Data processing to remove outliers and inliers: A systematic literature study¹

Processamento de dados para remoção de pontos outliers e inliers: Estudo sistemático da literatura

ABSTRACT

Outliers and inliers often arise during sample data acquisition. While outliers represent anomalous observations, inliers are erroneous data points within the main body of the dataset. It was aimed to conduct a systematic literature study (SLS) to survey methods and software employed for outlier and inlier removal, particularly within exploratory data analysis. The study was conducted in three phases: (i) systematic literature mapping (SLM), (ii) snowballing (SB), and (iii) SLR. Initially, 772 scientific studies were identified, subsequently narrowed down to 86 after applying selection criteria. Backward (BSB) and forward (FSB) snowballing further yielded 16 studies, resulting in a final pool of 102 studies for analysis. It was identified three outlier removal techniques (Chebyshev’s inequality, boxplot, and principal component analysis), one inlier removal technique (local Moran’s index), and thirteen commonly used software.

Key words:
exploratory analysis; precision agriculture; local Moran’s index; data cleaning

RESUMO

Outliers e inliers aparecem frequentemente na aquisição de dados amostrais. Outliers são observações anômalas e inliers são dados errôneos no interior do conjunto de dados. Esta pesquisa teve como objetivo realizar um estudo sistemático da literatura (SLS) para levantar os métodos utilizados para remoção de outliers e inliers e os softwares utilizados na análise exploratória dos dados. Este estudo sistemático da literatura foi realizado em três etapas: (i) mapeamento sistemático da literatura (SLM), (ii) bola de neve (SB) e (iii) revisão sistemática da literatura (SLR). Setecentos e setenta e dois estudos científicos foram obtidos e reduzidos para 86 após seleção. Foram acrescentados mais dezessete estudos selecionados por bola de neve (bola de neve para trás (BSB) e bola de neve para frente (FSB)), o que resultou em 102 estudos utilizados nesta pesquisa. Foram observadas três técnicas de remoção de outliers (desigualdade de Chebyshev, boxplot e análise de componentes principais), uma única técnica de remoção de inliers (índice de Moran local) e treze softwares.

Palavras-chave:
análise exploratória; agricultura de precisão; índice de Moran local; limpeza de dados

HIGHLIGHTS:

Sample data acquisition often exhibits outliers and inliers.

Outlier and inlier techniques include Chebyshev’s inequality, boxplot, principal component anal-ysis, and local Moran’s index.

This systematic literature search effectively identified and filtered the research papers.

Introduction

Higher crop yields have long been a priority, driven especially by the increasing global population. This has necessitated not only the expansion of productive areas but also the constant evolution of management methods. Extensive research has shown that the spatial variability of yield in agricultural areas has diverse causes (Trevisan et al., 2021).

“Precision Agriculture (PA) is a management strategy that gathers, processes and analyzes temporal, spatial and individual plant and animal data and combines it with other information to support management decisions according to estimated variability for improved resource use efficiency, productivity, quality, profitability and sustainability of agricultural production” (ISPA, 2024). PA is essential for maximizing output while minimizing input use, reducing environmental impacts, and ensuring sustainability (Karunathilake et al., 2023).

Raw and semi-processed agricultural data are typically collected from various sources, including the Internet of Things (IoT), sensors, satellites, weather stations, robots, farm equipment, farmers, and agribusinesses.

Before analyzing collected data, a statistical and exploratory data analysis is essential. This analysis utilizes techniques to gain deeper insights into the dataset, extract key variables, and identify outliers, inliers, and anomalies. Outliers are unexpected observations that deviate significantly from the majority of data points. Outlier detection and prediction are challenging tasks due to the inherent rarity of outliers (Reunanen et al., 2020). Inliers, on the other hand, are data points that differ from their immediate neighbors but still fall within the overall range of variation in the dataset (Córdoba et al., 2016; Vega et al., 2019).

However, some crucial questions remain regarding the descriptive and exploratory statistical information used in PA, particularly the methods and software employed for outlier and inlier removal. Therefore, this systematic literature study (SLS) (Fisch & Block, 2018; Abbasi et al., 2022) focused on identifying research related to data treatments in PA, specifically methods for removing outliers and inliers.

Material and Methods

This study employed three search techniques to identify relevant studies for data cleaning:

(i) Systematic Literature Mapping (SLM), which uses targeted keywords to uncover research on a specific topic across various databases. To do so, it was adhered to well-defined SLM principles outlined by previous studies (Talavera et al., 2017; Aikes Junior et al., 2021; Beneduzzi et al., 2022; Moreira et al., 2022), defining relevant keywords, selecting suitable databases, establishing selection criteria, analyzing the retrieved studies, and synthesizing their findings. To guide this keyword selection, it was formulated three key questions: 1. What are the most frequently used methods for outlier removal in precision agriculture (PA)? 2. What are the most common methods for removing inliers in PA? 3. Which software programs are most widely employed for cleaning harvester data?

The Science Direct database was accessed through the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) portal using the Federated Academic Community (CAFe) remote access platform (Figure 1). To capture the most recent advancements, it was searched for publications from 2009 to 2019. From each identified study, it was extracted specific details crucial for this analysis, including title, authors, journal, year of publication, abstract, keywords, any software used, and reported results.

Figure 1
Workflow for searches on scientific bases

(ii) Snowballing (SB), a complementary technique, leveraged the reference lists of identified studies to uncover additional relevant articles (Li & Zhan, 2022; Moreira et al., 2022). This boosted search efficiency, mitigated potential biases (Aikes Junior et al., 2021; Beneduzzi et al., 2022), and even unearthed classic texts from conventional agriculture (Beneduzzi et al., 2022) that might have been missed in the initial search.

Two types of snowballing were employed: 1. Backward snowballing (BSB), which included new studies related to those found in the initial SLM phase; and 2. Forward snowballing (FSB), which built upon BSB by using the reference lists of those identified studies to find even more relevant articles (Aikes Junior et al., 2021; Beneduzzi et al., 2022; Moreira et al., 2022).

(iii) Systematic literature review (SLR) then integrated the findings from both SLM and SB. To ensure a targeted and efficient review, the study selection followed the following steps (Figure 2): 1. Retrieving and deduplicating articles, where studies were retrieved from the database removing duplicates, resulting in a pool of 772 studies; 2. Title screening, where the titles were reviewed to identify relevant articles, narrowing the selection down to 427; 3. Abstract analysis, which consisted of further refinement through abstract review, leaving 156 studies for in-depth evaluation; 4. Full-text reading and assessment, where the remaining 86 studies were carefully read and assessed; 5. Snowballing integration, where additional studies identified through snowballing were incorporated (10 from BSB and 6 from FSB). This meticulous process yielded a final pool of 102 studies for analysis (Table 1).

Figure 2
Workflow used for Systematic Literature Study (SLS)

Table 1
Selection after reading the studies (102 selected). Systematic literature mapping (SLM, 86 references); Backward Snowballing (BSB, 10 references); and Forward Snowballing (FSB, 6 references)

Technique	Studies
SLM	(Lamsal et al., 2009); (Liu et al., 2009); (Pei et al., 2010); (Eugster et al., 2010); (Vašát et al., 2010); (Gianquinto et al., 2011); (Amirinejad et al., 2011); (Tesfahunegn et al., 2011) ; (Davatgar et al., 2012) ; (Henriques et al., 2012) ; (Li et al., 2012); (Castrignanò et al., 2012); (Sudduth et al., 2012); (Van Meirvenne et al., 2013); (Chung et al., 2013); (Oliver & Webster, 2014); (Eitel et al., 2014); (Yao et al., 2014); (Mat et al., 2014); (Kanellopoulos et al., 2014); (Waruru et al., 2015); (Landrum et al., 2015); (Kaniu & Angeyo, 2015); (Tripathi et al., 2015); (Wang et al., 2015); (Stockmann et al., 2015); (Calafat et al., 2015); (Haghverdi et al., 2015); (Knadel et al., 2015); (Driemeier et al., 2016); (Turner et al., 2016); (Mieza et al., 2016); (Castaldi et al., 2016); (Páscoa et al., 2016); (Bitencourt et al., 2016); (Morellos et al., 2016); (Gerstmann et al., 2016); (Rodriguez-Moreno et al., 2016); (Li et al., 2016); (Cavallo et al., 2016); (Córdoba et al., 2016); (Jordanova et al., 2016); (Pelosi et al., 2016); (Nouri et al., 2017); (Gili et al., 2017); (Demattê et al., 2017); (Bodner & Robles, 2017); (Rosemary et al., 2017); (Mirzaeitalarposhti et al., 2017); (Adeline et al., 2017); (Medina et al., 2017); (Paraforos et al., 2017); (Castrignanò et al., 2018); (Coelho et al., 2018) ; (Neave et al., 2018) ; (Paraforos et al., 2018) ; (Sirsat et al., 2018) ; (Camino et al., 2018); (Leroux et al., 2018); (Liang et al., 2018); (Fujinuma et al., 2018); (Schönhart et al., 2018); (Squalli & Adamkiewicz, 2018); (Sanches et al., 2018); (Altdorff et al., 2018); (Behera et al., 2018); (Gholizadeh et al., 2018); (Raj et al., 2018); (Uribeetxebarria et al., 2018); (Hong et al., 2019); (Barca et al., 2019); (Krishna et al., 2019); (Zhou et al., 2019); (Betzek et al., 2019); (González-Fernández et al., 2019); (Liu et al., 2019); (Gavioli et al., 2019); (Araujo et al., 2019); (Ali et al., 2019); (Moura-Bueno et al., 2019); (Prasad et al., 2019); (Shaddad et al., 2019); (Sanches et al., 2019); (Uribeetxebarria et al., 2019); (Mura et al., 2019); (Vega et al., 2019)
BSB	(Arslan & Colvin, 2002); (Yield et al., 2004); (Menegatti & Molin, 2004); (Amidan et al., 2005); (Ping & Dobermann, 2005); (Dray et al., 2006); (Taylor et al., 2007); (Sudduth & Drummond, 2007); (Maldaner & Molin, 2020); (Paccioretti et al., 2020)
FSB	(Hotelling, 1933); (Gnanadesikan, 1977); (Barnett & Lewis, 1994); (Anselin, 1995); (Blackmore & Moore, 1999); (Jolliffe, 2005)

In terms of the geographic distribution of the selected studies (Figure 3), every continent except Antarctica was represented by at least one research paper. As for the distribution across different publication outlets (Figure 4), the journals Computers and Electronics in Agriculture and Geoderma exhibited the highest number of selected studies, accounting for 19 and 16%, respectively. Journals featuring only one study in the review were consolidated into a single category labeled “others,” comprising 19% of the total.

Figure 3
Distribution of selected studies per country (where authors carried out the study and, in cases of theoretical manuscript, where it was published)

Figure 4
Scientific journals where the selected studies were published

Results and Discussion

Numerous sensors used for retrieving spatial data are integrated into agricultural machinery. However, errors in their data can arise during the construction of digital maps (Spekken et al., 2005). For instance, the movement of the harvester into and out of the crop field, as well as areas with minimal or no crop, can lead to gradual changes in yield readings rather than sudden fluctuations, as expected (Kharel et al., 2019). Another potential source of errors is associated with the GPS (Global Positioning System) signal receiver, now commonly referred to as the GNSS (Global Navigation Satellite System) receiver (Blackmore & Moore, 1999). The yield measurement using a monitor is automated, allowing for the collection of a large volume of data. Hence, errors may be introduced (Menegatti & Molin, 2004), including georeferencing errors, sensor inaccuracies, and operational errors (Sun et al., 2013).

Outlier detection represents a primary task preceding analysis, aiming to identify anomalies within extensive datasets. Various terms, such as noise detection, anomaly detection, deviation detection, or outlier detection, are used to describe this process. According to Barnett & Lewis (1994), outliers are observations that deviate significantly from the general pattern or distribution of the dataset, highlighting the importance of removing outliers before making agronomic decisions (Taylor et al., 2007). The removal of outliers is a crucial step that precedes the construction of thematic maps, ensuring the accuracy of agronomic decisions (Vega et al., 2019).

Identifying and potentially removing outliers during data collection and analysis is often imperative. Thus, it is essential to establish that a given methodology is both objective and efficient in identifying outliers for removal (Amidan et al., 2005). Additionally, several automated methods are available for detecting and eliminating outliers (Table 2).

Table 2
Outlier removal techniques

Technique	N	Studies
μ ± 1.5σ	1	(Gerstmann et al., 2016)
μ ± 2σ	4	(Pei et al., 2010); (Gianquinto et al., 2011); (Chung et al., 2013); (Rosemary et al., 2017)
μ ± 2.5σ	6	(Squalli & Adamkiewicz, 2018); (Castrignanò et al., 2012); (Cavallo et al., 2016); (Uribeetxebarria et al., 2018); (Uribeetxebarria et al., 2019); (Coelho et al., 2018)
μ ± 3σ	9	(Simbahan et al., 2004); (Liu et al., 2009); (Haghverdi et al., 2015); (Landrum et al., 2015); (Córdoba et al., 2016); (Driemeier et al., 2016); (Li et al., 2016); (Bodner & Robles, 2017); (Sanches et al., 2018); (Betzek et al., 2019); (Sanches et al., 2019); (Vega et al., 2019)
Boxplot	26	(Eugster et al., 2010); (Tesfahunegn et al., 2011); (Henriques et al., 2012); (Li et al., 2012); (Eitel et al., 2014); (Kanellopoulos et al., 2014); (Oliver & Webster, 2014); (Wang et al., 2015); (Castaldi et al., 2016); (Jordanova et al., 2016); (Pelosi et al., 2016); (Rodriguez-Moreno et al., 2016); (Turner et al., 2016); (Gili et al., 2017); (Medina et al., 2017); (Nouri et al., 2017); (Paraforos et al., 2017); (Fujinuma et al., 2018); (Liang et al., 2018); (Neave et al., 2018); (Paraforos et al., 2018); (Schönhart et al., 2018); (Sirsat et al., 2018); (Barca et al., 2019); (Liu et al., 2019); (Prasad et al., 2019)
PCA	15	(Hotelling, 1933); (Gnanadesikan, 1977); (Jolliffe, 2005); (Mat et al., 2014); (Waruru et al., 2015); (Kaniu & Angeyo, 2015); (Knadel et al., 2015); (Stockmann et al., 2015); (Morellos et al., 2016); (Páscoa et al., 2016); (Adeline et al., 2017); (Demattê et al., 2017); (Mirzaeitalarposhti et al., 2017); (Gholizadeh et al., 2018); (Moura-Bueno et al., 2019)

• N - Number of studies

Chebyshev’s inequality was developed to establish a lower bound on the percentage of data within a certain range of standard deviations from the mean. For data following a normal (bell-shaped) distribution, approximately 95% of the data typically lies within two standard deviations from the mean. Consequently, around 5% of the data would be expected to fall outside this range (Amidan et al., 2005).

Chebyshev’s inequality (Eq. 1) is applicable when the distribution of the data is unknown (Amidan et al., 2005):

$$P\left(\left|X-\mu \right|\le k\sigma \right)\ge \left(1-\frac{1}{k^2}\right)$$ (1)

where: X - data; µ - data mean; σ - standard deviation of the data; and, k - number of standard deviations of the mean.

Chebyshev’s theorem asserts that a minimum of 89% of data falls within the range of the mean ± 3 standard deviations, irrespective of the distribution (Córdoba et al., 2016). Table 2 outlines various other proposals for lower and upper limits based on the dataset (Table 2).

Adjusting the lower and upper limits of the standard deviation parameter for a specific field area can be accomplished through the iterative selection of values while observing the impact on the resulting yield data distribution (Sudduth & Drummond, 2007). The interval of ± 3 standard deviations was the most commonly cited in the studies (Table 2).

The boxplot graph (Tukey, 1977) is a useful tool that segments data based on four hidden boundaries: two inner fences and two outer fences (Figure 5). Typically, the interquartile range (IQR) is defined as Q3-Q1. The inner fences are Q1 - 1.5 IQR and Q3 + 1.5 IQR, while the outer fences are Q1 - 3 IQR and Q3 + 3 IQR. The whiskers extend to the most extreme data points within the inner fences. Data points outside the inner fences but within the outer fences are considered mild outliers, each marked with a symbol. Data points outside the outer fences are classified as extreme outliers and are marked with a different symbol. There is no consensus regarding the choice of symbols (Dawson, 2011).

Figure 5
Boxplot structure

Boxplots are effective tools for visualizing data distribution in terms of quartiles and identifying outliers (Prasad et al., 2019). Consequently, several studies (Table 2) have utilized boxplots for outlier detection and removal.

Principal Components Analysis (PCA) (Hotelling, 1933) is a multivariate technique outlined in Table 2, involving the creation of a new set of orthogonal synthetic variables known as principal components (PC). The primary objective is to reduce the dimensionality of a dataset containing numerous interrelated variables while preserving as much variation as possible (Jolliffe, 2005).

As described by Filzmoser et al. (2005), the covariance matrix characterizes the shape and size of multivariate data. The Mahalanobis distance is a commonly used distance measure that takes into account the covariance matrix. The Mahalanobis distance (Eq. 2) for a p-dimensional multivariate sample x_1, ..., x_n is given by:

$$M{D}_i={\left[{\left(x_i-t\right)}^T{C}^{-1}\left(x_i-t\right)\right]}^{\frac{1}{2}} for i=1, ..., n$$ (2)

where: t is the estimated multivariate location, and C is the covariance matrix. Typically, t is the multivariate arithmetic mean, the centroid, while C is the sample covariance matrix.

For multivariate normally distributed data, the squared Mahalanobis distances (MD_i ²) are approximately distributed as chi-square (χ_p ²) with p degrees of freedom. By equating the squared Mahalanobis distance to a specific constant, corresponding to a certain quantile of χ_p ², it becomes feasible to define ellipsoids that have the same Mahalanobis distance from the centroid (Filzmoser et al., 2005).

Inliers refer to data points that deviate significantly from their local surroundings but still fall within the overall range of variation of the dataset (Córdoba et al., 2016; Vega et al., 2019). The Local Moran’s Index of spatial autocorrelation (I_i) (Anselin, 1995) can be employed to identify inliers for each variable within the dataset. As described by Córdoba et al. (2016), I_i represents a Local Moran’s Index (LISA) applied individually to each neighborhood, indicating the degree of similarity or dissimilarity between the observation’s value and that of its neighbors (Table 3).

Table 3
Inlier removal techniques

Technique	N	Studies
Local Moran's Index (LISA)	4	(Lamsal et al., 2009); (Calafat et al., 2015); (Córdoba et al., 2016); (Vega et al., 2019)

According to Vega et al. (2019), the spatial autocorrelation index I_i can be computed for yield data as a tool for identifying inliers, utilizing the following equation (Eq. 3):

$$I_i=\frac{Z_i-\overline{Z}}{{\sigma }^2}\sum _{i=1.j\ne i}^n\left[W_{ij}\left(Z_j-\overline{Z}\right)\right] for i=1, ..., n$$ (3)

where: Z is the mean yield value, Z_i is the local yield at location i, Z_j is the yield at other locations (j ≠ i), σ² is the yield variance, n is the sample size, and W_ij is the weighted distance between Z_i and Z_j. Neighboring points are defined as continuous to calculate W_ij (Anselin, 1995).

A positive Local Moran’s (LM) index value indicates spatial clustering of similar values, whereas a negative value suggests clustering of dissimilar values. For instance, a site with a low yield value surrounded by neighbors with high yield values would result in a negative LM index value. The p-value associated with each yield data point evaluates the statistical significance of the LM value. These probability values are adjusted using Bonferroni’s criterion to account for the multiplicity of indices evaluated simultaneously within the field. Bonferroni’s adjustment is applied to each test performed to maintain the overall study’s error rate at 0.05 (Vega et al., 2019).

No studies comparing the efficiency of the reported data-cleaning methods were found. However, it is worth noting that the most recent data-cleansing software predominantly employs statistical methods, likely due to their ease of use and effectiveness.

Software used for detecting and removing outliers and inliers

An extensive array of sensors, such as yield monitors, is commonly integrated with agricultural machinery to collect spatial data. However, these data often contain systematic and random errors, as well as atypical values, necessitating post-processing for their elimination. Various methods and protocols have been developed to apply filter sequences and classify, identify, and remove outliers and inliers from grain yield data (Córdoba et al., 2016; Leroux et al., 2018; Sudduth et al., 2018; Vega et al., 2019). According to Vega et al. (2019), approximately 30% of yield data were removed after data cleaning. A total of 13 software tools were used in different studies for data cleaning, including both proprietary and free software options (Table 4).

Table 4
Software programs used in data cleaning

Program	N	Studies	License
FastMapping	1	(Paccioretti et al., 2020)	Free
JMP Pro	1	(Uribeetxebarria et al., 2018)	Proprietary software
MapFilter	-		Free
Matlab	4	(Liang et al., 2018; Paraforos et al., 2018, 2017; Sanches et al., 2019)	Proprietary software
Python	1	(Coelho et al., 2018)	Free
SAS	3	(Chung et al., 2013; Neave et al., 2018; Barca et al., 2019)	Proprietary software
Isatis	2	(Castrignanò et al., 2012; Cavallo et al., 2016)	Proprietary software
R Core	10	(Sudduth & Drummond, 2007a; Stockmann et al., 2015; Castaldi et al., 2016; Córdoba et al., 2016; Gili et al., 2017; Schönhart et al., 2018; Sirsat et al., 2018; Barca et al., 2019; Moura-Bueno et al., 2019; Vega et al., 2019)	Free
SPSS	5	(Tesfahunegn et al., 2011; Wang et al., 2015; Li et al., 2016; Medina et al., 2017; Rosemary et al., 2017)	Proprietary software
Statgraphics	1	(Gianquinto et al., 2011)	Proprietary software
Statistica	1	(Jordanova & Petrov, 2016)	Proprietary software
YieldEditor	2	(Sudduth & Drummond, 2007b; Sudduth et al., 2012)	Free

Conclusions

1. The systematic literature study (SLS) proved to be effective in identifying relevant research studies and enhancing understanding of the research subject.

2. The survey conducted through systematic literature mapping (SLM) yielded 772 scientific studies, which were narrowed down to 86 studies following the selection process. Additionally, sixteen more studies identified through snowballing (FSB and BSB) were incorporated, resulting in a total of 102 studies used in this research.

3. Three techniques for outlier removal were identified: (i) Chebyshev’s inequality, (ii) boxplot analysis, and (iii) principal component analysis. In terms of removing inliers, all studies employed the local Moran’s index. Furthermore, thirteen different software tools were identified across the analyzed studies.

Supplementary documents

There are no supplementary sources.

Conflict of interest

The authors declare no conflict of interest.

Financing statement

There are not financing statements to declare.

Acknowledgements

The authors would like to thank the Universidade Estadual do Oeste do Paraná (UNIOESTE), the Universidade Tecnológica Federal do Paraná (UTFPR), the Instituto Federal do Paraná (IFPR), the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES; finance code n° 001), and the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq).

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• ¹ Research developed at Universidade Estadual do Oeste do Paraná, Cascavel, PR, Brazil

Edited by

Editors: Toshik Iarley da Silva & Carlos Alberto Vieira de Azevedo

Publication Dates

• Publication in this collection
  22 July 2024
• Date of issue
  Sept 2024

History

• Received
  18 Sept 2023
• Accepted
  14 Apr 2024
• Published
  10 June 2024