of traffic condition) into consideration profit-maximization (Section 2.2); (3) Structural properties of the (Yuan, Zheng, Zhang, & Xie, 2013); (2) Where to, if not hunt, wait for intra-urban spatial interaction network derived from taxi trip origins potential passengers? And how long to wait? (i.e., waiting behavior). and destinations (Section 2.3). This operation behavior is strongly intertwined with the hunting strat- egy. In most circumstances, cabdrivers would choose to wait at, or near- 2.1. Passengers' mobility patterns by to, the previous drop-off location if the current location is a hotspot with massive potential passengers (Li et al., 2012) or the cost of hunting Patterns of city dwellers' travel behaviors have longstanding impor- next passenger is too high. It is also noteworthy that certain literature tance in time geography, transportation and urban studies. As early as in (Li et al., 2011) argues that hunting is a dominant strategy upon waiting 1970's, Hägerstrand proposed his initial space-time framework of for most cabdrivers