Data Intelligence Just Accepted MS. - Ricerca sull'intelligenza artificiale specializzata al MIT

Data Intelligence Just Accepted MS.
https://doi.org/10.1162/dint_a_00206

A knowledge graph-based deep learning framework for efficient
content similarity search of Sustainable Development Goals data

Irene Kilanioti1a, Giorgio A. Papadopoulosb

aSchool of Electrical and Computer Engineering, National Technical University of Athens, 9 Heroon Polytechneiou St.,
Zografou Campus Athens 157 80, Greece
bDepartment of Computer Science, University of Cyprus, 1 University Avenue, Aglantzia, CY-2109, Nicosia, Cyprus

Astratto

Sustainable development denotes the enhancement of living standards in the present without
compromising future generations’ resources. Sustainable Development Goals (SDGs) quantify
the accomplishment of sustainable development and pave the way for a world worth living in
for future generations. Scholars can contribute to the achievement of the SDGs by guiding the
actions of practitioners based on the analysis of SDG data, as intended by this work. We propose
a framework of algorithms based on dimensionality reduction methods with the use of Hilbert
Space Filling Curves (HSFCs) in order to semantically cluster new uncategorised SDG data and
novel indicators, and efficiently place them in the environment of a distributed knowledge graph
store. Primo, a framework of algorithms for insertion of new indicators and projection on the
HSFC curve based on their transformer-based similarity assessment, for retrieval of indicators
and load-balancing along with an approach for data classification of entrant-indicators is de-
scribed. Then, a thorough case study in a distributed knowledge graph environment experimen-
tally evaluates our framework. The results are presented and discussed in light of theory along
with the actual impact that can have for practitioners analysing SDG data, including intergov-
ernmental organizations, government agencies and social welfare organizations. Our approach
empowers SDG knowledge graphs for causal analysis, inference, and manifold interpretations of
the societal implications of SDG-related actions, as data are accessed in reduced retrieval times.
It facilitates quicker measurement of influence of users and communities on specific goals and
serves for faster distributed knowledge matching, as semantic cohesion of data is preserved.

Keywords: Content similarity; Distributed knowledge graphs; Sustainable Development Goals;
Hilbert space filling curves; Deep learning

1. introduzione

Sustainable development signifies the enhancement of living conditions in the present with-
out compromising future generations’ resources. Sustainable Development Goals (SDGs) [1]
were established by the United Nations (UN) in the framework of a 15-year plan, the UN 2030
Agenda, as a measurable international initiative to safeguard the future for the next generations,
by eradicating poverty, protecting the environment and maintaining peace and welfare. SDG data

1Corresponding

author:

Irene

Kilanioti

(E-mail:

eirinikoilanioti@mail.ntua.gr;

ORCID:

0000-0002-4157-3900)

© 2023 Chinese Academy of Sciences. Published under a Creative Commons Attribution 4.0 Internazionale
(CC BY 4.0) licenza.

Preprint submitted to Data Intelligence

Febbraio 24, 2023

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Data Intelligence Just Accepted MS.
https://doi.org/10.1162/dint_a_00206

A knowledge graph-based deep learning framework for efficient content similarity search of
Sustainable Development Goals data

consists of sustainable development goals, targets, indicators and data series for the quantifica-
tion of their accomplishment [2].

A lot of research has been conducted between 2015-2019 on the content and interactions
of the SDGs according to [3], especially about goals associated with responsible consumption,
sustainable cities and good health. The collaborative effort to accomplish the goals bears a trans-
formative view of our world and focuses on building a peaceful, equitable society that will ensure
protection of the environment and elimination of hunger and poverty. The collective effort to op-
timally harmonize sustainability goals bears a transformative view of the world and requires
the conscious social, fiscal and technological contribution of many societal agents among which
sustainable IT can also play a crucial role [4] [5]. “Data which are high-quality, accessible,
timely, reliable and disaggregated by characteristics relevant in national contexts” is required
(A/RES/70/01)[6].

From the IT perspective, the question of how we can leverage SDG data to estimate the im-
pact of various actions especially in the context of social welfare and sustainability is a highly
relevant topic and a challenge of great interest for society. Hence, we need to reduce access times
for SDG data analysis and improve semantic cohesion of uncategorized data. Efficient processing
and storage solutions for data in this respective field are necessary for practitioners, that entail in-
tergovernmental organizations, government agencies and social welfare organizations, cioè., civic
organizations and associations of persons engaged in the promotion of social welfare.

Heretofore, SDG-related information systems have included in essence solely monitoring
tools of SDGs data and metadata, and also mechanisms to enhance interoperability across in-
dependent information systems: UN [7] showcases use of mappings of terms to the UN Bib-
liographic Information System (UNIBIS) and the EuroVoc vocabularies and a SDG interface
ontology (SDGIO) has already been proposed [8]. In [9] Li et al. focus on the extraction of
information to map to an ontology defined in collaboration with sector experts, that will enable
the public to meet their knowledge needs related to social-impact funding. In [10] Warchold
et al. study the unification of SDG datasets from various sources. Tuttavia, to the best of our
knowledge, a generic storage scheme of SDG data based on their semantic similarity and lever-
aging the infrastructure of multiple servers across which the data is split, has not been addressed
yet. Subsequent improvements in the retrieval of data would facilitate all possible applications
for causal analysis, inference, and manifold interpretations of the societal implications of SDG-
related actions.

In this work, we propose dimensionality reduction methods to semantically cluster new un-
categorised SDG data as well as new indicators with internationally yet unestablished method-
ology or standards and keep them close in the underlying physical networking environment of a
distributed knowledge graph store. We introduce a framework of algorithms for insertion of new
indicators and projection on the HSFC curve based on their similarity assessment, for retrieval
of indicators and load-balancing. An approach for data classification of entrant-indicators is also
described. The algorithms are based on HSFCs as the line of projection where new, gradually
more refined, semantic categories are directly mapped onto. Our work proposes and experi-
mentally corroborates the use of HSFCs to efficiently store distributed knowledge graph data,
ensuring reduced access times and preservation of semantic closeness.

Sezione 2 describes the methodology we followed for use of an additional distributed envi-
ronment layer based on HSFCs to map conceptually close, uncategorised according to existent
SDG schema, dati. Primo, in the subsection 2.1 the proposed algorithms for insertion of new
indicators and projection on the curve, for filtering and refinement as well as load-balancing,
and an approach for data classification of entrant-indicators over this layer are described. Then,

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Data Intelligence Just Accepted MS.
https://doi.org/10.1162/dint_a_00206

A knowledge graph-based deep learning framework for efficient content similarity search of
Sustainable Development Goals data

subsection 2.2 describes a detailed case study in a distributed knowledge graph environment,
that experimentally evaluates our algorithm. Dataset and experimental setup are thoroughly dis-
cussed. The results are presented in Section 3 and discussed in light of theory and the actual
impact they can have for practitioners in Section 4. Sezione 5 summarizes the paper’s contribu-
tion and discusses future extensions of our work.

2. Methodology

2.1. Proposed algorithm

2.1.1. Hilbert Space-Filling Curves

Figura 1: Construction of approximations of the Hilbert curves of increasing order τ=2; . . . ;5 In 2 dimensions.

A true Hilbert curve [11] is the limit of τ → ∞ of the τth discrete approximation to a Hilbert
curve. HSFCs of 2 dimensions can be depicted on a NXN grid and the coordinates on the grid
range in the space x, y ∈ [0, N − 1].

N = 2τ

(1)

In Fig. 1 next order curve comprises of four gyrated reiterations of the previous order curve.
In the next repetition, quadrants are split up into four sub-quadrants each and so on. The line is
repetitively folded in such a way that passes by successive neighboring points without intersect-
ing itself and with infinite iterations of the curve construction algorithm it will not omit any point
on a continuous plane. HSFCs are always bounded by the unit square, with Euclidean length
exponentially growing with τ. Continuity of the curve ensures that affinity of bins on the unit
interval signifies affinity in the unit square as well. Two points (x1, y1) E (x2, y2) with affinity in
HSFC of order τ1 depict affinity in HSFC of order τ2 >τ1 as well. Hilbert approximations result
in more efficient maintenance of local features as opposed to that achieved by linear ordering,
while locality properties degrade with the increase of dimensions.

2.1.2. Knowledge Graphs

A knowledge graph comprises of sets of triples that relate a subject entity to an object entity
and encode domain and application knowledge. Knowledge graphs complimentarily serve for
explainability that cognitively facilitates human-level intelligence. They serve for the represen-
tation of generic data interlinked by many relationships as well as for specific domains, ad esempio
biomedical research and manufacturing [12, 13]. They cover diverse application fields includ-
ing search, data governance, question answering and recommendation. Distributed knowledge
graphs integrate multiple and heterogeneous data sources, as their data are disseminated in a
decentralised way across the web.

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Data Intelligence Just Accepted MS.
https://doi.org/10.1162/dint_a_00206

A knowledge graph-based deep learning framework for efficient content similarity search of
Sustainable Development Goals data

SDG ontology comprises substantially sustainable development goals, targets, indicators and
data series for the quantification of their accomplishment [2], and the full taxonomy is acces-
sible as linked open data at [14]. Depending on the grade of development of internationally
established methodology and standards as well as regularity of production of relevant data, IL
afore-mentioned indicators are categorised into tiers. Tier III indicators are not associated with
any existent methodology / standards. The distinguishing element between the first two tiers is
the fact that data of Tier I indicators are collected on a regular basis for not less than half of the
countries and population in every relevant region [15].

Challenges associated with the uptake of distributed knowledge graph technologies include
their efficient storage and use at scale [16]. Heretofore, SDG-related systems have included
in essence solely monitoring tools of SDGs data and metadata and mechanisms to enhance in-
teroperability across independent information systems, per esempio., [7]. Tuttavia, to the best of our
knowledge, a generic storage scheme of SDG data based on their semantic similarity to facili-
tate all possible applications for causal analysis, inference, and manifold interpretations of the
societal implications of SDG-related actions, has not been addressed yet.

2.1.3. Insertion of SDG Tier III indicators in HSFCs

We propose an algorithm (Alg. 1) for the efficient placement of Tier III SDG indicators in

the underlying physical networking environment.

Algorithm 1 Algorithm for insertion of SDG Tier III indicators in HSFCs

Input: HS FC dims, HS FC order, indicator sentence, probe sentence, µ
Output: M = (indicator, T = (x tuple, sì) ∈ N)
Parameters:
bin,
N, Hilbert Space Filling Curve HS FC
Initialisation :

indicator number,

indicator,

bin size,

T =(X,sì)

∈

1: HS FC ← ConstructHS FC( HS FC dims, HS FC order)
2: bin size ←
3: A ←compute embedding for probe sentence
4: for indicator = 1 to indicator number do

|µ|
|(2HS FC order)2|−1

5:
6:

B ←compute embeddings for indicator sentence[indicator]
compute s=semantic similarity = ·A·B
∥A∥∥B∥
if s( probe sentence, indicator sentence[indicator]) ≤ T hresholds then

bin ← ⌊ indicator
bin size ⌉
T ← ObtainHS FCCoordinates( bin, HS FC)

7:
8:
9:
10:
11: end for

end if

The order of the HSFCs used defines the range of possible coordinates. We incorporate a
binning mechanism to ensure that each new indicator can be projected to a tuple of coordinates
in the higher dimension space. Bins hold consecutive elements of the data vector. The suggested
mapping represents the indexing mechanism for the data in the distributed knowledge graph
storage prototype we develop.

The first layer of the distributed knowledge graph store (Fig. 7) will entail semantic represen-
tation of data. In the next layer, which acts as a substrate of the network topology, we split up the
indexing area in semantically homogeneous areas through HSFCs. Use of curves in this build-
ing block proves beneficial for preserving the neighbourhood property of concepts expressed by

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Data Intelligence Just Accepted MS.
https://doi.org/10.1162/dint_a_00206

A knowledge graph-based deep learning framework for efficient content similarity search of
Sustainable Development Goals data

the indicators, as semantically related terms, more probable to respond to a user query, will be
placed in the vicinity. In our suggestion linearization is implemented as an overlay upon exist-
ing two-dimensional search structures and the distributed file system, that ensures distribution
and sharding that scale. Multidimensional queries upon the distributed knowledge graph can be
mapped to two-dimensional queries, that range from the minimum to maximum linearization
points of the initial query (Fig. 7).

We are interested in relative positioning that expresses affinity. The reverse process of HS-
FCs mapping, when a position in the description space for higher-order partitioning needs to be
translated into a position in the indicators vector, is not applicable and does not cause any issue in
our scenario. The algorithm can be further modified to scale with new entries in terms of targets,
goals and other potential refinements of the SDG ontology with corresponding increase in the
order of the HSFC.

2.1.4. Similarity Assessment

For the similarity assessment of the indicators, we compute semantic textual similarity as
calculated in Sentence-BERT (SBERT) [17], that extracts and compares semantically meaningful
sentence embeddings and is based on deep learning transformers model BERT. We quantify the
semantic textual similarity of each probe sentence, that is a candidate entrant-indicator, con
existent SDG indicators (indicator).

Firstly, words in the sentencei are preprocessed. Then each processed word in the sentence
is encoded into vectors vi j of 300 dimensions. Embedding in the vector space is conducted
with Word2vec. The vector representation for sentencei is based on the average of such vi j
vector representations for j = {io, w}, where w is the number of words in the sentence. Sentence
embeddings for all existent indicators in the SDG taxonomy are precalculated. They are assumed
to be close in the 300 dimensional vector space if they are similar. Computing cosine similary
between the (300 dim) vector representation provides ideally score 1 for identical sentences and
score 0 for sentences maximally dissimilar to each other.

Therefore, for the regression objective function the cosine-similarity between the two sen-
tence embeddings u and v of two indicators is calculated (Fig. 9), and mean-squared-error loss
is used at inference stage as the objective function.

For the computation of the classification objective function, per esempio., to tune the model, sentence
embeddings u and v of two indicators are concatenated with their element-wise difference and
multiplied with the trainable weight Wt ∈R3z×ω:

o = so f tmax(Wt(tu, v, |u − v|))

(2)

where z is the dimension of the sentence embeddings and ω the number of labels, and cross-

entropy loss is optimized according to [17].

Fig. 8 depicts the transformer architecture for an entrant indicator of Tier III and Fig. 9
visualizes the architecture among existent indicators categorised according to SDG schema. IL
SBERT Algorithm is implemented with 12 stacked transformer layers and indicators can be de-
picted according to various available dimensions, including standard demographic info, location,
eccetera.

2.1.5. Data Classification of Entrant-Indicators

We aim to avoid unnecessary congestion of specific subquadrants in the HSFC mapping, così
we team up semantically close entrants, namely indicators of Tier III. In this direction, we aim to

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Data Intelligence Just Accepted MS.
https://doi.org/10.1162/dint_a_00206

A knowledge graph-based deep learning framework for efficient content similarity search of
Sustainable Development Goals data

categorize points in Rn without exploiting SDG schema features. For the data classification, we
use a dataset of NDC individuals described by Q categorical variables and construct the NDC × J
indicator matrix Z, Dove:

J =

Q(cid:88)

q=1

(3)

rows denote the datasources, namely nodes of the graph store where data associated with the
indicators reside, and columns denote the indicators of the uncategorised SDG data. We calculate
a matrix of proportions P where pi j = ni j/n and n is the sample size, summing up all values of
NDC. r and c are the sums along the rows and along columns respectively.

Categorization is based on chi-squared distances between two entrant-indicators:

dist2

χ2 (ind j, ind j′ ) =

NDC(cid:88)

i=1

1
ri

(

pi j
c j

−

pi j′
c j′

(4)

The distance is reduced when there is overlapping between individuals belonging to multiple
categorie. Our aim is to project the points onto a subspace of lower dimensionality, within which
the eigenvectors uk are the result of eigenvalue decomposition of PD−1
. So we solve the
equation:

c PT D−1
R

1
Q

ZD−1ZT uk = λkuk

(5)

where Z is the indicator matrix, Dr, Dc the diagonal matrix of row and column masses re-

spectively.

2.1.6. Retrieval of indicators

The algorithm for matching k-semantically closest indicators is based on multi-step filtering
and refinement, that consecutively removes irrelevant results and narrows the candidate set (Alg.
2). In order to optimally calculate distances, we use the algorithm proposed in [18], that performs
optimally as far as the number of distance calculations is concerned, and modify it for HSFC
representation. We create a ranking by means of the lower bound lδH, that for all objects o1,
o2 ensures that lδH(o1, o2) ≤ δH(o1, o2) for a distance function δH among HSFC projections.
Reranking takes place provided that the lower bound does nor surpass the kth-nearest neighbor
distance and the results are updated with objects of smaller distances.

The process of refining multi-dimensional data to answer a query of k-closest semantically
indicators after projecting on a HSFC is depicted in Fig. 2. After having reduced dimensionality
with application of HSFCs, the query for semantically similar indicators can be handled as a
nearest neighbor search and implemented with a multi-step filter-and-refine approach [18] [19]
in an efficient way. The main idea is to filter at a later stage results falsely retrieved at first stage.
Creating a lower bound with a simple distance function filters out initially irrelevant results, E
in the next step evaluation of results returned at the previous stage takes place with the use of
the original distance function. There are multiple properties describing each observation (dati
entry) and their Statistical Data and Metadata eXchange (SDMX)-standardized code equivalents
are also provided. Dimensions (standard demographic info, the whole variety of different age
profiles, eccetera.), time periods and area codes, described through the UNM49 standard are available
in the dataset for each indicator from 2000 onwards.

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Data Intelligence Just Accepted MS.
https://doi.org/10.1162/dint_a_00206

A knowledge graph-based deep learning framework for efficient content similarity search of
Sustainable Development Goals data

Algorithm 2 Algorithm for filtering similarity search results

Input: HS FC dims, HS FC order, indicator sentence, probe sentence, k, query q, distances

lδH, δH

Output: result set S
Parameters:
N, Hilbert Space Filling Curve HS FC

bin size,

bin,

1: S ← ∅
2: RH ←ranking(q, lδH )
3: ξ ←next value ∈RH
4: while lδH(q, ξ) ≤ maxα∈S δH(q, α) do

S ←S ∪ξ

5: if |S | < k then 6: 7: else 8: 9: 10: 11: 12: end if 13: ξ ←next value ∈RH end if if δH(q, ξ) ≤maxα∈S δH(q, α) then S ←S ∪ξ S ←S − argmaxα∈S δH(q, α) end 14: return S indicator, indicator number, T =(x,y) ∈ l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u d n / i t / l a r t i c e - p d f / d o i / i . t / / 1 0 1 1 6 2 d n _ a _ 0 0 2 0 6 2 1 2 7 0 1 9 d n _ a _ 0 0 2 0 6 p d . / t i f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Figure 2: Process of refining SDG multi-dimensional data to answer a query of k-closest semantically indicators after projecting on a HSFC. After having reduced dimensionality (standard demographic info, the whole variety of different age profiles (AP), etc.), time periods and area codes, described through the UNM49 standard) with application of HSFCs, the query for semantically similar indicators can be handled as a nearest neighbor search and implemented with a multi- step filter-and-refine approach. Creating a lower bound with a simple distance function filters out initially irrelevant results, and in the next step evaluation of results returned at the previous stage takes place with the use of the original distance function. DataIntelligence 7 L4L3L2Q3Q2Q1AP1AP2AP3Q4AP4L1TimeLocationDemographicinfosimilaritysearchrefinedistanceDatasetexactdistancecandidatesetresultset07012345612345670123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263o1•o2• Data Intelligence Just Accepted MS. https://doi.org/10.1162/dint_a_00206 A knowledge graph-based deep learning framework for efficient content similarity search of Sustainable Development Goals data 2.1.7. Load-balancing Algorithm 3 Algorithm for load balancing Input: HS FC dims, HS FC order, indicator sentence, probe sentence Output: assignment of virtual nodes Parameters: bin, virtual node, load threshold, load Initialisation : bin size, Hilbert S pace Filling Curve HSFC, HS FC node, load ←0 for virtual node=1 to virtual nodes number do 1: assign virtual nodes to HS FC node 2: for HS FC node=1 to HS FC nodes number do 3: 4: 5: 6: 7: load(HS FC node) ← (cid:80)n−1 if load(virtual node) > load threshold then

divide virtual node to a set of virtual nodes

i=0 load(virtual node)ı

end if
if load(physical node) > load threshold then

assign virtual node to argminHS FC node(load)

8:
9:
10:
11:
12:
13: end for

end if
end for

Introduction of load balancing mechanisms at runtime or periodical batch-level processing
of data ensures that in case of skewed distributions (more occurences of specific indicators or
semantic categories) the equivalent subquadrants in the HSFC unit square will not be congested
[20], [21]. We run a load-balancing algorithm (Alg. 3) based on existence of HSFC-physical
nodes, that correspond to the physical placement of HSFC bins, and HSFC-virtual nodes Y1, Y2,
…Yϕ, that correspond to the physical node Y. Existence of virtual nodes can be beneficial in terms
of fair splitting of computational power for heterogeneous nodes and decentralization in case of
failure on a single physical node. Physical nodes can host several virtual nodes and their load
is calculated with aggregation of the load of the virtual nodes they host. Exceeding the allowed
threshold for a virtual node means that the node will be divided into more than one virtual nodes.
When a physical node surpasses the load threshold, some of its virtual nodes will be assigned to
less burdened physical nodes.

2.2. Case study

2.2.1. Dataset

We harvested a dataset of 2,21M. entries in total that includes all dimensions (standard de-
mographic info, the whole variety of different age profiles, eccetera.), time periods and area codes, Di-
scribed through the UNM49 standard available for each indicator from 2000 onwards. We used
the API of UN Statistics Division [22] with a set of scripts written in TypeScript and ran in the
node.js environment. Dataset was particularly focused on indicators and list of all available SDG
indicators was our starting point in the API, providing all available indicators in a self-contained
risposta. Within the indicator related datasets, we collected 3 core datasets, while others were

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Data Intelligence Just Accepted MS.
https://doi.org/10.1162/dint_a_00206

A knowledge graph-based deep learning framework for efficient content similarity search of
Sustainable Development Goals data

[UN]

[B]

Figura 3: (UN) IndicatorData dataset indicative excerpts for indicators 1.1.1, 1.2.1 E 2.1.1 (B) SDG schema of the dataset
depicting structure of the UN SDG ontology.

mostly redundant data provided for different data access or interpretation. Our dataset Indicator-
Data includes 169 targets, 248 indicators (con 13 replicated under two/three different targets),
as they were described in the 2022 refinement of the SDGs, as well as 663 data series for the
quantification of the SDGs’ accomplishment [2]. Since 2022 the classification entails 136 In-
dicators of Tier I, 91 indicators of Tier II and 4 indicators consisting of modules of disparate
tiers [15]. The dataset includes series information and goal – target hierarchy with overall 663
series across 248 indicators (Fig. 3). The number of data entries per each indicator is 4150 after
removal of 20% of top and tail outliers. There are multiple properties describing each observa-
zione (data entry) and their Statistical Data and Metadata eXchange (SDMX)-standardized code
equivalents are also provided. Tavolo 3 depicts number of occurences of uncategorised indicators
in graph store nodes and Table 4 describes potential uncategorised entrant indicators, that are not
included in the dataset we harvested and do not follow SDG schema beforehand.

PivotData dataset returns a list of observations pivoted by year. This dataset contains all
data described in IndicatorData aggregated for the whole observation period and showing only
pivoting years in the years property of each data entry. The property was serialized and we
deserialized it for the convenience of data manipulation.

There are 247.251 entries in total, con 550 entries per indicator after removal of 20% Di

outliers (top and tail).

2.2.2. Experimental Setup

We evaluate our algorithm in an experimental distributed environment over a key-value store
of SDG data, that we collected. We use multiple servers and Hypertext Preprocessor (PHP)
clients as APIs to handle cached values in a scheme built on Memcached, an optimized dis-
tributed hash map-based mechanism. Placement of data with HSFCs is compared to default
placement scheme of the prototype distributed cache mechanism in terms of response time for
the executed SELECT queries and in terms of disk I/O. Experimental setup settings are described
in Table 2. In order to make clusters for entrant indicators and put their content in close Hilbert
areas, we use the Agglomerative Hierarchical Clustering (AHC).

The similarity threshold we choose is minimum to allow augmentation of data with the whole
set of entrant indicators. AHC proceeds with combination of clusters from the simple level of
clusters-individuals to merging pairs of them with a bottom-up approach. The metric used in our

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{”goal”:”2”,”target”:”code”:”2”descriptio”tier”:”1”,”uri”:”/v”series”:[{”goal”:[”2”],”target”:[”2.1”],”indicator””2.1.1”],”release””code”:”descriptio”uri”:”/v},{”goal”:”1”,”target”:”code”:””descriptio”tier”:”1”,”uri”:”/v”series”:[{”goal”:[”1”],”target”:[”1.2”],”indicator””1.2.1”],”release”:”code”:”S”descriptio”uri”:”/v}]},[{”goal”:”1”,”target”:”1.1”,”code”:”1.1.1”,”description”:”Proportionofthepopulationlivingbelowtheinternationalpovertylinebysex,age,employmentstatusandgeographiclocation(urban/rural)",”tier”:”1”,”uri”:”/v1/sdg/Indicator/1.1.1”,”series”:[{”goal”:[”1”],”target”:[”1.1”],”indicator”:[”1.1.1”],”release”:”2022.Q1.G.03",”code”:”SIPOVDAY1”,”description”:”Proportionofpopulationbelowinternationalpovertyline(%)",”uri”:”/v1/sdg/Series/SIPOVDAY1”},TaxonomyconceptsTargetIndicatorGoalSeriesdct:subjecthasIndicatorhasSeriesdct:subjectdct:subjectdct:subjecthasTarget

Data Intelligence Just Accepted MS.
https://doi.org/10.1162/dint_a_00206

A knowledge graph-based deep learning framework for efficient content similarity search of
Sustainable Development Goals data

setup is the Euclidean distance for pairwise observations.

[UN]

[B]

Figura 4: (UN) Similarity among existent SDG indicators. (B) Entrant indicators’ AHC dendrogram based on their number
of occurences in datasources.

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[B]

Figura 5: PCA of new indicators. (UN) Scree plot with first two axes F1, F2 contributing. The Principal Component
Analysis (PCA) scree plot indicates that two dimensions F1, F2 suffice for the visual interpretation of the analysis, since
the sum of first two eigenvalues is sufficient percentage of variance. (B) Biplot PCA denoting the suggested division of
layer to two Hilbert areas. The biplot verifies the split up of the datasources to two main semantic categories with active
observations corresponding to the selected datasources and active variables corresponding to selected indicators.

3. Results

3.1. Cost-aware Data Classification of Entrant Indicators

Firstly, the approach for cost-aware data classification of entrant-indicators is verified. Contro-
cerning the uncategorised indicators of Table 4, cutting the dendrogram (Fig. 4) at the height
of the dotted line verifies a coarser clustering of two semantic categories, namely of datasources

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DataIntelligence

Data Intelligence Just Accepted MS.
https://doi.org/10.1162/dint_a_00206

A knowledge graph-based deep learning framework for efficient content similarity search of
Sustainable Development Goals data

[UN]

[B]

Figura 6: (UN) Response time differences for HSFC mapping assigned to Memcached keys and (B) Disk I/O times for
HSFC mapping passed as Globalparam. We notice significant reduction in average response times for selection queries
of combined indicators. Time difference between HSFC storage scheme and baseline distributed key-value store approach
is more obvious in the case of disk I/O times (Global parameters used). There is also improvement in response times
when HSFC mapping is loaded into Memcached keys directly, which is more obvious for combinations of sets of up to
4 indicators in our setup.

(1,5,9,10) covering topics (1,4,5,6,7,8,10,12) associated with data and those of the rest data-
fonti (2,3,4,6,7,8) associated with animal issues (2,3,9,11). Explicit reference to terms (”ani-
mal”, ”data”) here is irrelevant. Così, datasources (1,5,9,10) and datasources (2,3,4,6,7,8) should
be put in two separate subquadrants in the Hilbert unit square. As for existent SDG indicators,
Fig. 4 depicts their comparison in terms of semantic similarity.

The Principal Component Analysis (PCA) scree plot indicates that two dimensions F1, F2
suffice for the visual interpretation of the analysis, since the sum of first two eigenvalues is
sufficient percentage of variance. The quality of the fit is measured by the percentage of inertia
related to the two-dimensional map, namely the ratio of variance of coordinates of individuals on
the axis to the total variance of coordinates of individuals. The quality is high for our dataset of
restricted size (10 individuals (datasources) E 14 categorical variables (indicators)) and high
data interlinking. With the eigenvalue λd equal to the variance of the points of each indicator on
d-dimension:

(λ1 + λ2)/

9(cid:88)

d=1

λd = 70, 41%

(6)

the biplot verifies the split up of the datasources to two main semantic categories with active
observations corresponding to the selected datasources and active variables corresponding to
selected indicators (Fig. 5).

3.2. Response Time Reduction

We ran multiple sets of queries in an experimental distributed environment over a key-value
store of SDG data with multiple servers and PHP clients as APIs to handle cached values in a
scheme built on Memcached. After each set of queries the Memcached server was reset. Noi

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76543210204060NumberofindicatorsinqueryResponsetimeinmsecsResponsetimesdifference(Memcachedkeys)DefaultHSFC76543210100200300400NumberofindicatorsinqueryResponsetimeinmsecsDiskI/Otimes(Globalparam)DefaultHSFC

Data Intelligence Just Accepted MS.
https://doi.org/10.1162/dint_a_00206

A knowledge graph-based deep learning framework for efficient content similarity search of
Sustainable Development Goals data

notice significant reduction in average response times for selection queries of combined indica-
tori. Time difference between HSFC storage scheme and baseline distributed key-value store
approach is more obvious in the case of disk I/O times (Global parameters used). There is also
improvement in response times when HSFC mapping is loaded into Memcached keys directly,
which is more obvious for combinations of sets of up to 4 indicators in our setup (Fig. 6). IL
improvement in terms of memory response times can be further increased with further paging
configuration, due to the nature of Memcached custom memory manager (slabs hold objects
within specific ranges and slabs contain pages, split up in chunks) and the fact that a single
indicator’s entries reach up to 20MBs in our detailed dataset.

4. Discussion

In light of the HSFC theory, HSFCs can map multidimensional data to two dimensions main-
taining spatial locality, namely affinity in the multidimensional space means relative affinity in
the two-dimensional space. Our work is based on this observation and further extends it to har-
vest the benefits of a framework for similarity search for domain-specific knowledge graphs.
Previously, HSFCs [11] have been used along with Gray code and Z-order curves for heuristic
multi-dimensional indexing via linearization. The wide spectrum of applications includes im-
age compression, data visualization and peer-to-peer architectures [23, 24, 25]. McSherry et al.
[26] observed that edge ordering based on a HSFC substantially improves cache performance for
single-threaded PageRank. Schmidt et al. [27] implemented a Distributed Hash Table (DHT)-
based Web service discovery system leveraging HSFCs and mapped points of multidimensional
space corresponding to service description components to DHT keys. Wang et al. [28] leveraged
the spatial locality of HSFCs to store and display on request point-based spatial data in a spatial
triple store.

In the suggested framework the locality in the multidimensional space describing the se-
mantically associated indicators indicators is preserved after their mapping, as input items with
higher semantic similarity are mapped to nearby addresses. Hence, nearby mapping is leveraged
and the placement of conceptually close SDG indicator data on an HSFC as the line of projec-
tion indeed reduces retrieval times. The suggested topological mapping scheme is nondisruptive
in terms of space and maintains local feature correlations of the original space. Inoltre, our
framework evades bottlenecks with avoidance of unnecessary congestion of specific subquad-
rants in the HSFC mapping via the approach of data classification of entrant indicators and the
load-balancing mechanism that we suggest.

In our work HSFC points were coarsely equivalent to servers in the experimental distributed
ambiente. Therefore, further refinement at a graph store node level and per server could lead
to even better results in terms of response times, because communication cost among servers
would be alleviated. The observed improvement in terms of memory response times can also
be further increased with further paging configuration, due to the nature of Memcached custom
memory manager (slabs hold objects within specific ranges and slabs contain pages, split up in
chunks) and the fact that a single indicator’s entries reach up to 20MBs in our detailed dataset.

The practical impact of our work is that data retrieval times are reduced for semantically close
dati, that have not been categorised according to the prevailing SDG schema. Our approach
empowers SDG knowledge graphs for causal analysis, inference, and manifold interpretations
of the societal implications of SDG-related actions, as data are accessed in reduced retrieval
times. The framework facilitates quicker measurement of influence of users and communities

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Data Intelligence Just Accepted MS.
https://doi.org/10.1162/dint_a_00206

A knowledge graph-based deep learning framework for efficient content similarity search of
Sustainable Development Goals data

on specific goals and serves for faster distributed knowledge matching, as semantic cohesion is
preserved.

Specifically, the suggested framework’s impact on actions of organizations that harvest and
process SDG datatakes is based on the consideration that the pursued goals and undertaken ac-
tions can be thematically interweaved and mutually influenced: one agent may pool interrelated
existing content from federated repositories or one undertaken action may affect currently ongo-
ing activities of other agents. Knowledge graphs are augmented with quicker similarity search,
that reduces response times for manifold interpretations of the societal implications of actions
that apply to each SDG goal, for association of contributions of actions to concrete SDG targets
and quantification of the exerted influence. Concerning SDGs, knowledge graphs can quicker:
io) support explainable decisions and insightful recommendations, ii) measure the influence of
users and communities and iii) improve the user experience, as they facilitate extraction and or-
ganization of knowledge in a distributed manner and serve for quicker distributed knowledge
matching.

5. Conclusions

Our work aims to support the efficient processing of SDG data and the seamless integration of
novel indicators. An efficient storage scheme is needed for new uncategorised SDG data as well
as indicators with internationally yet unestablished methodology and standards. in questo documento, we
propose a framework of algorithms for insertion of new indicators and dimensionality reduction
based on their similarity assessment, for retrieval of indicators and load-balancing along with an
approach for data classification of entrant-indicators. The mapping method is based on HSFCs
as the line of projection where semantic categories of conceptually close SDG indicator data,
uncategorised according to the existent schema, are directly mapped onto. A case study on real
SDG data in a distributed knowledge graph store validates that data retrieval time is reduced.
The proposed algorithms can be adapted for targets, goals, and potential future refinements of
the SDG ontology.

Our approach empowers SDG knowledge graphs for causal analysis, inference, and mani-
fold interpretations of the societal implications of SDG-related actions, as data are accessed in
reduced retrieval times. It facilitates quicker measurement of influence of users and communities
on specific goals and serves for faster distributed knowledge matching, as semantic cohesion of
data is preserved.

We aim, furthermore, to study how increasing order of HSFCs affects performance. In an-
other direction, we intend to explore geolocation features of indicators to leverage multiple HS-
FCs for spatial joins and range queries, as well as optimize queries to correspond to global search
trends on SDG data.

The collective effort to optimally harmonize sustainability goals requires the conscious tech-
nological contribution of sustainable IT for timely and reliable data. Our work aspires to con-
tribute in this direction and prove useful for all practitioners gathering and assessing SDG data.

Author Contributions

All authors including I. Kilanioti (eirinikoilanioti@mail.ntua.gr) e Giorgio A. Papadopou-
los (george@ucy.ac.cy) took part in writing the paper. Inoltre, IO. Kilanioti conceived the
idea, designed the algorithms and experiments, collected the data, conducted the experiments
and performed the data analysis.

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Data Intelligence Just Accepted MS.
https://doi.org/10.1162/dint_a_00206

A knowledge graph-based deep learning framework for efficient content similarity search of
Sustainable Development Goals data

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[22] UN, “SDG API.” [Online]. Available: https://unstats.un.org/SDGAPI/swagger/
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filling curve,” IEEE Trans. Knowl. Data Eng., vol. 13, NO. 1, pag. 124–141, 2001.

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[26] F. McSherry, M.

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’04, vol. 7, NO. 2. Springer, 2004, pag. 211–229.

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Data Intelligence Just Accepted MS.
https://doi.org/10.1162/dint_a_00206

A knowledge graph-based deep learning framework for efficient content similarity search of
Sustainable Development Goals data

[28] C.-J. Wang, “Database indexing for skyline computation, hierarchical relational database, and spatially-aware

sparql evaluation engine,” Ph.D. dissertation, 2015.

Appendix A Appendix

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Figura 7: Suggested knowledge graph-based framework for efficient content similarity search of SDG data consisting
of i)semantic representation of data, ii) a substrate of the network topology, where the indexing area is divided into
semantically homogeneous areas through HSFCs, iii) SDMX-standardized code equivalents of data entries, iv) mapping
to SDG ontology, when applicable.

Figura 8: Transformer Architecture for Entrant indicator, implemented with 12 stacked transformer layers and consisting
of token, position and segment embeddings.

DataIntelligence

Inputdocument[CLS]abolishunnecess.animaltesting[SEP]oftenineffective[SEP]TokenembeddingE[CLS]EabolishEunnecess.EanimalEtestingE[SEP]EoftenEineffectiveE[SEP]+++++++++Soft-positionembeddingEAEAEAEAEAEAEBEBEB+++++++++SegmentembeddingE0E1E2E3E4E5E6E7E8EntrantIndicatorofTierIII-InputEmbeddingMulti-HeadAttentionAdd&NormFeedForwardAdd&NormSoftmaxOutputclassTransformersLayerx12

Data Intelligence Just Accepted MS.
https://doi.org/10.1162/dint_a_00206

A knowledge graph-based deep learning framework for efficient content similarity search of
Sustainable Development Goals data

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Figura 9: SDG Goal 17 consists of targets, such as Target 17.1: ”Strengthen domestic resource mobilization” and entails
indicators such as 17.1.2: ”Total government revenue as a proportion of GDP, by source” [1]. Various indicators are fed
into either Sentence-BERT (SBERT) [17] architecture with classification objective function, per esempio., to tune the model, O
SBERT architecture with the regression objective function, per esempio., to compute indicator similarity scores.

DataIntelligence

SoftmaxClassifier(tu,v,|u−v|)uvPoolingPoolingBERTBERTSentenceASentenceB−1…1Cosine-sim(tu,v)uvPoolingPoolingBERTBERTSentenceASentenceB17PARTNERSHIPSFORTHEGOALS17.1Strengthendomesticresourcemobilization17.2ImplementODAcommitments17.3MobilizeadditionalfinancialresourcesforDC17.4AssistDCattainlongtermdebtsustainability17.5Implementinvest-mentpromotionregimes17.6Enhanceaccesstoscience,technology17.7Environmentallysoundtechnologies17.8Enablecapacitybuildingmechanism17.9Enhanceeffectivetargetedcapacity-building17.10Promotenondis-criminatorytrading17.11Increaseexportsofdevelopingcountries17.12Realizeduty-tree&quota-freemarketaccess17.13Enhanceglobalmacroeconomicstability17.14Enhancepol-icycoherenceforSD17.15Respectcountry’spolicyspace,leadership17.16EnhanceglobalpartnershipforSD17.17Encour-agepartnerships17.18EnhancecapacitybuildingsupporttoDC17.19DevelopprogressmeasurementsonSD17.1.1Totalgovernmentrevenuewasapropor-tionofGDP,bysource17.1Strengthendomesticresourcemobilization17.1.2DomesticBud-getfundedbytaxes

Data Intelligence Just Accepted MS.
https://doi.org/10.1162/dint_a_00206

A knowledge graph-based deep learning framework for efficient content similarity search of
Sustainable Development Goals data

Tavolo 1: Notation Overview for knowledge graph-based framework for efficient content similarity search of Sustainable
Development Goals data

grid size
Hilbert dimension
Hilbert order
indicator sentence
number of indicators
probe sentence
size of the reference set
bin number
bin size
HSFC coordinates
tuple

Insertion of Indicators:
N
HS FC dims
τ, HS FC order
indicator sentence
indicator number
probe sentence
µ
bin
bin size
T =(X,sì) ∈ N
M = (indicator, T = (X , sì) ∈
N)
Similarity Assessment:
sentenceı
w
tu, v
Wt ∈R3z×ω
z
ω
vi j
Data Classification of Entrant Indicators:
NDC
Q
Z
J
P
N
R, C
dist2
uk
λd
Dr, Dc
Filtering of Similarity Search Results:
δH
lδH
k
q
RH
nH q
Load Balancing:
physical node
virtual node
virtual node number
HS FC node number
load threshold
load(HS FC node)
load(virtual node)

χ2 (ind j, ind j′ )

physical node
virtual node
number of virtual nodes
number of physical nodes
load threshold
load of HSFC node
load of virtual node

ith sentence
number of words in the sentence
sentence embeddings
trainable weight
dimension of sentence embeddings
number of labels
vector representation of a word in sentenceı

individuals
categorical variables
indicator matrix
datasources
matrix of proportions
sample size
sums along the rows and along columns
chi-squared distances between two entrant-indicators
eigenvectors from eigenvalue decomposition of PD−1
c PT D−1
R
eigenvalue, variance of the points of indicator on d-dimension
the diagonal matrix of row and column masses respectively

distance function for HSFC projection
lower bound
maximum number of indicators in similarity search
similarity search query
rankings by means of lower bound
number of HSFC nodes with matching data for query q

DataIntelligence

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Data Intelligence Just Accepted MS.
https://doi.org/10.1162/dint_a_00206

A knowledge graph-based deep learning framework for efficient content similarity search of
Sustainable Development Goals data

Tavolo 2: Setup settings in an experimental distributed environment over a key-value store of SDG data

Parameter
Dataset
Number of servers
Number of virtual nodes per physical node
Queries
HSFC dimensions
HSFC order
Memcached server chunk size
Memcached server page size

Value
2,21M. entries
3
1
SELECT for similarity search
2
3
1MB
40

Tavolo 3: Number of occurrences of uncategorised Tier III entrant indicators in datasources, namely nodes of the graph
store where data associated with the indicators reside

Tavolo
Datasource
1
2
3
4
5
6
7
8
9
10

I1
16
15
16
14
16
15
16
14
16
16

I2
16
18
17
18
16
17
17
18
16
16

I3
16
18
17
16
16
15
17
17
15
15

I4
16
14
15
14
16
15
15
14
16
16

I5
17
16
16
16
16
15
15
15
17
16

Indicators
I6
17
16
16
18
17
17
16
16
18
17

I7
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15
14
16
16
15
15
16
16
16

I8
16
16
17
16
16
16
18
16
15
16

I9
16
17
18
17
15
17
17
18
16
15

I10
16
16
16
17
16
16
17
16
16
17

I11
16
17
17
18
16
18
17
18
16
16

I12
16
15
16
16
16
15
15
15
16
16

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Tavolo 4: Tier III entrant indicators

Indicator
I1
I2
I3
I4
I5
I6
I7
I8
I9
I10
I11
I12

Description
inclusive access to knowledge
abolish unnecessary animal testing
stop animal caging
access to infrastructure
cross border processing
data erasure
data portability
data literacy
improve animal welfare
promote research
improve farm conditions
equitable access to knowledge

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DataIntelligence

Data Intelligence Just Accepted MS.
https://doi.org/10.1162/dint_a_00206

A knowledge graph-based deep learning framework for efficient content similarity search of
Sustainable Development Goals data

Author Biography

Dr. Irene Kilanioti works as Teaching Staff at NTUA. She received
(Advanced Information Systems) from the De-
her B.Sc. and M.Sc.
partment of Informatics and Telecommunications, National Kapodistrian
University of Athens (best student award). She received after evaluation
one of the three scholarships of the Greek State Scholarships Foundation
for a Ph.D. in informatics abroad (2012-2015). She received her Ph.D.
(2016) entitled Improving Content Delivery with OSN-Awareness from
the Department of Computer Science of the University of Cyprus. She
has been a PostDoc researcher with the Ludwig-Maximilians-Universit¨at
in Munich (2018, 2019) and was accepted after evaluation at the LMU
Mentoring Programme. Her research interests include Complex net-
works, Data mining and Big Data, Knowledge analysis, Content Delivery
Optimization, Distributed computing and Adaptive educational software.
She has publications in peer-reviewed conferences, journals and books and holds the best paper
award in the 13th IEEE International Conference on Knowledge Graph 2022, Orlando, USA. She
has been vice-coordinator for the use case Delivering Social Multimedia Content with Scalability,
WG1, and trainer for the EU Cost action cHiPSet High-Performance Modeling and Simulation
for Big Data Applications (2017-2019). She is an Editor for the journal Frontiers in Digital
Education. She has worked as an informatics teacher in Greece and Germany and has served
from seconded positions (National School of Public Administration, Information Society Office
of the Greek Ministry of Education), as a software engineer (Vodafone, Enterprise Systems De-
velopment Department) and a teaching assistant (Design and Use of Database Systems, NKUA,
Information-theoretic Data Mining, LMU). https://www.ece.ntua.gr/en/staff/489

Dr. Giorgio A. Papadopoulos holds the (tenured) rank of Full Pro-
fessor in the Department of Computer Science, University of Cyprus.
His research interests include Advanced Software Engineering, Ubiq-
uitous Computing, Cloud Computing, Parallel and Distributed Program-
ming Models, Technology Enhanced Learning, Medical Informatics, As-
sistive Technologies, Context Aware and Recommender Systems, E
Internet Technologies. He has published over 150 papers as book chap-
ters or in internationally refereed journals and conferences, he is a cur-
rent or past member in the Editorial Board of 18 international jour-
nals and is serving or has served as a Chair or Steering or Program
Committee member in more than 200 international conferences. Pro-
fessor Papadopoulos is a recipient of a 1995 ERCIM-HCM scholarship
award. He has been involved or is currently participating, as coordi-
nator or partner, in more than 100 internationally and nationally funded projects (total bud-
get for his participation close to 9.5 MEURO) and has been invited by the E.U. as an Expert
Evaluator or Reviewer more than 50 times. Among his other activities, he is the Focal Point
of Cyprus in COL’s (https://www.col.org/) VUSSC (https://vussc.col.org) project.
He is the Director of the Software Engineering and Internet Technologies (SEIT) Laboratory
(http://www.cs.ucy.ac.cy/seit). More information can be found on his personal web site
at: http://www.cs.ucy.ac.cy/~george/. His email is george@ucy.ac.cy.