Discovering Urban Functional Zones By Latent Fusion of ... › pdf › 2004.09720.pdf · known Geohash geocoding system is adopted to segment the map into equal-sized regions. geohashes

Discovering Urban Functional Zones By Latent Fusion of Users GPSData and Points of InterestsWen Tanga,∗ (Student), Alireza Chakerib and Hamid Krima

aDepartment of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC 27606, USAbValassis Digital, 3020 Carrington Mill Blvd, Morrisville, NC 27560, USA

A R T I C L E I N F O

Keywords:Functional Zones discovering, Latentregion representation learning, Sparseand bias POIs, GPS data, ConditionalRandom Filed Clustering, Function An-notation

A B S T R A C T

With rapid development of socio-economics, the task of discovering functional zones becomes criti-cal to better understand the interactions between social activities and spatial locations. In this paper,we propose a framework to discover the functional zones by analyzing urban structures and socialbehaviors. The proposed approach models the inner influences between spatial locations and humanactivities by fusing the semantic meanings of both Point of Interests (POIs) and human activities tolearn the latent representation of the regions. A spatial based unsupervised clustering method, Condi-tional Random Filed (CRF), is then applied to aggregate regions using both their spatial informationand discriminative representations. Also, we estimate the functionality of the regions and annotatethem by the differences between the normalized POI distributions which properly rank various func-tionalities. This framework is able to properly address the biased categories in sparse POI data, whenexploring the unbiased and true functional zones. To validate our framework, a case study is evaluatedby using very large real-world users GPS and POIs data from city of Raleigh. The results demonstratethat the proposed framework can better identify functional zones than the benchmarks, and, therefore,enhance understanding of urban structures with a finer granularity under practical conditions.

1. IntroductionThe development of the network infrastructures and cell-

phone hardwares led to massive amount of mobile data withgeographical information. In order to leverage the knowl-edge of such huge mobile data, it is critical to develop adigital map and its functional zones. Functional zones notonly help individuals to understand a complex city, but alsosuggest a scientific urban planning. Additionally, functionalzones are also useful for business sites management andtourism pattern discoveries, since they reveal the intentionof human activity trajectories. It also answers the key ques-tions of where and why people go visiting. On the otherhand, the urbanization and modern civilization recently oc-cur at an unprecedented rate. Hence, the task of functionalzones discovery becomes essential in order to understandthe interactions between social characters and spatial loca-tions.

To address this problem, two main strategies Yuan et al.(2015); Wang et al. (2018); Liu et al. (2015) have recentlybeen developed. One is to reveal and visualize the com-plex spatial interactions between different functional zonesGuo (2009); Yan and Thill (2009), where any spatial inter-action is quantified on the basis of the trips associated witha location and a timestamp of origin/destination; Zhang etal. Zhong et al. (2014) defined a weighted network, wherenodes are urban areas, edges are travel records and theirweights are the number of trips. They then detected thegraph centralities and clustered graph community structuresto obtain the hubs, centers and borders. In Liu et al. (2015);

∗Corresponding [email protected] (W. Tang); [email protected]

(A. Chakeri); [email protected] (H. Krim)ORCID(s): 0000-0003-0283-5493 (W. Tang)

Demsar et al. (2014), the authors used community detec-tion methods to identify the functional regions. Peng et al.Peng et al. (2012) applied Non-negative Matrix Factoriza-tion (NMF) to estimate different patterns and clustered theminto areas. However, the quantitative analysis of spatial in-teractions did not carry enough information to explore thefunctional zones.

Another strategy is to introduce POIs to jointly combinethem with the spatial interactions in order to discover func-tional zones Gao et al. (2017); Yuan et al. (2015); Wanget al. (2018); Liu et al. (2015); Yuan et al. (2018); The au-thors in Yuan et al. (2015); Gao et al. (2017); Yuan et al.(2018) applied the Latent Dirichlet allocation (LDA) basedtopic model to POIs and human activity behaviors, such as,user check-in data and taxi trajectories. Han et al. Han et al.(2015) clustered the bus smart card data and identified dif-ferent functional zones using POIs. Wang et al. Wang et al.(2018) used NMF method in Boarnet and Crane (2001) toidentify functional regions based on POI data and taxi tra-jectory data. They then quantitatively analyze the spatio-temporal information for annotation.

However, all above methods neither leverage a real in-trinsic structure between POIs and human activity patterns,nor deal with extremely sparse and biased real-world data.Additionally, the spatial information is also failed to be con-sidered when the regions are aggregated. Generally, themethods in the literature assumed that the data follow somefixed probability distributions. However, our real-world datais highly sparse and less than 1% of the regions carry POI in-formation. This is insufficient to estimate such parametersof the distributions. Also, compared to their POIs wherethey are generally unbiased and contain all different cate-gories, in our dataset, only the commercial related POIs areprovided. In order to cope with such biased and sparse in-

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Discovering Urban Functional Zones

Figure 1: Framework of Functional Zones Revealing.

formation, we propose a novel functional zone identificationframework to fuse the information between POI and humanactivity patterns. Instead of using probability assumptions,we introduce and transfer an intrinsic interaction structurebetween POIs and human activity patterns that was discov-ered in Wang et al. (2017) with unbiased data to bring the ex-tra knowledge to alleviate the biased effects, and cooperateswith matrix factorization to address the high sparsity, with-out any non-negative constraints. Moreover, the prior spatialknowledge is also used for region aggregation to confrontagainst the bias issue. A novel optimization method is alsoproposed to learn the latent regions representation based onsuch intrinsic interaction structure, which is applicable tobiased/unbiased and sparse/non-sparse data. To reduce thebias influence, an unsupervised clustering method, CRF, isapplied to functional zones to preserve spatial informationand their discriminative representations. The difference ofnormalized POI is then computed for functional zones an-notation to emphasize the significance of different function-alities. The very large real-world users GPS and POIs dataof city of Raleigh are used to evaluate our framework anddemonstrate a better functional zones identification and afiner granularity than the benchmarks. The proposed frame-work is summarized in Figure. 1.

Our main contributions can be summarized as:

(1) A novel latent region representation learning methodis proposed based on intrinsic interaction of unbiasedPOIs and human activity patterns to overcome the bi-ased data.

(2) To exploit the prior spatial information and alleviateboth bias effects and the imbalance POIs of map seg-mentation, CRF is used as an unsupervised clusteringmethod, which is regularized by the spatial relation-ship.

(3) A novel and efficient functional zone detection frame-work is proposed for both biased/unbiased and sparse/non-sparse data. This achieves a better functional zonesidentification and a finer granularity than the bench-marks based on real data.

The rest of the paper is organized as follows: Section 2introduces the preliminaries and the details on the latent re-gion representation learning procedure. Functional regionsaggregation and identification methods based on functionestimation are discussed in Section 3. The results are shownin Section 4. Finally, Section 5 concludes the paper.

2. Latent Region Representation LearningIn order to discover different functional zones, we seg-

ment our city into small rectangle regions, which are consid-ered as the basic region units. Based on these region units,a novel algorithm is proposed to learn latent semantic rep-resentation of each region unit that captures the interactioninformation between POIs and human activities.

2.1. Map SegmentationTo speed up the map segmentation procedure, the well-

known Geohash geocoding system is adopted to segment themap into equal-sized regions. geohashes express the girdedregions by short alphanumeric strings. The greater precisionis obtained with a longer string and a larger Geohash level.For example, two 156.5km×156km rectangle areas of Geo-hash level 3 can perfectly cover the city of Raleigh, whereasit can also be accurately represented by 64 39.1km×19.5kmregions of Geohash level 4 as shown in Figure 2. In total,there are 12 levels of Geohashes to present different areagranularity. Geohash level 6 is used in our experiments.



Figure 2: Examples of Geohash level 3 and Geohash 4 Seg-mentation. 2 big Geohash level 3 regions cover 64 Geohashlevel 4 regions.

2.2. Region Feature Learning2.2.1. PreliminariesDefinition 1. Trajectory: A trajectory of a user is a sequenceof time stamped location points, i.e.,T raj = (lp1,… , lpn),where lpi = (lat, lon, t), represents the latitude and longi-tude at time ti, ∀i = 1,… n.

Definition 2. Distance and Time Period: The geospatial dis-tance between two points lpi and lpj is defined asD(lpi, lpj).Time period TP (lpi, lpj) = |lpi.t− lpj .t| is the time intervalbetween two points.

Definition 3. Human Activity: A human activity ℎi of auser is defined such that the user stays in a geographicalregion within a given Dr distance over a given time pe-riod T r. ℎji is decided by a set of consecutive points L ={lpk, lpk+1,… , lpm}. In particular, when for all k < i ≤ m,D(lpk, lpi) ≤ Dr, D(lpk, lpm+1) > Dr and TP (lpk, lpi) ≤T r, ℎi = (lat, lon, ta, tl), where ta = lpk.t is the arrivaltime and tl = lpm.t is the corresponding leaving time. Also,ℎi.lat =

1|L|

∑mi=k lpi.lat and ℎi.lon =

1|L|

∑mi=k lpi.lon are

respectively the latitude and longitude of the human activitygeospatial location.

Definition 4. Human Activity Trajectory: A human activ-ity trajectory is a sequence of human activities, i.e. HT ={ℎ1 → ℎ2⋯ → ℎq} where ℎi is a human activity.

Definition 5. Human Activity Information: A human activ-ity information A is a triplet consisting of the origin regionRo, the destination region Rd and departure time tl or ar-rival time ta. Leaving human activity information is definedas AL = (Ro, Rd , tl), and arriving human activity informa-tion is then defined as AA = (Ro, Rd , ta). For each humanactivity ℎi in the human activity trajectory HT , a map fhas been used to map the geospatial location to differentGeohash regions, i.e., Ri = f (ℎi.lat, ℎi.lon). The leavingand arriving time are respectively obtained by tl = ℎi.tl andta = ℎi.ta.

Definition 6. Bag-of-POIs: Let assume that there are p dif-ferent POI categories, and pj shows the number of the jth

POI category in the map. Then, the bag-of-POIs for the ithregion unit is defined as poii = (pi1,… , pip), ∀i = 1,… , p.

Since the bag-of-POIs uniquely represents different func-tional zones, it can be used to represent each region to re-serve the functional information and obtain the POI infor-mation matrix P as in the following:

Definition 7. POI Information Matrix: Let each column ofthis matrix be the Bag-of-POIs of itℎ region unit, i.e.

P =[

poiT1 poiT2 … poiTp

]

.

Definition 8. Human Activity Pattern (HAP) Matrix: Basedon each human activity information AL = (Ro, Rd , tl) andAA = (Ro, Rd , ta), let each element of matrix Ck = [ckij]represents the number of AL (or AA) from itℎ region unit tojtℎ region unit, during the time period k. Then we define theHAP matrix as

T =[

C1, C2,… , Cs]T

Each time period is defined as one hour. 24 time periodsare considered in one day. That is, tl ∈ [0 ∶ 00, 1 ∶00),… , tl ∈ [23 ∶ 00, 24 ∶ 00). In our experiment, bothT based on AL and AA are concatenated together.

2.2.2. Latent Region Representation LearningIn order to discover the functional zones, we need to

explore the discriminative representations of various func-tional zones. One useful functional zone related informa-tion is POIs, as different POIs (such as fast food, coffee bar,shopping mall) attract individuals for different purposes. Inaddition, more POIs translates into higher probabilities fortheir corresponding functionalities. As a result, the Bag-of-POIs were introduced in our framework.

However, POIs are not only the determining factor ofthe region functions. The region function is also decided bythe intention of individuals trajectories. The authors in Chenet al. (2015) discovered that various region functional zoneshave their corresponding HAPs varies in different time pe-riods. This implies that HAPs which reflect semantic mean-ings of Human intentions, is another important factor forfunctional zones. Therefore, HAPs in different time periodsis also embedded into our framework.

It is insufficient for small number of biased POIs to pre-cisely estimate the parameters of assumed distributions. In-stead of directly using the LDA topic model in Yuan et al.(2015); Gao et al. (2017), we hence purpose an intrinsicinteraction between POIs and HAPs inspired from Wanget al. (2017). The authors in Wang et al. (2017) exploredthat 80% HAPs can be successfully predicted by POI in-formation, which means that POIs information can almostentirely reconstruct HAPs. This discovery was data-drivenand leveraged on unbiased data. Therefore, to cope withsmall number of biased data, such intrinsic knowledge be-tween POI and HAP are transferred as the reconstruction



Figure 3: Latent Region Representation Learning Model.

between latent POIs and latent HAPs into our framework.Additionally, since region functions are critical to affect hu-man travel behaviors and infers traffic pattern, there shouldexist a transformation between latent region representationand latent HAPs. In order to address the high sparse dataand learning the latent region representations, we also de-compose the POI into latent POI features and latent regionfeatures.

Consequently, as shown in Fig. 3, the POI informationmatrix P is decomposed into two latent and dense spacesU and V . And HAP matrix T is transformed by matrix Qinto a semantic latent space Z to reduce the dimensions andpreserve useful information. According to the transferredintrinsic knowledge leveraged from unbiased data, the trans-formed HAP Z is also reconstructed by some important la-tent POI features U that are gleaned from the original POIinformation in a latent space. The coefficients matrix A thatregularized by L1 norm are used to select the important la-tent POI features in U for each region. Meanwhile, the la-tent HAP representation Z also influences the latent regionrepresentation V that is also derived from POI informationin the same latent space. Besides, to avoid the lack of com-plete POI information, an indicator mask is also used to dealwith the sparsity of POI matrix.

Hence, our final information fusion method for the latentregion representation learning is formulated as follows:

arg minU,V ,QW ,A,Z

12‖I◦(P − UV )‖2F +

�12‖QT −Z‖

2F

+�22‖Z − UTA‖2F + �3‖A‖1 +

�42‖V −WZ‖

2F

+�52(‖U‖2F + ‖V ‖2F + ‖Q‖2F + ‖W ‖

2F ),

(1)

where I is a indicator mask. Ii,j = 1 for non-empty en-tries and Ii,j = 0 for others, ◦ is an element-wise product.�1, �2, �3, �4, and �5 are tuning parameters. P ∈ ℝp×r isdecomposed into two latent semantic matrices U ∈ ℝp×k

and V ∈ ℝk×r. T ∈ ℝq×r is transformed into its latenttransition pattern matrix Z ∈ ℝk×r by a transform matrixQ ∈ ℝk×q . The latent transition pattern Z receives the in-formation from the latent POI features by using sparse coef-ficients A ∈ ℝp×r to choose a specific POI in U , and propa-

gates the information back to the latent region feature V byW ∈ ℝk×k regression. The last term in Equation (1) is theregularization for avoiding overfitting.

We, therefore, alternatively search one variable whenothers are fixed. The updating rule of each variable basedon gradient descent are also summarized in Algorithm 1.

Algorithm 1 Latent Region Representation Learning

Input: POI matrix P , HAP matrix T , and hyper-parameter�1, �2, �3, �4, and �5

Output: Latent POI feature U , latent Region representa-tion V , Sparse Coefficients A, transform matrix Q, latenttransition pattern matrix Z, and regression matrix Wt=1;while t < maxIteration and Lt − Lt+1 > " doUt+1 = Ut − �(−I◦(P − UV )V T − �2A(Z − UTA)T + �5U )Vt+1 = Vt − �(−UT I◦(P − UV ) − �4(V −WZ) + �5V )Qt+1 = Qt − �(�1(QT −Z)T T + �5Q)Zt+1 = Zt − �(−�1(QT −Z) + �2(Z − UTA) − �4)W T (V −WZ)At+1 = ��3

(

At − �(−�2U (Z − UTA)))

Wt+1 = Wt − �(−�4(V −WZ)ZT + �5W )� = �� % � is a decay factor

end whilereturn U, V ,Q,Z,A,W

After solving the algorithm, the latent region representa-tion V comprehensively fuses both information of POI andHAP and the transferred knowledge. The latent transitionpattern matrix Z also contains the semantic meanings ofHAP.

3. Functional Zone Identification3.1. Region Aggregation

To aggregate the regions, clustering is a good way toperform it, as the ground truth of region labels are not avail-able at this moment. Regions in the same clusters shouldhave similar functions, and those in different clusters shouldprovide various functions. For each region unit r, its cor-responding features in V is column r (vr1,… , vrk). Basedon these features, a K-means clustering method is a naiveway to cluster region units to functional zones. However,K-means does not consider the spatial information of eachregion. When the segmentation grids is very small, a big



place may segmented into different region units and carry-ing different number of POIs. For instance, a shopping mallis segmented into 3 region units. One of them carry themajority of POIs of different stores, while another two ofthem only have a few stores. There is then a huge differ-ence among POI features of those region units. If only thedistance among feature element-wise comparison, such asK-means, is considered without the spatial location infor-mation, these 3 region units would be assigned into 2 clus-ters. In order to confront against such imbalance that causedby the fine-grids, we take the spatial location of each regionunits into account. The cluster labels of the 8 neighbor re-gion units that surround this region units should be moreprobably share the same cluster label. Hence, the Condi-tional Random Field (CRF) method is used to cluster re-gion units. The CRF method aims to maximize a posterior(MAP) inference over each region unit, which will maxi-mize cluster label agreement between similar region unitsto induce more smoothness Krähenbühl and Koltun (2011).Each region unit can be regarded as a k-dimensional datapoint that is generated by a probability distribution, suchas Gaussian. And a label agreement penalty is also jointlyused to calculate the label generation probability of differ-ent region units. In our paper, the Gaussian distribution isregarded as the generative distribution of each region unit,and only 8 neighbors of each region units are used in CRFto penalize the label agreement. The process of CRF can beformulated as follows:(1) Let functional Zone = {l1,… , lc} have c differentfunctional zones, and random variable Y = {y1,… , yr} de-note region-unit-level labeling, such as {cluster1,… , clusterr}that are un-annotated and finally assigned to each regionunit, and random variable R = {r1,… , rr} denote a featureof each region. In our experiment, the random variable R isthe latent region feature V . Then the conditional probabilityof label Y = lK is assumed to follow a normal distribution:

P (Y = lK |R) = N(�lK ,ΣlK ), (2)

(2) For each region unit Ri, the joint probability of labelingyi ∈ r in CRF is given by:

P (yi, yj) = exp{−∑

(i,j)∈NV (i, j)},

V (i, j) = ��(yi, yj) =

{

� if yi = yj−� else

,(3)

whereN is the neighbor set of regionRi. (3) The final targetfunction is formulated as follows:

argmaxy∈r

P (r, y) = 1FΠiP (yi|ri)Πi,jP (yi, yj), (4)

where F is a normalization term.The join probability in Eq.(4) can be solved by different

approaches, such as Expectation-maximization (EM) algo-rithm.

3.2. Functionality EstimationTo estimate the functionality of each cluster for func-

tional zone annotation, the uniform POI distribution is sup-posed to be adequate to carry the functionality of each re-gion unit, as each region unit is a rectangle region. How-ever, the actual number of POIs is not the same in each re-gion units. And the number of region units in each cluster isalso different. Thus, to emphasize the significant function-ality of different POIs in each cluster, the maximum nor-malized POI distributions is adopted for comparison, whichreflects the importance proportion of contributions of differ-ent POIs. For the stℎ cluster, the vector of POI distributionis hence formulated as follows:

PRs = (∑

i∈S pi1

|S|,… ,

∑

i∈S pip

|S|), (5)

where S is a set of region units whose labels of the func-tional zone are ls, and |S| is the number of elements in theset S. The normalized distribution then is:

NPRs = PRs

max(PRs). (6)

3.3. Region AnnotationRegion annotation is to associate the real functions with

clusters. However, it is far from enough to name a func-tional zone by only using the frequency of POIs. Becausemany functions may appear in the same cluster, which leadsto a hard region annotation. In our method, we use the dif-ference of functionality to assign some semantic terms toeach functional zone to understand its real function. Thefollowing conditions is utilized to annotate different func-tional zones:

(1) The difference in the normalized POI distribution.The difference Gs of stℎ functional zone is calculatedas follows,

Gs = (|| − 1)NPRs −∑

j∈,j≠sNPRj , (7)

where || is the number of functional zones. The pos-itive elements ofGs is the significant POIs in the func-tional zone s.

(2) Land-use maps of government. Compared withland use or zoning map, it is more accurate for usto understand different functional zones we obtained.For example, several big industrial regions can helpus fast locate such functional zones.

(3) Human-labelling. As some information may lack inthe POI information, people know more about well-known or common places that never show up in thePOI information, such as, the label of universities,which is missing in our experiments.

All the examples of the metrics of the functionality esti-mation and the region annotation are shown in Fig. 4.



(a) PR

(b) NPR

c G#

Figure 4: Example of PRs, NPRs and Gs. Comparing (a)PRand (b)NPR, it easy to show that the magnitude of the sig-nificant functionalities changed comparable for different clus-ters after normalization. From the example of G1 in (c), aftercalculating the difference of G1, and only G1 > 0 is consid-ered for annotation, it is clear that financial service (the pointin the black circle) is not so significant for Cluster 1 whencomparing with Cluster 2 and Cluster 3. Because, althoughthere are many financial services in Cluster 1, it also appearsmany times in Cluster 2 and Cluster 3, thus it does not differ-entiate among these clusters. Therefore, the difference Gscould keep more significant and distinct functionality.

Index POI Category Index POI Category1 fast food 15 fitness2 coffee bar 16 financial service3 eateries 17 theater4 fuel 18 hotel5 convenience store 19 electronics store6 grocery 20 pets/veterinary7 supermarkets 21 retirement8 pharmacy 22 auto dealers9 amusement 23 auto rental

10 tutoring school 24 auto service11 shopping mall 25 auto supply12 shopping center 26 machinery13 home improvement 27 shipping store14 personal care 28 park/lake(camping site)

Table 1POI Category

POI Dataset Statistics#POI 6,725#Regions with POIs / #Segmented Regions 1,233/16,384Sparsity of POI Matrix 99.11%User GPS Dataset Statistics#Users 1,026,726#HAP 27,930,027#Regions with HAP / #Segmented Regions 16,321/16,384Sparsity of HAP Matrix 99.97%

Table 2POI Statistics

4. Experiments and Results4.1. Experiment Settings

Our experiments are evaluated on the following datasets:

(1) Raleigh POI dataset is updated starting 2014. The cat-egory of POI has be listed in Table 1. There are 6,725POIs and 1,233 regions with POI information. Thesparsity of POI matrix P is 99.11%.

(2) User GPS dataset is collected during the workdaysof March 15tℎ to May 20tℎ in 2018. In this dataset,there are 1, 026, 726 users GPS records that locatedin Raleigh. They are then transformed to 27,930,027Human Activity Information. The number of regionswith HAP is 16,321. The sparsity of HAP matrix T is99.97%.

(3) Region Segmentation: We transformed Raleigh Mapin to 1200m×609.4m small rectangle regions that cod-ing by Geohash level 6. We totally obtain 16,384 seg-mented regions.

The statistics of all three datasets are listed in Table 2.

4.2. BenchmarksIn our experiments, the dimension of the latent region

representation is set to 10.In order to emphasize the important POI in each region,

TF-IDF has been applied to the POI matrix to adjust POIs,which follow the method in Yuan et al. (2015); Wang et al.



(2017). We compared our results with the following bench-marks, and all benchmark methods build up on the POI ma-trix prepossessed by TF-IDF:

(1) POI Distribution: The POI distribution based methodis to directly apply k-means and CRF clustering meth-ods on the POI distribution features.

(2) Collaborative POI: In addition, to considering latentstructure and avoiding missing data in TF-IDF basedBag-of-POIs, collaborative filtering methods have beenused to obtain latent semantic representation of POIsYuan et al. (2015) . In our comparison, collaborativePOI is obtained by SVD decomposition and repre-sented by the eigenvecotrs that are associated with thetop t-th maximum eigenvalues. Then, k-means andCRF clustering methods are respectively employedbased on collaborative POI features.

(3) Topic Modeling: Topic modeling is to use LDA clus-tering only based on the HAP and then cluster func-tional zones by k-means. For LDA model, we choose10 topics with 1000 iterations, following the settingsin Yuan et al. (2015) .

In our experiment, we learn our latent region represen-tation by Algorithm 1. Two clustering approaches: k-meansand CRF are utilized on our latent region representations tocluster S different functional zones. We also cluster our la-tent semantic HAP by just using k-means to compare withTopic Modeling method Yuan et al. (2015).

To verify our results, we compare our results with landuse map of Raleigh and check whether most famous regionsare assigned into their proper functional zones.

4.3. Results4.3.1. Functional Zones Comparison

We aggregate 4 functional zones by hereabove methodsfor Raleigh city and indicated by different colors, as shownin Fig. 5g. In order to better compare the different meth-ods, we zoom in on the results of major parts of Raleigh anddemonstrate them in Fig. 5a-5f. It is noting that differentcolors in different figures may indicate different functionalzones. The results shown in Fig.5a, 5b, 5d and 5e are onlybased on clustering of the POI information, while the resultsshown in Fig.5c and 5f are based on clustering the fusionfeatures of both POI and HAP information. Fig. 5a-5c areall based on k-means clustering, while Fig. 5d-5f are allbased on CRF clustering. Fig. 5h and 5i in the third rowfigures are based on the clustering of only the HAP infor-mation.

Like second and third-tier cities, Raleigh contains veryfew POIs. There are only 7.52% regions with POI infor-mation in our experiments, and the sparsity of POI matrixis up to 99.11%. The black clusters in Fig. 5a-5f repre-sent missing the POI information group. Since this group isreally large, other undistinguished features are easily clus-tered into this missing POI information group. As shown inFig. 5b, only using POI distributions is not discriminative

enough, many regions are regarded similar to the missingPOI information one.

For the benchmark (1), after directly using k-means clus-tering on POI distribution, the regions containing POI infor-mation significantly decreases from 7.52% to 5.97%, whichmisses 20.61% information. In Fig. 5b, it shows that onlythe top parts of downtown Raleigh that circled in red are notblack and carrying POI information.

For the benchmark (2), in order to reduce the sparsityand increase the latent semantic meanings of POI informa-tion, SVD is then applied on POI matrix. However, withlimited data in POI matrix, SVD decomposition can not ex-plore more latent structure. The result in Fig. 5a is evenworse than just using the POI distribution, i.e., the bench-mark (1). It also shows that most regions are clustered into3 groups (the black, yellow and pink ones), when 4 groupsshould be clustered. Additionally, only 5.27% regions con-tain the POI information, while 5.97% regions preserve thePOI information for the benchmark (1). This loses 29.92%of all the information, which is mainly caused by a lack ofdiscriminative features in Collaborative POI.

In Fig. 5c, our latent region representations are fusedboth POI and HAP information. It shows that such latentregion representations are distinguished enough to preserveall of the 7.52% POI information regions, i.e., 100% in-formation is preserved. Most of the regions with similarfunctions are in the same clusters. For example, the majorparts of the regions in the red circle are assigned a greencolor, which actually is the downtown area of Raleigh. Andhalf of the regions in the blue circle are assigned an or-ange color, where the university area should be located. Ourlatent region representation is more disciminative than theother benchmarks.

In our experiments, since the city map is segmented intosmall rectangular regions, many functional zones are parti-tioned into different small parts with different kinds of POIsand various numbers of POIs, thus introducing more vari-ance into the same functional zones. To reduce such vari-ance effects, the region locations are incorporated into theclustering method. CRF is then applied to different features.

Comparing with the results of k-means shown in Fig.5a-5c, the results of CRF in Fig. 5d-5f are more consis-tent. Most of the regions are assigned the same colors. Theblocks of regions in the same color are more numerous thanthose of using k-means.

For the benchmark (2), although the CRF result based onCollaborative POI in Fig. 5d is much better than k-meansone, most of the regions are in the same functional zones, which lose its meanings to discover the functional zones.For example, the functionality of the downtown part that iscircled in red should be different from the university areathat is circled in blue.

For the benchmark (1), the CRF result is based on POIdistributions. As shown in Fig. 5e, it has a more uniformclustering result than benchmark (2), which is more mean-ingful. But it is still not so consistent as the results of ourlatent region representation shown in Fig. 5f. In Fig. 5e,



(a) SVD of POI + K-means (b) POI + K-means (c) Our Latent Representation + K-means

(d) SVD of POI + CRF (e) POI + CRF (f) Our Latent Representation + CRF

(g) Our Latent Representation + CRF for theWhole Map Area

(h) LDA topics + K-means (i) Our semantic HAP + K -means

Figure 5: Comparison of different region representations.

Ranked Green G1 Orange G2 Pink G31 fast food 0.538 financial service 0.453 shipping 1.1722 financial service 0.453 fast food 0.352 fuel 0.8713 coffee bar 0.308 auto service 0.208 tutoring 0.1104 auto service 0.259 auto supply 0.207 hotel 0.0975 eateries 0.257 pharmacy 0.114 grocery 0.0876 pharmacy 0.232 eateries 0.095 home improvement 0.0827 pet 0.195 convenience 0.092 auto rental 0.0108 personal care 0.173 auto dealers 0.055 park/lake(camping site) 0.0049 home improvement 0.099 grocery 0.041 machinery 0.004

10 shopping center 0.089 coffee bar 0.035 - -

Table 3Map Color and Its Significant POIs with Ranked Difference Gs

parts of the region functionalities in the university area cir-cled as blue are the same as those in the downtown areacircled as red. Also, there are many industries located inthe purple circle, which should have similar functionality asthe university area, especially for workdays. However theseregions in the purple circle are assigned half green and halforange in Fig. 5e. To look at the regions in both the blueand purple circles in Fig. 5f, they are almost assigned toorange color. Therefore, our latent region representation

is still discrimative than other benchmarks. Additionally,the CRF clustering of our latent region representations hasa more consistent result than the k-means clustering does asshown in Fig. 5c and 5f. A more detailed comparison ofland-use map and the results of both k-means and CRF areshown in Fig. 6.

For the benchmark (3), since Yuan et al. (2015) demon-strated that LDA model has a similar result of functionalzones as the one of DMR model, and DMR model which



takes the POI information into account only change few ar-eas but spending more time and memory for training, it isfair to choose LDA to be the benchmark for comparison.As constrained memory limitation for LDA training, we useGeohash level 5 4900 m × 4900 m grids to segment thesame city map and show its results in Fig. 5h. As shownin Fig. 5h, the result of LDA nicely indicates that the mapis segmented into 4 different parts based on the spatial lo-cations. However, there are still some not well clusteredregions. For example, the green part that is circled in radand labeled with "A" is the downtown area of Raleigh, andit should be a high-level-activity area. However, the activ-ity level in other green areas in Fig. 5h is much lower thanthe ones of downtown Raleigh. That is, downtown Raleighshould not be assigned to the same group as other green ar-eas are. Also, the orange area covers for the most part cities,while many vacant and nature places are also included inthis orange area. For a fair comparison, we also used k-means to cluster our semantic HAP and show its results inFig. 5i. In Fig. 5i, the centre green areas are the major cities,such as, Raleigh, Durham, Chapel-Hill, Cary and Apex. Theorange areas represent a middle-level activity area, and thepink areas denote a low-level-activity area. Our latent tran-sition pattern Z is capable highlight how urban these areasare, while LDA still blurs the high-level-acitivity area withother level-activity areas. It worth nothing that, our pro-posed method is based on the Geohash level 6 (1 region unitof Geohash level 5 covers 32 region units of Geohash level6), which has a finer granularity than LDA does.

Overall, using the CRF to cluster our latent region repre-sentations that fused both POI and HAP information achievesa superior performance than other approaches. The latentregion representations are more disriminative. The CRFmethod achieves a more consistent clustering result. Andour proposed framework supports a finer granularity with apractical implementation time.

4.3.2. Functional Zones AnnotationAccording to our functionality estimation, we calculate

the normalized POI distribution NPR for each differentfunctional zone. The difference Gs of each functional zoneis then computed, and the components of Gs > 0 are listedby decreasing the significance in Table. 3. Since areas andcities in our experiment are not modern cities, they do nothave a complex city structure. We thus consider 4 differentfunctional zones in our experiments. The area annotationsare based on the results of clustering our latent region repre-sentations by CRF, as shown in Fig. 5f or 5g. As the blackareas are where no POI information regions are, and mostregions in black are residential, vacant and natural areas, wedid not list them in Table. 3. In terms of the ranked differ-ence of significant POIs in the table, we annotate the regionsas follows:Commercial/Downtown/Entertainment Area (Green re-gions): The distinguished POI in this functional zone arePet, Personal Care and Shopping center, which are muchsignificant in this area than others. Pets, Personal Care and

Figure 6: Comparison of different clustering methods basedon Latent Region Representation.

Shopping center all provide service and merchandise, whichindicates this functional zone is probably a commercial area.The other highly ranked POIs in this area also follow thecharacteristics of the commercial area, such as, financialservice and coffee bar. Additionally, the famous shoppingmalls, such as Southpoint and Crabtree are all located inthis functional zone.Working/Education Area Mixed with Commercial Areain Inner City (Orange regions): Since we only count forthe workdays, this area is annotated as a mixed use area.During the working time, its function is working/education.During other times, its commercial area. The Gs of this areafocus on the financial service, fast food, and auto service,which is easy to compose a commercial area. Meanwhile,looking at the Fig. 6, both industrial and Public and institu-tions are mixed with commercial part and located in orangeregions, such as NC state, Duke, Chapel-Hill and Wake techUniversities.Working/Education Area in Outer City (Pink regions):Most significant POIs in this functional zone are shipping,fuel, hotel and auto rental, which all refers to a outer-side ofa city. Additionally, as our dataset is based on the workdays,and some industrial and tutoring are also located in the outercity, so this area is implied to be a working/education area.Consequently, this functional zone is annotated as a work-ing/Education area in outer City. Since this area include fewcommercial area, it is different from above mixed with com-mercial one. According to Fig. 5g, it is easy to find pink area



is in outer side of centralized area. Moreover, the ResearchTriangle Park (RTP), a large company area is also assignedin the pink area, where it locates in middle part among thetriangle part that consisted by the outer side of the cities ofRaleigh, Durham and Chapel Hill.

5. ConclusionIn this paper, we proposed a framework for discovering

functional zones on the basis of a novel algorithm to learndiscriminative latent representations of regions and spatialclustering method. The proposed new algorithm leveragesthe latent effects between POIs and HAP, and successfullyfuses the information of highly sparse POIs and HAP, andsimultaneously enhances the discriminiatve ability. An in-trinsic knowledge that explored from the real data are trans-ferred in our framework to cope with biased data. Moreover,we also utilize the label consistency of CRF to preserve thespatial information when aggregating the functional zones,which unites the clustering of fine-girded regions. The dif-ference of normalized POI distributions is employed to esti-mate the functionalities for a better annotation. Comparingwith LDA-based methods, our method produces better re-sults and a finer granularity with practical implementationconditions. The proposed framework can efficiently dis-cover different functional zones and help designers to fullyunderstand the urban structure.

6. AcknowledgementWe would like to thank Valassis Digital to support this

research and provide access to their data. We would like toalso show our gratitude to Schaun Wheeler, Mark Lowe andJeff Hicks for sharing their valuable inputs and suggestionsduring the course of this research.

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