Handling Missing Data in a Tree Species Catalog Proposed for

Reforesting Mexico City

ector Javier V

azquez

and Mihaela Juganaru-Mathieu

Departamento de Sistemas, Universidad Autonoma Metropolitana, Unidad Azcapotzalco,

Avenida San Pablo 180, Mexico D.F., Mexico

Institut H. Fayol, Ecole Nationale Sup

erieure des Mines, 158, cours Fauriel, 42023, Saint Etienne, France

Keywords:

Data Mining, Handling Missing Attribute, Multiple Correspondence Analysis, Clustering.

Abstract:

In this paper we present an application of handling missing attribute values for some data about urban forest

in Mexico City. The missing attribute values are about pollution tolerance of the trees, around 42% of our

observations are incomplete. Classical methods are non applicable without introducing noise. Our proposal

is to use successive steps of multiple correspondance analysis. The estimations values are validated with a

clustering approach. The complete data can be used for a variety of future applications.

1 INTRODUCTION

Trees are a vital component of the human

environment and city landscape. Because of

the many functions and beneﬁts trees provide,

it is impossible to imagine urban life without

them (Burden, 2008). Even though trees have been

a part of urban environments since cities began to

develop, the study of urban trees is recent, and our

knowledge about this important asset is limited. It

wasn’t until the second half of the 20th century,

as urbanization increased, that city trees began

to receive special attention, as evidenced by the

emergence of such disciplines as urban forestry and

arboriculture. The last comprehensive review of

scientiﬁc literature about urban tree planting was in

1997 (Watson, 2011). Since that time, researchers

have begun to focus on how to apply knowledge about

plant biology, soil structure, and soil composition

to improve tree survival in urban environments. In

spite of those advances, our knowledge about urban

trees remains incomplete and many questions stay

unanswered (Carter, 1993).

Considering the importance of these valuable

assets, many cities have adopted policies and

strategic plans and initiated various programs for tree

maintenance and planting. Highly populated Mexico

City (Federal District and its metropolitan suburban

area), long one of the most polluted regions of the

world, is no exception. Mexico City’s weather and

geographic location offer ideal conditions for the

growth and adaptation of a great diversity of tree

species. However, the characteristics of the city and

its huge population are obstacles to tree survival. As is

true in many cities, trees in Mexico City are located in

both private and public spaces. In public spaces, they

are planted along or in sidewalks, in road medians,

and in gardens, parks, sport ﬁelds, and cemeteries.

Unfortunately, it is common for urban trees to

suffer severe injuries and diseases originated from

their environment: air, soil and water pollution,

insects, parasites, lack of water, impediments to

growth, such as cabling, planting pits and soil

compaction, and damage from vandalism. Because

trees provide many beneﬁts, one of the goals of

authorities in charge of tree resources and green

areas is to increase tree survival rates and improve

conditions adequate for growth. Educating urban

green areas’ administrators, home owners and the

general public about the beneﬁts of trees and

providing information about tree planting and care

are among the ways to accomplish the goal – for

example, the local secretary of the environment

has published several technical manuals for the

integral management of urban green areas (SMA,

2000). In particular, two of these manuals (one for

pruning, felling, transplanting and an other to assess

species’ tolerance to pollution) include a catalog of

species recommended for planting in the Federal

District. For each species it is included information

about appropriate planting sites and environmental

conditions for growth, but they do not provide

457

Vázquez H. and Juganaru-Mathieu M..

Handling Missing Data in a Tree Species Catalog Proposed for Reforesting Mexico City.

DOI: 10.5220/0005158404570464

In Proceedings of the International Conference on Knowledge Discovery and Information Retrieval (KDIR-2014), pages 457-464

ISBN: 978-989-758-048-2

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

comprehensive information about species’ response

to air pollution. Accordingly, the goal of the current

study was to explore a method to replace missing data

concerning species’ response to air pollution through

the use of multiple correspondence analysis (MCA).

It is important to obtain these data because species

tolerance to pollution might be a key factor for tree

survival (EPA, 2010) in a city like Mexico City –

where pollution levels vary depending on season,

urban area, or even time of day.

Section 2 presents our data along with a brief

description of various methods to replace missing

values. Section 3 proposes an imputation-approach

based on the MCA. The results of this method are

detailed in section 4. Finally, conclusions and future

work plans are presented in section 5.

2 TREE’S SPECIES DATA SET

The data set is generated from the fusion of attributes

of recommended species included in two technical

manuals. However, some attributes related to species’

response to air pollution are missing. In this section

data is described and brieﬂy analyzed, followed by

a short presentation of methods for handling missing

values.

2.1 Tree’s Species Data Set

The data set is generated from the information

contained in two technical manuals published by the

local secretary of the environment of Mexico City:

• The ﬁrst manual gives guidelines for pruning,

felling and transplanting trees and shrubs (SMA,

2000). It includes relevant information about 134

species with key features such as:

– Group 1: nominal characteristics (species

name, genus, origin)

– Group 2: basic characteristics (tree, shrub,

palm, fruit, evergreen)

– Group 3: tolerance to some general

environmental conditions (to cold (tcold),

to dryness (tdry), to mistreatment (tmiss) and

to soil salinity (tsal))

– Group 4: a recommended list of planting

sites (streets and middle-roads (s street), urban

recreational parks (s urbrp), parking lots

(s parlot), beneath electric lines (s beleclin),

cemeteries (s cem), sport ﬁelds (s sport f ),

urban forest (s urb f or))

• The second manual (SMA, 2001) offers

information about environment and pollution

in M

exico city and it includes information, about

species’ response to pollution (sensitivity = 1,

tolerance = 2, resistance = 3, and adaptation = 4)

to four levels of air pollution. Unfortunately this

manual includes information for only 77 species

of the 134 species listed in the ﬁrst. Pollution

levels are classiﬁed by primary component (SO

= sulphur dioxide, NO

= nitrogen dioxides, CO

= carbon monoxide and PST = total suspended

particles) in metric tonnes per year. The four

pollution levels form the following variables in

Group 5:

– veryhighpollution = (SO

> 500, NO

> 2000,

CO > 3000, PST > 2000)

– highpollution = (251 < SO

< 500, 500 <

< 2000, 500 < CO < 3000, 500 < PST <

2000)

– mild pollution = (101 < SO

< 250, 100 <

< 500, 100 < CO < 500, 100 < PST <

500)

– lowpollution = (SO

< 100, 10 < NO

100, 10 < CO < 100, 10 < PST < 100).

From these two sources a database resulted with

134 species, each of which has 4 columns (nominal

variables) to account for general characteristics of

group 1, 15 columns with 1 indicating presence and

0 indicated absence of the related characteristics of

groups 2, 3 and 4, and four more columns to indicate

response to one of the four pollution levels. Some

codes names are based on the characteristics, for easy

reference. These characteristics are not exclusive: the

same species may have more than one characteristic

of the same group (for example, a species that is both

a shrub and fruit). In the case of species’ response

to pollution, a given species might have the same

response to one or more pollution levels. Among

responses to different pollution levels, there is an

implicit order, this is to say, that if a given species

is resistant to high pollution, it can be also resistant

or adapted to lower levels of pollution, but it can’t be

tolerant or sensible to lower pollution levels. Given

that all species are recommended for the urban forest

(s urb f or) and are adapted to low pollution levels

(lowpollution), these variables are not included in the

analysis. Data can be obtained from the following

address http://www.emse.fr/∼mathieu/data/trees/.

The 134 species are from 65 genera. Of those

genera, 72.39% are trees, 50% are shrubs, 4.48%

are palms, 11.94% are fruit, 66.42% are evergreen,

82.84% resist cold, 49.25% resist dryness, 32.09%

tolerate soil salinity, and 29.10% are tolerant to

mistreatment. With regard to planting site, 52.99% of

the genera are proposed for planting along, 97.01%

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458

Figure 1: Distribution of modalities and missing values for

variables related to pollution (the percentage of the 134

species is shown in parentheses).

in urban recreational sites, 54.48% beneath electrical

lines, 86.57% in cemeteries, 78.36% in parking lots,

and 89.55% at sport ﬁelds.

Figure 1 shows the distribution of modalities

concerning species’ response to the three different

levels of pollution considered.

2.2 Classical Handling Missing Values

In the literature (Han and Kamber, 2006) different

non exclusive options to handle missing values are

proposed:

1. to ignore the values or the whole n-tuple

2. to replace missing values with a global value

3. to assign a value considering a statistical measure

like: the tendency, the most probable value

or the values generated, by simulating a given

distribution

4. to establish relationships, models or groups

obtained between non missing attributes of the

data set and values of variables, where missing

data is present. The use of statistical or

data mining techniques might be applied to

establish relationships and to obtain one or several

estimations of the missing value.

The results obtained are then used to replace

missing data. More details about all these methods

can be found in (Grzymala-Busse and Grzymala-

Busse, 2005).

Most of these methods are related to handle

missing numerical information and suppose that

information is missing due to error. Some of them

may delete information or add dummy information to

account for missing values.

In the case of the trees species data set work,

missing information is categorical and it is not due

to error. As shown in Figure 1 there are 57 missing

values (coded NA) on variables mild pollution and

highpollution; and 58 missing values on variable

veryhighpollution.

The simplest way to solve the problem of missing

values is to delete the corresponding observations or

the pollution variables (group 5) that have missing

values (method 1). However, that information is

an important factor, and eliminating it would result

in 42.45% of observations deleted, or 20% of the

pollution variables.

Another option is to assign missing modalities

according to frequency (method 3). The variable

lowpollution has just one modality (adequate), so

it would be assigned to all species. For the

other three variables in group 5, assigning the most

frequent modality means deﬁning all the trees as

sensitive to very high pollution, tolerant of high

pollution, and adequate in tolerance to mild pollution.

The drawback to eliminating the missing values is

homogenization of the variables. Furthermore, if

random assignment of modalities is performed (even

according to frequency distribution), it could result in

instances, with not logic (without taking into account

the implicit order discussed before), for example a

tree may be categorized as sensitive to mild levels

pollution and adapted to high levels. These drawback

might be solved by considering just the distribution of

the triplets (of the three pollution levels) observed in

the instances with non missing values.

Finally a relationship might be established

between one or all variables of the groups 1 to 4, and

the three variables (group 5) related to pollution. The

use of multiple correspondence analysis as a mean

to ﬁnd multiple relationships and to estimate missing

data is an example of this approach.

3 HANDLING MISSING VALUES

BY MULTIPLE

CORRESPONDENCE

ANALYSIS

Multiple correspondence analysis (MCA) is one

of the most widespread methods for analyzing

categorical multivariate data tables with I individuals

in rows and J variables (with at least two modalities)

in columns. Using the χ

distance helps to identify

the primary sources of variability and to examine

HandlingMissingDatainaTreeSpeciesCatalogProposedforReforestingMexicoCity

459

Figure 2: Indicator matrix generated from data.

and describe information contained in the original

categorical data using a reduced number of variables

(referred to as main factorial axes or components).

Each individual observation, variable or modality

can be represented by its coordinates relative to the

factorial axes. Categorical information is thereby

transformed through MCA into numerical form.

If k

, k

, . . . k

, . . . , k

are are the number of

modalities for each respective variable, then an

indicator matrix X with I lines and K columns can

be constructed, where K =

∑

j=1

. For this, each

variable j in one column is decomposed in a group

of k

columns formed with k

− 1 zeroes and one to

indicate the presence of the modality. See ﬁgure 2

indicating this decomposition.

From X a Burt matrix B = X

× X is

constructed a contingency table from which classical

correspondence analysis (CA) can be applied to ﬁnd

the factorial components (Lebart et al., 2006).

With non-missing data, it is possible to

reconstitute 100% of the original data from the

coordinates relative to the factorial components.

However, as the number of components used to

reconstitute original data is reduced, the error

increases.

To better understand this approach to handling

missing values, suppose that an individual species

has no value (coded NA) for a given modality of

a categorical variable with four modalities (s, t, r, a).

For the sake of simplicity, we assume that there is

not other more missing information. It then becomes

possible, based on the proportion of each modality,

to assign a missing value. Say, for example, that the

guess is [s = 0.3,t = 0.2, r = 0.1, a = 0.3]. MCA

is applied, and a number of S < K components is

retained to reconstitute the X matrix. To use MCA,

it is necessary to fulﬁll certain conditions, such as

having the same sum for all lines of the indicator

matrix; therefore, some corrections should be made

on the run. Suppose that, after several iterations, the

results are [0.5, 0.1, 0.1, 0.2]; NA is then substituted

by the modality s.

The algorithm, based on the work of (Josse et al.,

2012), is:

1.- Initialization:

l ← 0 imputation of missing modalities on

the indicator matrix X

(0)

(i.e., with proportions);

Verify conditions to apply MCA

2.- Iteration step for l

a) Estimation:

Perform MCA on the indicator matrix X

(l−1)

;

Obtain factorial components and retain S < K

components;

Get

(l)

, size J × S, and coordinates

(l)

, size

I × S;

Estimate missing values with

(l)

←

(l)

(

(l)

)

;

b) Imputation:

Get the new indicator matrix X

(l)

by adding

the new values to the X:

(l)

← W × X + (1 − W ) ×

(l)

;

with w

i j

= 0, if x

i j

is missing, and w

i j

= 1, if

it is not missing;

Update proportions and verify conditions to

apply MCA;

3.- Repeat step 2 until convergence, that is to

minimize

C =



W × X

(l)

−

F ×



S is chosen a priori, F are the coordinates, U are the

factorial axes and W the weights

This algorithm is extended to multiple imputations

to take data variability into account and to regularize

eigenvalues to avoid overﬁtting. Further details about

these modiﬁcations, validation tests with different

percentages for missing values, and applications to

other domains can be found in (Husson and Josse,

2013; Josse et al., 2012).

Once the indicator matrix is fully reconstituted

and there are no more missing modalities, MCA

is applied to examine and describe information,

as discussed earlier, on a reduced number of

components. The primary MCA results are a set

of factorial axes (or components) that represent an

important percentage of inertia and the coordinates

for individuals, variables, and modalities with respect

to those components. Data are examined by

visualizing the distribution of projections on the

coordinate plans generated by the factorial axes

and are conﬁrmed using indicators such as the

contribution (individual, variable, or modality) to the

axes, the quality of representation, and correlation.

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Signiﬁcant values are selected based on the t.values.

Validation is performed by applying an algorithm

such as agglomerative hierarchical clustering (AHC)

to the retained coordinates. Algorithms to perform

multiple imputation, MCA and AHC are, respectively

in R libraries MissMDA and FactoMineR (R Core

Team, 2014).

4 RESULTS

MCA is applied directly to the Tree species data

set to assess the importance of missing values in

terms of inertia, their variability and the degree of

distinction from the individuals and variables without

missing values. Then the algorithm described above

is applied to estimate and to impute missing values.

Finally MCA is applied to imputed data and the

description of variables (as well as modalities) and

species distribution is realized in function of the main

components retained. AHC is used to deﬁne and to

identify groups of species.

4.1 Before Handling Missing Values

To evaluate the importance of missing values, an

MCA data exploration was performed for all 134

species and the 18 associated categorical variables:

tree, shrub, palm, fruitful, evergreen, tcold, tdry,

tmiss, tsal, s street, s urbrp, s parlot, s beleclin,

s cem, s sportf, veryhighpollution, highpollution and

mildpollution. Given that all species are proposed

for urban forest (s urbfor) and are adapted to low

pollution levels (lowpollution), these variables are

not included in the analysis. Direct application of

MCA with missing values requires addition of a new

variable to code missing values. The primary results

are as follows:

• The ﬁrst three components represent, respectively

25.58%, 25.46% and 13.40% of total inertie, for

an accumulated inertia of of 64.44%.

• All 18 variables can be identiﬁed on the ﬁrst

two components, although the pollution variables

appear to be outliers because they clearly separate

from the group

• Contributions, of each group of variables, to the

formation of the ﬁrst there components are:

– C1.- Group 2: 28.56%, Group 3: 7.05%, Group

4: 36.16% and Group 5: 28.22%.

– C2.- Group 2: 2.53%, Group 3: 10.09%, Group

4: 18.19% and Group 5: 69.18%.

– C3.- Group 2: 27.97%, Group 3: 40.68%,

Group 4: 14.42% and Group 5: 16.91%.

Figure 3: Results of MCA using initial data.

• The variables veryhighpollution, highpollution

and mildpollution represent an important

percentage of the inertie for each component.

• The missing modalities’ contribution of the

variables veryhighpollution, highpollution and

mildpollution are respectively: 12.20%, 12.78%

and 12.77%.

• Missing modalities are high correlated and very

well represented by the second axis; the quality of

representation values are close to 1 ( 0.87, 0.87 y

0.86).

• The contribution of species with missing values

to the formation of the ﬁrst two components is

respectively: 34.17 and 48.29.

• Almost all specie with missing values, except one,

form a very well deﬁned cluster.

The major contribution of the missing values

makes it difﬁcult to analyze information with non-

missing information, but the fact that all individuals

comprise one cluster allows the possibility for

handling them with the same approach. Figure 3

depicts the ﬁrst application of MCA to the initial data

with missing values.

Variable’s projections on the ﬁrst two MCA

components show the pollution variables as outiliers,

which is the result of the high contribution of missing

values.

4.2 MCA Handling Approach for

Missing Values

The results of ”cross validation” and ”leave one out”

tests suggest retaining ﬁve components to reconstruct

the indicator matrix. From these components missing

data are estimated and used to reconstruct the

indicator matrix. Multiple correspondence analysis is

then applied to reconstructed data, again for all 134

species and the 18 categorical associated variables.

The distribution of modalities after MCA application

HandlingMissingDatainaTreeSpeciesCatalogProposedforReforestingMexicoCity

461

Figure 4: Results of MCA after handling missing values.

is presented in Figure 1. The primary MCA results

are as follows:

• The ﬁrst three components represent, respectively,

34.15%, 19.89% and 12.97% of total inertia, for

an accumulated inertia of 67.01%. This is almost

the same as the one obtained before handling

missing values, but there is a slight increase in the

ﬁrst component with a corresponding decrease in

the second.

• All 18 variables can be identiﬁed on the ﬁrst

two components, although pollution variables no

longer appear to be outliers.

• Contributions of the groups of variables to the

formation of the ﬁrst there components are:

– C1.- Group 2: 24.46%, Group 3: 11.86%, Group 4:

36.29% and Group 5: 27.38%.

– C2.- Group 2: 33.81%, Group 3: 31.02%,Group 4:

11.92% and Group 5: 23.23%.

– C3.- Group 2: 12.95%, Group 3: 14.59%,Group 4:

60.76% and Group 5: 11.69%

• The contribution of the variables

veryhighpollution, highpollution and

mildpollution has been reduced. No modalities

were created to handle missing values.

• The contribution of species that had missing

values to the formation of the ﬁrst two

components is 43.49 and 48.17, respectively. This

means that no information was missing; therefore,

the contribution to both axes was balanced.

• No particular cluster for species that had missing

values was observed.

• No important change was observed when

modalities with low percentages were removed.

Figure 4 displays the pollution variables mixed

with the other variables.

These ﬁndings allow the components to be

described, as presented in the following section.

4.3 Data Exploration with MCA and

AHC

Description is based on variables correlation

(p.value < 0.05) with each of the ﬁrst three

components (C1, C2 and C3) generated by MCA.

Variables correlation is indicated between parenthesis

and species are described according to the signiﬁcant

variables modalities (t.value > 1.96) on each side

(positive or negative) of the speciﬁc component:

• Component 1: shrub (0.44), high pollution

(0.44), below electric lines (0.40), streets and

middle roads (0.33), tree (0.30), very high

pollution (0.31), parking lots (0.28), sport ﬁelds

(0.25), tolerance to cold (0.22) and genus (.79).

– Positive side: Species that are shrubs but

not trees; recommended for planting below

electric lines; not recommended for planting

in streets/medians, parking lots, and sport

ﬁelds; tolerant to high pollution and very high

pollution levels; not tolerant to cold.

– Negative side: Species that are trees but

not shrubs; recommended for planting in

streets/medians, parking lots, and sport ﬁelds;

not recommended for planting below electric

lines; sensitive to high and very high pollution

levels; tolerant to cold.

• Component 2: evergreen (0.39), fruitful (0.37),

tolerance to dryness (0.35), high pollution

(0.32),tolerance to soil salinity (0.27), genus

(0.80), tolerance of mistreatment (0.23), tolerant

of mild pollution levels (0.24)

– Positive side : not evergreen; not fruit;

not tolerant of dryness, soil salinity, and

mistreatment; tolerant to mild and high

pollution levels.

– Negative side : evergreen; not fruit; tolerant

to dryness, soil salinity, and mistreatment;

resistant to mild pollution.

• Component 3: recreational parks (0.37),

cemeteries (0.34), below electric lines (0.26),

parking lots (0.24), tolerance to cold (0.18), very

high pollution (0.19), shrubs (0.15), trees (0.11),

tolerance of dry conditions (0.11), genus (0.69).

– Positive side : not recommended for planting

in recreational parks, cemeteries, and parking

lots; not recommended for planting under

electric lines.

– Negative side : Species with characteristics

opposite the positive characteristics.

Species identiﬁcation is easier if cluster analysis,

such as Agglomerative Clustering Analysis

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(AHC) (Jain and Dubes, 1998; Grabmeier and

Rudolph, 2002) is applied to the species coordinates

generated by MCA. For example, AHC with the Ward

method and Euclidean distance, pre-establishing four

clusters (to identify observations on the four

quadrants obtained with components C1 and C2),

gives the results shown in Figure 4. For each cluster,

1 through 4, the following description can be made

regarding genera:

• Cluster 1 - Located on the second and third

cuadrants : Abies, Alnus, Pseudotsuga, Quercus,

Arbutus, Salix, Toxodium, Ulmus, Calocedrus,

Cedrus, Celtis, Chamaecyparis, Chirantoendrom,

Cupressus, Fraxinus, Junglans, Legerstroemia,

Liquidambar, Magnolia, Acer, Pinus, Alnus,

Platanus, Podocarpus, Populus.

• Cluster 2 - Centered and spread through the

ﬁrst, third, and fourth quadrants: Quercus,

Araucaria, Robinia, Rosa, Schinus, Tamarix,

Thuja, Washingtonia, Yucca, Acacia, Cedrus,

Cupressus, Erythrina, Eucalyptus, Acacia,

Ficus, Ginkgo, Grevillea, Jacaranda, Juniperus,

Ligustrum, Magnolia, Olea, Phoenix, Acer,

Pinus, Pittosporum.

• Cluster 3 - In the fourth quadrant: Quercus,

Schinus, Beaucarnea, Buddleia, Buxus,

Calistemon, Cassia, Casuarina, Acacia,

Eucalyptus, Juniperus, Acacia, Ligustrum,

Nerium, Pittosporum, Populus, Prosopis.

• Cluster 4 - In the ﬁrst quadrant: Prunus, Citrus,

Crataegus, Cydonia, Elaeagnus, Eryobotria,

Ficus, Malus, Morus, Musa and Persea.

These results provide insight into the validity of

the approach presented in this work. For example,

fruit species are found in Cluster 4. Cluster 1

primarily includes large trees appropriate for planting

along streets and in medians and that are tolerant of

high levels of pollution. Cluster 3 includes evergreen

species (not fruit) that can tolerate dryness, soil

salinity and mistreatment.

These results open the way for deeper data

explorations. For example, it would be interesting to

separate Cluster 2 into a group of trees and palms

and to evaluate the differences between species in

Cluster 1 and Cluster 2 because they are the same

genera. However, such an evaluation should be done

with care, considering the diverse characteristics of

Quercus and Pinus presented in this study.

Figure 5: Application of hierarchical clustering with Ward

method and euclidean distance, for 4 clusters.

5 CONCLUSIONS

After considering different options for handling

missing values pertaining to trees species tolerance

of and sensitivity to air pollution in Mexico City and

given that it is not currently possible to obtain reliable

information from ofﬁcial sources, this paper presents

an option for estimating and imputing missing values

of pollution related variables based on MCA.

The proposed approach has important advantages

because MCA is an adequate and well proven

technique for treating categorical variables. The

approach to estimate missing information does not

require to delete information, and it does not add

spurious information to account for missing values.

In theory basic data structure is not modiﬁed with

this approach, for example, in terms of importance

or possible associations between individuals and

variables with non-missing information. However it

would be worthwhile to apply other approaches to

estimate missing information and to explore changes

in data structure.

Further explorations with imputed missing values

should be undertaken, changing the number of

clusters generated, including the possibility of

evaluating the results with the assistance of an expert

in arboriculture in analysis of species similarities

within a genus. Nevertheless, the exploratory

results presented in this study agree with associated

variables such as genus and some important species

characteristics. These interpretations are, for the most

part, validated by the clustering results.

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ACKNOWLEDGEMENTS

ector Javier V

azquez acknowledges the Universidad

Aut

onoma Metropolitana (Azcapotzalco) and

the Mexican National Council for Science and

Technology (CONACYT) for the Grant (Proposal

No. 208133-2013, Multidisciplinary Area 8).

Authors acknowledge Peggy Currid for her advice in

copyediting.

REFERENCES

Burden, D. (2008). 22 beneﬁts of urban street trees. http://

km.fao.org/uploads/media/streettrees22beneﬁts.pdf.

Carter, E. J. (1993). The potential of urban forestry

in developing countries: a concept paper. http://

www.fao.org/docrep/005/t1680e/T1680E01.htm.

EPA (2010). Air pollution. http://www.epa.gov/airtrends/

2010/report/airpollution.pdf.

Grabmeier, J. and Rudolph, A. (2002). Techniques of

cluster algorithms in data mining. Data Mining and

Knowledge Discovery, 6(4):303–360.

Grzymala-Busse, J. W. and Grzymala-Busse, W. J. (2005).

Handling missing attribute values. In Maimon, O. Z.

and Rokach, L., editors, Data mining and knowledge

discovery handbook, volume 1. Springer.

Han, J. and Kamber, M. (2006). Data Mining : Concepts

and Techniques. Morgan Kaufmann.

Husson, F. and Josse, J. (2013). Handling missing values in

multiple factor analysis, food quality and preference.

Food Quality and Preference, 30:77–85.

Jain, A. K. and Dubes, R. C. (1998). Algorithms for

Clustering Data. Prentice Hall.

Josse, J., Chavent, M., Liquet, B., and Husson, F.

(2012). Handling missing values with regularized

iterative multiple correspondence analysis. Journal of

Classiﬁcation, 29:91–116.

Lebart, L., Morineau, A., and Piron, M. (2006). Statistique

Exploratoire Multidimensionnelle. Dunod.

R Core Team (2014). A language and environment for

statistical computing. http://cran.r-project.org/web/

packages/missMDA/missMDA.pdf and http://cran.

r-project.org/web/packages/FactoMineR/

FactoMineR.pdf.

SMA (2000). Manual T

ecnico para la Poda, Derribo y

Transplante de

Arboles y Arbustos de la Ciudad de

exico, Secretar

ıa del Medio Ambiente del Distrito

Federal. Secretar

ıa del Medio Ambiente del Distrito

Federal, M

exico, D.F. http://www.sma.df.gob.mx/

drupc/ capacitacion/ manual tecnico poda derribo

trasplante arboles.pdf.

SMA (2001). Manual T

ecnico para el Establecimiento

y Manejo Integral de la

Areas Verdes Urbanas

del Distrito Federal. Folleto Pr

actico. Secretara

del Medio Ambiente del Distrito Federal, M

exico,

D.F. http://www.paot.org.mx/centro/ceidoc/archivos/

pdf/manual manejo areas verdes folleto practico.pdf.

Watson, G. (2011). Fifteen years of urban tree planting

and establishment research, trees, people and the built

environment. In Proceedings of the Urban Trees

Research Conference, pages 63–72.

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