Time-Based Joining Method for GeneratingPhylogenetic Trees of Architectural Plans

Sungil Ham, Ph.D.1; and Ghang Lee, Ph.D.2

Abstract: A method has been developed for automatically generating a phylogenetic tree of architectural plans based on graph theory,

according to the properties of the plans and the timing of their appearance. A phylogenetic tree of architectural plans is a branching diagram

that shows transitions of the architectural plans by period. In previous studies, researchers analyzed structural similarities and differences

between architectural plans by comparing one floor plan to another. Such manual classification processes sometimes result in inconsistent

classifications and are inefficient, especially when a large number of plans are compared and analyzed. In this paper, a new algorithmic

approach is proposed, termed the time-based joining (TBJ) method, for quantitatively evaluating structural similarities between architectural

plans and creating a phylogenetic tree of the analyzed architectural plans. The validity and consistency of the TBJ method’s results were tested

by generating a phylogenetic tree of 422 collective housing unit plans in Seoul, South Korea, constructed from 1970 to 2010. DOI: 10.1061/

(ASCE)CP.1943-5487.0000626. © 2016 American Society of Civil Engineers.

Author keywords: Phylogenic tree; Time-based joining method; Spatial similarity.

Introduction

A phylogenetic tree of architectural plans is a branching diagram

that shows transitions in architectural plans by period, considering

topological spatial relationships and the times at which various

types appeared. For a long time, many studies have been conducted

to generate a phylogenetic tree or a classification of architectural

plans, especially in the context of architectural history and theo-

ries (Alexander 1979; Caniggia and Maffei 2001; Franck and

Schneekloth 1994; Madge 2007; Rapoport 1969). As biological

terms are commonly used to describe concepts and elements of

hierarchical structures in many fields of study, such as inheritance,

class, family, child node, and parent node in computer science,

the previous studies on phylogenetic trees and classifications of ar-

chitectural plans also commonly borrow terms from biology, such

as genotype (Bafna 2001; Dahabreh 2006; Gero and Ding 1997),

ancestor, decedent, child, and parent.

Early architectural-plan studies often compared one floor plan

to another based on the researchers’ judgment regarding the

characteristics of floor plans. Such manual analysis processes are

time-consuming and may produce biased or inconsistent results.

To overcome these limitations, several efforts have been under-

taken for developing a quantitative floor plan analysis (Manum

2005; Markus 1993) and classification method (Bafna 2001;

Bandyopadhyay and Merchant 2006; Bustard 1999; Dahabreh

2006; Guney and Wineman 2008; Hanson 2003; Hillier and

Hanson 1984; Lee 2004; Seo 2005). Still, the generation of a phy-

logenetic tree of architectural plan types in these efforts also

depended primarily on the qualitative judgment of researchers

and was also time-consuming.

This study proposes a new graph theory–based algorithmic

approach, the time-based joining (TBJ) method. In this method,

structural similarities and differences between architectural plans

are quantitatively evaluated, plans are categorized by type, and a

phylogenetic tree of the analyzed architectural plan types is gen-

erated. In assessing the similarity of tree structures, several

algorithms are commonly deployed, such as the unweighted

pair group method with arithmetic mean (UPGMA) (Sokal and

Michener 1958), the transformed distance method that supplements

UPGMA (Farris 1977), the neighbor’s relation method (Sattath and

Tversky 1977), and the neighbor-joining (NJ) method (Saitou and

Nei 1987); these are also commonly used in creating biological

phylogenetic trees (Bergstrom and Dugatkin 2011).

The authors preliminarily tried to adopt these phylogenetic tree

generation algorithms. However, these methods returned trees that

were nonsensical in terms of the timing of the appearance of the

architectural plans, because the algorithms rely only on the simi-

larity of subjects’ features and do not include the timing of their

appearance as a factor. Thus, in the TBJ method, the timing of

the appearance of the architectural plans was added as a key addi-

tional factor in analyzing the similarities between architectural

plans—hence, the naming of the newly proposed method as the

time-based joining (TBJ) method.

This study focuses especially on the transitional history of ar-

chitectural plans for collective housing in South Korea. Collective

housing is the main residential building type in South Korea,

exceeding 70% of housing types in 2010 (Statistics Korea 2010);

the detached house is the main type of residential building in most

countries. This unique culture was initiated in the 1970s by the

Korean government, which tried to supply a large amount of fine-

quality residences in the shortest time possible to the people who

had lost their houses during the Korean War in the early 1950s.

In Korea, collective housing units are called apartments, whether

they are rented or owned by the occupants.

As a research subject, collective housing is an interesting res-

idential building type, because it reflects the culture of the times

better than any other type of residential building, especially because

1Research Professor, Dept. of Interior Architecture and Built Environ-

ment, Yonsei Univ., Seoul, Korea. E-mail: archispace@yonsei.ac.kr2Professor, Dept. of Architectural Engineering, Yonsei Univ., A512

Engineering Hall I, 50 Yonsei-ro, Seodaemun-Gu, Seoul 120-749, Korea

(corresponding author). E-mail: glee@yonsei.ac.kr

Note. This manuscript was submitted on June 20, 2015; approved on

June 29, 2016; published online on September 26, 2016. Discussion period

open until February 26, 2017; separate discussions must be submitted for

individual papers. This paper is part of the Journal of Computing in Civil

Engineering, © ASCE, ISSN 0887-3801.

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collective housing is designed and built according to the utilitarian

philosophy of “the greatest happiness of the greatest number”

rather than according to personal preferences.

The next section reviews previous studies on the theories related

to space phylogenetic trees, the similarity analysis methods in

graph theory, and algorithms that are commonly used for generat-

ing phylogenetic tress. Then, the TBJ algorithm is described and

validated by comparing the analysis results between TBJ and the

NJ method, the most commonly used phylogenetic-tree generation

method.

Previous Studies

In this section, the basic premise of space phylogenetic tree studies

based on existing theories is discussed first. Second, previous

studies focusing on quantitative analyses of architectural plans

are reviewed; a broader review regarding qualitative analyses of

transitions of architectural plans is impractical because these have

been a key topic in architectural history, theory, and criticism, and

thus are too numerous to review with both coherence and brevity.

Third, methods are described for evaluating similarities between

graphs. Finally, existing studies on phylogenetic tree generation

algorithms based on graph similarity are reviewed.

Premise of Space Phylogenetic Tree Studies

Buildings are social objects (Markus 1993) and tend to change over

time, reflecting the sociocultural changes. However, the basic

premise of a space phylogenetic tree is that building design tends

to remain consistent, especially for residential buildings within

a region. With very few exceptions, designs do not randomly or

radically change according to immediate demands, but tend to con-

form to factors that do not easily change, such as natural environ-

ment, customs, and traditions. Generation after generation, the

principles of spatial structure and social and cultural factors affect

how designs change, but the modified principles of spatial structure

are never completely new—they are modifications of previous prin-

ciples. This is because there are basic principles of spatial structure

to which any modifications in design must adhere. Bafna (2001)

defined these principles as genotypes. Genotypes represent socio-

logical principles and structures of spatial structure in architecture

that cannot be changed arbitrarily. An architectural space changes

and develops as it forms a type. A plan type is a category of archi-

tectural plans that shares common topological characteristics. Such

changes and transitions create a family. A family is a certain group

of architectural plan types that share similar topological character-

istics (Simpson 2010).

The tree diagram produced through studying families has been

used as a basic categorization method not only in biology but also

in the humanities, sociology, and computer science. Although the

phylogenetic approach has been recognized for providing a new

framework for thinking as it was applied to fields other than

biological evolution, it has also received a lot of criticism and

discussion about the appropriateness of applying it to various other

fields. However, it has contributed greatly to establishing many

hypotheses and to explaining transitional processes of change

and development.

Previous studies use many terms and concepts related with the

phylogenetic tree. This study also adopted them. The definitions of

terms frequently used in this paper are listed in Fig. 1 with an illus-

trated example. A graph consists of objects and their relations. An

object is often represented as a circle or polygon, and a relation as a

line between objects. A graph can be divided into many subgraphs.

In architecture, graphs have commonly been used to represent

the topological relationships between spaces (rooms) rather than

representing the transitional relationships between floor plan

types. The topological relationships between spaces (rooms) are

generally referred to as a plan type. The transitional relationships

between floor plan types are referred to as a space phyloge-

netic tree.

A plan type is the minimum unit (object, node) that constitutes a

space phylogenetic tree. The connection in a space phylogenetic

tree represents the transitional relationships between plan types.

A plan type is often expressed in the form of a justified graph

(j-graph) (Hillier and Hanson 1984). An example of a plan type

is a plan.

A family is generated by finding the most similar plan types and

connecting them to one another. A space phylogenetic tree is com-

posed of families of similar plan types. Members of the same family

branch out from preceding plan types in a space phylogenetic tree

similar to the branching of a person’s family tree.

Quantitative Analyses of Architectural Plans

Quantitative studies of architectural plan types are generally based

on graph theory (Carpenter 1959; Mitchell 1990). The architectural

type is determined by, among other things, “details like the shapes

and peculiar forms of the rooms” (Kourouniotes et al. 1933).

Quantitative analytical studies on spatial structures and types

became active when “Ideas are in things: An application of the

space syntax method to discovering house genotypes” was pub-

lished in 1987 (Hillier et al. 1987). This study analyzed the archi-

tectural plans of 17 residential buildings in Normandy, France,

using j-graphs. The findings showed that there is a certain pattern

by which architectural plans can be categorized by type, and that a

study can be conducted on genotypes of space construction using

this pattern.

Based on this methodology, a study was conducted on collective

housing units in Ankara, Turkey, from 1920 to 1990 (Guney and

Wineman 2008), reporting that a specific arrangement is found

when architectural plans are categorized by the mean depth and

integration values using relative asymmetry (RA) values of rooms

(Hillier and Hanson 1984). Bandyopadhyay and Merchant (2006)

studied residential buildings during the colonial era in India and

stated that there exists a consistent pattern in the real RA (RRA)

value (Hillier and Hanson 1984). In addition, in a study of residen-

ces in Chaco Canyon, New Mexico (Bustard 1999), the integration

value (Hillier and Hanson 1984), defined as the inverse of RRA

(1/RRA), of a room was found to differ by period, and each period

had its own space type. Dalton and Kirsan (2008) introduced a

more developed methodology in which they deleted, inserted,

and substituted the points and lines that represent the relationship

between spaces to calculate the cost, which is the number of mod-

ifications required for one space graph to become the same as

another. To validate their algorithm, they analyzed the similarities

of architectural plans of residential buildings in Cyprus and

obtained a type.

In summary, previous studies used the network distance be-

tween certain rooms (j-graph and mean depth), integration of

rooms (RA and RRA), and the geometric cost of transforming

one plan to another. The methods proposed in previous studies have

many advantages in deriving the common factors (genes) between

spatial structural patterns (plan types) as well as the relationship

between plan types. However, there are other broadly used graph

similarity analysis methods and phylogenetic tree generation

methods. The next section reviews these methods.

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Graph Similarity Analysis

Graphs have been used in various fields, not only in architecture but

also, for example, for data modeling, geographic information sys-

tems, and chemistry, and to study the timeline of human evolution.

Several mathematical and statistical approaches for analyzing

graph similarity have been developed for various purposes (Bunke

1997; Bunke et al. 2000; Fernandez and Valiente 2001; Stevens

1957). This section reviews the iterative method used for graph

similarity analysis and phylogenetic tree generation methods.

The iterative method (Jeh and Widom 2002; Kleinberg 1999;

Melnik et al. 2002) is the most commonly used graph similarity

analysis method. It has a special characteristic in that it analyzes

the relationship between nodes by not only calculating the distance

between them, but also assigning weights to neighboring nodes.

Based on the iterative method, bipartite graph matching

(Heymans and Singh 2003) evaluates the similarity between fam-

ilies by comparing the similarity between metabolic pathways. This

approach has the advantage of having an analysis library and graph

comparative metabolic pathway tool (PWComp) (Adelman 2003).

The bipartite (similarity) score between graphs G1 and G2 is

calculated through the following process (Heymans and Singh

2003): The bipartite score of all node pairs (a, b) in which a ∈ G1

and b ∈ G2 is calculated by repeating the calculation process.

The similarity between two nodes (a, b) can be computed by

adding the similarity of connected nodes and then subtracting

the difference. In the second stage, the obtained bipartite score

is used to find the best matching between graphs. In this way, bi-

partite graphs are formed and mutual graph matching is performed.

Once the G1’s set V1 and G2’s set V2 are obtained, the bipartite

graph G ¼ ðV1;V2; SÞ, containing similarity matrix S, can be gen-

erated. In the third stage, the bipartite evaluations between all pairs

of compared nodes are recalculated. The similarity score can be

obtained through the optimal matching that was previously derived

from graphs G1 and G2. Finally, the bipartite score of the two

graphs is calculated by summing up the bipartite scores of com-

pared nodes and standardizing the resultant values. For details

on the bipartite graph-matching algorithm, refer to Heymans and

Singh (2003).

Phylogenetic Tree Generation Methods

Graph similarity analysis methods do not generate phylogenetic

trees. Developed from traditional phylogenetic studies in biology,

computer-based statistical methods are used for phylogenetic

studies in molecular biology for comparing deoxyribonucleic acid

(DNA), genes, and metabolic routes. Very complex arithmetic op-

erations are required to calculate which phylogenetic tree best

explains the evolutionary process based on similarities between

categories. Grouping and categorizing objects based on similarity

is called clustering or distance calculation. This technique generates

Architecture

Spatial phylogenic treeGraph

Subgraph Family

Plan typeObject

PlanInstance

Example

Fig. 1. Terms used in the spatial phylogenetic tree

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pairwise distance matrices, allowing comparisons of similarity

among all categories. The distance between categories is then cal-

culated by using many statistical algorithms that reorganize the

phylogenetic tree.

The distance matrix method is the oldest method for generating

a phylogenetic tree, and it uses a very simple calculation. This

method includes UPGMA, the transformed distance method that

supplements UPGMA (Farris 1977), the neighbor’s relation

method (Sattath and Tversky 1977), and the NJ method (Saitou and

Nei 1987). Among these, the NJ method is the most commonly

used. The NJ method supplements the UPGMA to offset its disad-

vantage of ignoring the evolution rate. It is able to generate the most

ideal phylogenetic tree by applying the minimum evolution method

based on “the assumption that the tree with the smallest sum of

branch length estimates is most likely to be the true one” (Rzhetsky

and Nei 1993).

In the Comparative Analysis section, to test the proposed TBJ

method’s validity, a phylogenetic tree generated by the TBJ method

is compared to a phylogenetic tree generated by the NJ method. The

next section describes the TBJ method.

Time-Based Joining Method

This study proposes a new phylogenetic tree generation method,

the TBJ method, to support the generation of a space phylogenetic

tree. A key difference between floor plan categorization and organ-

ism categorization is that the time of occurrence is known for the

former. The statistical method of generating the phylogenetic tree,

which was explained earlier, is an algorithm that infers the common

ancestor without any information on when each taxon appeared;

then, it categorizes the taxa by their ancestors. By using the stat-

istical method without considering the time of occurrence, the tree

is formed by considering only the ideal evolutionary direction.

However, there are cases of dedifferentiation, in which descendants

evolve against the direction of natural evolution. Dedifferentiation

can lead to a phylogenetic tree with an incorrect branching

order.

Unlike the biological taxon, it is possible to identify when each

architectural plan type was introduced by looking at its year of con-

struction, except for very old buildings. Suppose that architectural

plans made before the other plans have become precedent types,

and other architectural plans branch off from the precedents. Then,

among the second oldest architectural plan types, the architectural

plan types that are similar to the oldest precedent types become the

second generation precedent cases. A phylogenetic tree is gener-

ated when these precedent–descendent architectural plan types

are connected. The proposed method is called a time-based joining

method because it groups topologically similar floor plan types as

a family using the time of occurrence as an additional factor to

increase the accuracy of classification.

Fig. 2 summarizes TBJ. The first step is to collect and number

floor plans. The second step is to group floor plans with the same

j-graph (i.e., topologically identical room arrangement) as a plan

type. The year of the plan type is the earliest construction (move-in)

year among all plans in the plan type group. The third step is to

calculate similarity scores between each pair of different plan types.

The fourth step is to generate a phylogenetic tree by connecting the

pairs of plan types with the highest similarity scores among the

potential precedent–descendent groups as precedent–descendent

pairs. Between the two plan types in a selected pair, the plan type

with the earlier construction (or move-in) year is assigned as a prec-

edent and the other as a descendent.

Algorithm 1. TBJ

FOR all plans in plan list

IF find group of plan THEN

Continue

ELSE make new plan types

ENDIF

FOR all plans numbered higher than the number of previous

plans in the plan list

Calculate similarity scores between each pair of plans

IF similarity score is equal to one THEN group the pair of

plans

ENDIF

ENDFOR

ENDFOR

Set year of earliest plan as the year of each plan type

Sort plan types by descending year order

FOR all plan types in plan types list

Initialize maximum similarity score as zero

FOR all plan types numbered higher than the number of previous

plan types in the plan types list

Calculate similarity scores between each pair of plan types

IF similarity score is greater than the maximum similarity

score THEN

Pair the two plan types as having the relation of maximum

similarity

Set maximum similarity score to the similarity score

ENDIF

ENDFOR

Draw link between each plan type and its most similar plan type

ENDFOR

Eight architectural plans of collective housing units, depicted

in Fig. 3, are used in this paper to explain in detail how TBJ gen-

erates a phylogenetic tree. This study excludes spaces that cannot

be considered as independent rooms, such as built-in closets, utility

rooms, and storage. Balconies are also excluded because it is not

possible to determine whether a balcony is connected with a sliding

door or a window (a relation through which passing is not possible)

by consulting a plan only.

First, in TBJ, architectural plans are expressed as j-graphs, topo-

logical graphs of the space. Fig. 3 illustrates the eight example

cases and their j-graphs.

The eight architectural plans, which have the same j-graph, are

grouped into four different architectural plan types, as shown in

Fig. 4. The time of occurrence of each type is defined as the

move-in year of the collective housing unit that was built the ear-

liest among the architectural plans with the same j-graph. For ex-

ample, the year of Plan type 7 was considered to be 1984, because

Hongeun Misung (1984) was the first built among the four plans in

Plan type 7 (Fig. 4).

In the third step, the similarities between plan types (not be-

tween plans) are calculated, as shown in Table 1, before generating

a phylogenetic tree. TBJ uses bipartite graph matching, developed

by Heymans and Singh (2003), to analyze the similarity between

plan types. One assumption is that the oldest plan type cannot be a

descendent of other plan types. For example, the appearance year of

Plan type 1 is 1970. Logically, Plan types 5, 7, and 9, which ap-

peared in 1980, 1984, and 1988, respectively, cannot be precedent

types of Plan type 1. For the same reason, Plan type 5 is a potential

precedent of Plan types 7 and 9, not vice versa.

Finally, TBJ assigns the plan type with the highest similarity

score to be an ancestral plan type of a plan type of interest. For

example, Plan type 7 is more similar to Plan type 5 than to the

other option, Plan type 1. Thus, Plan type 5 is determined to be

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Fig. 3. Example architectural plans of collective housing units and j-graphs for generating a phylogenetic tree

Fig. 2. Process of generating a phylogenetic tree by using the TBJ method: (a) collection of architectural plan cases; (b) grouping of architectural

plans with the same j-graphs into types; (c) calculation of similarity scores for each pair of architectural plan types; (d) pairs of plan types with the

highest similarity scores are assigned as precedent–descendent pairs

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the precedent of Plan type 7. Plan type 9 is the most similar to Plan

type 5 among the three precedent options (Plan types 1, 5, and 7).

Thus, both Plan types 7 and 9 become descendants of Plan type 5,

as shown in Fig. 5.

Comparative Analysis

To validate TBJ, phylogenetic trees were generated from 442 ar-

chitectural plans in South Korea from 1970 to 2010: one by using

TBJ and one by using the NJ method described in “Previous

Studies.”

The j-graph of 422 apartment unit plans from 1970 to 2010 used

in the analysis was prepared using the plan images in Sejin-Gihoek

(Editorial Department 2006) (from 1970 to 2006) and KB (2016)

(from 2006 to 2010).

Using these plan images as backgrounds, the drawings were

prepared using a computer-aided design software application.

These drawings were prepared pursuant to the rules of the space-

connector model so that they could be analyzed through the

program. A space-connector model (Ham and Lee 2010) is a sim-

plified spatial map on which spaces are represented as closed poly-

gons based on the inside dimensions of a space, and the relation

between the spaces are represented by the various types of connec-

tors (doors, windows, and virtual boundaries) with different geo-

metric and property values. The space-connector model enables

researchers to analyze not only relationships between spaces but

also physical attributes of spaces, such as the areas of spaces, dis-

tances between them, and the strength of connection (e.g., the width

of a door). Nevertheless, the present study required only j-graphs

that show topological relationships between spaces. As the final

step, j-graphs were extracted from the space-connector maps that

were created in the previous steps. Fig. 6 illustrates this j-graph

generation process using an example.

The subjects of the analysis included architectural plans of

collective housing units that were built for the past 40 years:

between 1970, when South Korea started to build large apartment

complexes, and 2010. For consistency, subjects (422 cases) were

selected to exclude rare apartment unit types and include only

the most common apartment unit type in South Korea, i.e., the

three-bay, two-unit staircase-type (as opposed to multiple-unit

corridor-type) collective housing plans in Seoul, with a floor usa-

ble area of 85 m2. A three-bay unit is a unit whose main area

is composed of three bays, typically a living room between two

bedrooms. A two-unit staircase-type plan is a type of collective

housing floor plan in which two units on the same floor share a

staircase and often also an elevator shaft. The floor usable area

excludes common service areas such as stairs, corridors, and park-

ing lot space.

A total of 422 architectural plans were grouped into 60 different

plan types, as shown in the Fig. 11. A phylogenetic tree of the

60 plan types was generated using TBJ (Fig. 7). To generate a

Plan type 1 (1970) Plan type 5 (1980) Plan type 7 (1984) Plan type 9 (1988)

Ichon Hangang (1970) Myeongil Samik Green

(1980)

Daechi Sunkyung I (1983)

Hongeun Misung (1984)

Myeongil Hanyang (1986)

Ssangmun Dongik (1987)

Beondong Jugong I (1991)

Hagye Hyundai (1988)

Fig. 4. Plan type groups with the same spatial structure and j-graphs that represent them

Table 1. Similarities between Plan Types

Descendent Similarity score Possible precedents

Plan type 5 (1980) 0.85 Plan type 1 (1970)

Plan type 7 (1984) 0.88 Plan type 1 (1970)

0.89 Plan type 5 (1980)

Plan type 9 (1988) 0.77 Plan type 1 (1970)

0.89 Plan type 5 (1980)

0.79 Plan type 7 (1984)

Note: Plan types with earlier move-in years are candidates for precedent

plan types.

Descendent Similarity

score Ancestor Phylogenetic tree

Plan type 5

(1980) 0.85

Plan type 1

(1970)

Plan type 7

(1984) 0.88

Plan type 5

(1980)

Plan type 9

(1988) 0.89

Plan type 5

(1980)

Fig. 5. Phylogenetic tree completed based on precedent–descendent relationships between architectural plan types

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phylogenetic tree using NJ, a phylogeny-inferring program

(PHYLIP) (Felsenstein 1989) was used, and the resultant NJ phylo-

genetic tree was visualized by using a program named TreeView

(Page 1996) (Fig. 8).

The plan types categorized by TBJ and NJ can be grouped

into Groups A, B, and C (Figs. 7 and 8). Generally, plan types were

categorized similarly by the two methods, but certain differences

existed between the TBJ and NJ methods. Table 2 lists plan types

in each group and lists the types that were not grouped the same

way by both TBJ and NJ.

The order of transition of each group was also compared.

Without modification, the TBJ tree shown in Fig. 7 was used to

Fig. 7. TBJ phylogenetic tree of 60 plan types generated from 422 apartment unit plans in Seoul, South Korea, from 1970 to 2010

Fig. 8. Rooted phylogenetic tree generated by NJ, using the same data set as that used in the TBJ phylogenetic tree

Fig. 6. Steps to create a space-connector map and a j-graph: (a) select a plan to analyze; (b) extract interior lines; (c) add connectors; (d) create a

simplified space-connector map; (e) extract a j-graph (except balconies)

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analyze the order of transition of each group. However, the NJ tree

had to be reanalyzed first, because, as mentioned previously, NJ

does not consider the occurrence time of a plan type as a classifi-

cation factor, and the orders of branching off in NJ did not follow

the order of the occurrence times.

To learn which plan types are closer to the archetype, the lengths

of branches, which mean the degrees of transition, were analyzed

along with the orders of branching off in the unrooted phylogenetic

tree shown in Fig. 9. For analytical purposes, cases with short

branches that branched off in the beginning were assumed to be

common precedent types.

Table 3 lists the inferred precedent–descendent relationships.

The transition routes of the two trees were very similar in general.

However, several nonsensical cases were observed in the transition

routes of the NJ tree. In eight instances, the more recent plan type

Fig. 9. NJ unrooted phylogenetic tree generated by NJ, using the same data set as that used in the TBJ phylogenetic tree

Table 3. Comparison of the Transition Routes in TBJ and NJ Phylogenetic

Group

Transition routes

in the TBJ tree

Transition routes

in the NJ tree

A1 6-11-18-22-28-34-38 6-11-38-34-22-28

A2 6-11-14-17-20 6-14-11-17-20

A3 6-8-21-56 6-56-21-8

B1 2-3-12-37 3-2-12-37

B2 2-3-13-19-30-54 3-2–13-19-30–54

B3 2-3-13-19-24-31-45 3-2–13-19-24

3-2–13-31-45

C1 5-9-16-25 5-16-9-25

C2 5-9-15-42-44-60 5-9-15

5-42-44-60

C3 5-9-15-39-49 5-9-15-49

5-39

Table 2. Groupings and Mismatches between Phylogenetic Trees Generated by TBJ and NJ

Group TBJ plan types NJ plan types Discording types

Group A 6, 8, 11, 14, 17, 18, 20, 21, 22, 28, 32,

34, 38, 41, 48, 56, 57

8, 11, 14, 17, 20, 21, 22, 28, 32, 34,

38, 42, 44, 48, 56, 60

6, 18, 42, 44, 57, 60

Group B 2, 3, 4, 10, 12, 13, 19, 23, 24, 26, 27,

29, 30, 31, 36, 37, 40, 45, 46, 53, 54, 55

2, 3, 4, 12, 13, 18, 19, 23, 24, 26,

27, 29, 30, 31, 36, 37, 39, 40, 41,

45, 46, 47, 51, 53, 54, 55, 57

10, 18, 39, 41, 47, 51, 57

Group C 5, 7, 9, 15, 16, 25, 33, 35, 39, 42, 43,

44, 47, 49, 50, 51, 52, 58, 59, 60

9, 10, 15, 16, 25, 33, 35, 43, 49, 50,

52, 58, 59

5, 7, 10, 39, 42, 44, 47, 51, 60

MR R R B DK

R

H

E

LL DK B R

H

E

R MR

B

MRRBDK

R

H

E

L

B

TBJ Method

NJ Method

Plan Type 6 Plan Type 11 Plan Type 18 Plan Type 22 Plan Type 28

Plan Type 38 Plan Type 34

0.85 0.84 0.77 0.80

0.89 0.89

0.76

0.89

L DK

B

R

H

E

R MR

B

L

DK

B R

H

E

R MR

B

L DK B R

H

E

R MR

MRRBDK

R

H

E

L

B

Fig. 10. Comparison of the NJ and TBJ methods regarding the transition routes of Group A1

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1: 70(1) 2: 73(1) 3: 76(1), 06(1) 4: 78(1), 02(1) 5: 80(1), 83(1) 6: 83(1)

7: 84(1), 86(1),

87(1), 91(1)8: 88(1) 9: 88(1) 10: 90(1), 03(1)

11: 90(2), 91(1),

98(1), 01(2),

03(1), 06(1)

12: 91(1), 05(1),

06(1)

13: 92(1), 94(1),

95(1), 96(1),

00(1), 01(1),

02(1), 03(6),

04(1), 05(5),

06(4), 07(2)

14: 92(1), 93(1),

05(3), 06(1),

07(1)

15: 92(1), 01(4),

02(9), 03(23),

04(31), 05(37),

06(22), 07(21)

16: 92(1), 93(3),

94(3), 95(3),

96(2), 97(5),

98(1), 99(3),

00(8), 01(1),

02(10), 03(24),

04(8), 05(19),

06(12), 07(1)

17: 93(1) 18: 93(1)

19: 94(1), 99(2),

00(5), 01(4),

02(1), 04(1)

20: 94(1)21: 94(1), 01(1),

05(1), 07(1)22: 95(1) 23: 97(1)

24: 99(1), 00(1),

01(2)

25: 99(1), 01(3),

02(2), 03(5),

05(3), 06(1)

26: 99(1) 27: 00(1) 28: 00(1) 29: 00(1) 30: 00(2)

Fig. 11. Sixty plan types

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was assigned to be a precedent of an older plan type in the NJ tree.

The numbers of these plan types (e.g., 38–24, 14–11, and 56–21 in

the A group) are bolded in Table 3. In addition, in some cases, plan

types with relatively low similarity values were categorized as

immediate family in the NJ tree. Double dashes represent cases

in which remote relations were assigned as immediate family.

Another difference was that Subgroups B3, C2, and C3 in the NJ

phylogenetic tree had two branches, whereas these subgroups had

only one branch in the TBJ phylogenetic tree; this discrepancy

arose because the NJ algorithm minimizes the sum of branch

lengths.

Fig. 10 gives a step-by-step illustration comparing the transition

routes of group A1 in the TBJ and NJ trees. Both TBJ and NJ chose

Plan type 6 as the archetype of Group A1. In Plan type 6, all spaces

are directly accessible from the hall (H) except for one room (B).

During the transition through Plan types 11, 18, 22, and 28, the

number of the spaces directly accessible from H decreased, and

the depth of the space from the entry (E) increased. There was

31: 00(1) 32: 00(1) 33: 00(1)34: 01(1), 06(1),

07(1)35: 01(1) 36: 02(1)

37: 02(1) 38: 02(1)

39: 02(1), 03(3),

04(8), 06(1),

07(3), 08(1)

40: 02(1) 41: 02(1)42: 02(1), 04(1),

05(2), 07(3)

43: 02(1), 07(1) 44: 03(1) 45: 03(2) 46: 03(1) 47: 04(1) 48: 04(1)

49: 04(1), 05(1),

07(1)50: 04(2), 05(1) 51: 04(1) 52: 04(1) 53: 05(1), 06(1) 54: 05(1)

55: 05(1) 56: 06(1), 07(1) 57: 06(1) 58: 06(1) 59: 06(1) 60: 06(1)

R: room, MR: main room, L: living room, H: hall, E: entrance, D: dining, K: kitchen, B:

bathroom, P: Powder room or dressing room

Fig. 11. (Continued.)

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discordance between TJB and NJ regarding Plan types 34 and 38:

these types must be placed after Plan type 28 because Plan types 34,

38, and 28 appeared in 2001, 2002, and 2000, respectively, despite

the fact that Plan type 34 resembled Plan type 11 more than Plan

type 28 (see Fig. 11 for the earliest year of each plan type). How-

ever, NJ categorized Plan types 34 and 38 as precedent types of

Plan type 28 because NJ groups similarly structured plan types

closely regardless of the appearance year. Such errors are analogous

to the error of reversing a mother–daughter relationship when the

daughter resembles her grandmother more than the daughter resem-

bles her mother.

In summary, because the NJ method does not use information on

the time of occurrence for each case, it generates phylogenetic trees

by following the direction of transition that can be best explained

by evolutionary theory. However, sometimes the direction of tran-

sition can be inverted. For this reason, the time of occurrence has

been added as a factor in TBJ. Comparing the TBJ method with the

existing NJ method demonstrates that their results are not radically

different; however, the new method improves on the existing

method by addressing its dedifferentiation errors.

Conclusions

Many quantitative and qualitative research methods have been used

to analyze types and phylogenies of architectural spaces. However,

an algorithmic approach for generating a full space phylogenetic

tree has not been previously undertaken. In this paper, a new phylo-

genetic tree generation method was proposed based on phyloge-

netic tree generation concepts and adding the year of occurrence

as an additional factor. Previous studies were examined that dealt

with quantitative analysis of the similarity between spatial struc-

tures of floor plans, graph similarity analysis, and phylogenetic tree

generation algorithms. The proposed method, TBJ, was developed

based on these.

To validate TBJ, 422 architectural plans of collective housing

units in Seoul, South Korea, constructed between 1970 and 2010

were analyzed. The analysis results of TBJ were compared with

those of NJ, a phylogenetic tree generation algorithm commonly

used in biology. The results of this comparison demonstrated that

TBJ could reduce nonsensical dedifferentiation errors caused by

failing to consider plan types’ times of occurrence.

Despite the promising results of this study, the TBJ method has

limitations that warrant follow-up studies. An improved method

would take into account the importance of each space, spatial struc-

ture, and the location of the structure, as well as neighboring

relations, visual relations, and location changes.

The automatically derived phylogenetic tree of architectural

plans per se does not provide sociocultural interpretation of the

changes in architectural plans. Nevertheless, the proposed algo-

rithm has scientific contributions in that it opens a possibility of

mass-processing a large amount of architectural plan types, and that

it provides a basis for further sociocultural analyses.

The phylogenetic trees generated by the proposed method are

not limited to unit plans of collective housing; it also provides a

framework that can be used to analyze the relationship between

types and factors of change in categorizing architectural space

types and tracking changes in other building types.

In total, 60 plan types were derived from 422 architectural plans

of collective housing units with an exclusively usable area of

85 m2, of the three-bay, two-unit staircase type. The move-in years

were between 1970 and 2010. In Fig. 11, 70(1) refers to a plan with

a move-in year of 1970, of case number 1.

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