Conducting Vessel Data Imputation Method Selection
Based on Dataset Characteristics
Tirana Noor Fatyanosa1 Neni Alya Firdausanti1 Luis Japa1
Israel Mendonça1 Putu Hangga Nan Prayoga2 Masayoshi Aritsugi1[1][2]

Kumamoto University, Kumamoto 860-8555, JapanMTI Co., Ltd., Tokyo 100-0005, Japan

E-mail: fatyanosa@dbms.cs.kumamoto-u.ac.jp,
nenialya@dbms.cs.kumamoto-u.ac.jp, japa-luis@dbms.cs.kumamoto-u.ac.jp,
israel@cs.kumamoto-u.ac.jp, putu.hangga@monohakobi.com,
aritsugi@cs.kumamoto-u.ac.jp
Abstract. Time series datasets collected from marine sensors inevitably undergo missing data problems.
This cause unreliable sensor data to assist the decision-making process. Many methods are offered to impute
missing values. However, selecting the best imputation method is not a trivial task, as it usually requires
domain expertise and several trial-and-error iterations. Furthermore, when imputations are carried out
in a careless way, it generates a high error factor that can lead stakeholders to wrong assumptions. This
paper provides a systematic approach that is able to extract characteristics of underlying data and, basedon it, recommends the less error-prone imputation method. We evaluate our proposed method using ninereal-world vessel datasets. In total, we generated 3859 data samples consisting of 17 inputs and 1 target
feature. Experimental results show that the proposed approach is capable of obtaining a weighted F1-Scoreof 92.6%. Additionally, when compared with the application of careless selected imputation methods, ourwork is able to gain up to 86% on the average imputation score, with the worst case gain being of 5%. We
empirically demonstrate that the proposed approach is efficient when selecting the best imputation methods.

1. Introduction
Time series are important in practical applications as time series data must be handled correctly to avoid
erroneous and biased results, eventually leading to a flawed decision-making process [1]. However,missing values are inevitable in time series caused by unexpected events, such as malfunctioning sensors
or missing signals. Ignoring the observation with missing values is an easy alternative. There is no big
issue when there are only a few observations with missing values. However, a significant amount of
information is lost when several observations have missing values. Additionally, it reduces the data’s
statistical power and effectiveness. Therefore, reliable imputation methods are required to address themissing data problem [2].
In a time series dataset, missing block patterns might be highly random and diverse. Additionally, thedataset may have quite various properties depending on the length and number of series, the frequency ofrepetitions (seasonality) within a series, and the connection between series. There may be a complete
continuous block of entries missing from a time series or several different time series. Depending on thesize of the block, its position to other missing blocks, patterns within a series, and correlation (if any) withother series in the dataset, the signals from the rest of the dataset that are most relevant for imputing a
missing block will vary. Interpolation with close neighbors may be helpful if only one entry is missing.

Repeated patterns within the series and trends from connected series may be helpful if a range of values
from a particular time series is lacking. Only patterns within a series will be helpful if the same time
range is missing from many series [3].
In the context of data analysis, data imputation is a pre-processing stage aiming to estimate pinpointed
missing values in order to avoid the under-utilization of data. Hence, if missing values are not tackled, theresults obtained may be unreliable and inaccurate, leading to biases in further phases due to inadequate
models implemented in the decision-making process [4]. Although time series’ data imputation is awell-researched subject, the choice of the best missing data handling technique is still a challenging issue.
It relies on several variables, and trade-offs between various elements and there is no golden standard
that can be used in every case and have optimal results; instead, selecting the optimal method depends
on a combination of interrelated factors [5]. Moreover, it is presumed that the dataset’s characteristics
may have some bearing on the algorithm. This hypothesis drove us to model the relationship between thedataset’s characteristics and the effectiveness of each missing value imputation method to select the best
method accordingly.
Our main contributions are described below:• We study the datasets and propose 17 features obtained from their characteristics.
• We provide 3859 dataset samples that can be used directly to study the effects of different imputation
methods.
• We assess our proposed approach using nine real-world vessel datasets. We investigate eight
imputation methods. As a result, interpolation and MissForest [6] became the most dominant
imputation methods.
The remainder of this paper is structured as follows: Section 2 provides related work. Section 3 shows
the proposed methodology. Section 4 reflects the experimental setup. Section 5 presents results anddiscussion of the implementation of the proposed methodology. Lastly, Section 6 concludes the overall
results.
2. Related Work
The major approaches employed to handle missing values are categorized into three groups: deletion
methods, donor-based methods, and model-based methods. Deletion methods are approaches that remove
the rows that contain missing values [7]. These approaches are a common strategy if the percentage of
missing data is less than 5% [8]. Contrarily, if the percentage of missing data is more than 5% then donorbased imputation or model-based imputation are recommended. In donor-based imputation the missing
values in a record (row) are filled with data from another record (or records) with similar characteristics.
Some examples of donor based imputation methods are: hot-deck imputation and k-Nearest Neighbours(kNN) imputation. Regarding model-based imputation, a predictive model is designed for each target
variable in the data set that contains missing values. Usually, this model is fitted on the available data andthen used to impute the missing values.
Another possible way in which imputation methods can be divided is into the two following groups:
single imputation methods and multiple imputation methods. In single imputation methods the missing
values are imputed just once, without defining a model for the partially missing data. Some methods
included in this category are mean, mode, median, interpolation and k-Nearest Neighbour (kNN)
imputation. Mean, mode, and median imputation are methods that use statistical values (average, modeand median, respectively) to impute missing values. Further, interpolation is an imputation technique thatassumes a linear relationship between missing and non-missing values. Finally, kNN imputation finds the
k-most similar observations by taking into account all of the other features and averages them to fill themissing values. Inside the family of kNN, [9] proposed GkNN, which is able to efficiently handle datawith mixed-attributes.
In contrast to single imputation, multiple imputation techniques combine the results of several
imputed datasets to arrive to a final solution. Some examples of commonly used multiple imputation

Figure 1. Data selection and preparation based on the data information.
methods are: MissForest, Multiple Imputation by Chained Equations (MICE), Multiple Imputation
Using Denoising Autoencoders (MIDA) and Missing Data Imputation using Generative Adversarial Nets
(GAIN). MissForest is a random forest-based iterative imputation method proposed in [6]. This method
first imputes all the missing data using a single imputation method, such as mean or mode, and thenfits a random forest on the observed part of the data in order to predict the missing values. MICE wasdeveloped in [10] and it fills the missing values through an iterative series of predictive models. Similar
to MissForest, at the beginning the missing values are "initialized" using another imputation method.
Common choices for this step are mean and mode. Then, at every iteration the MICE algorithm imputes
the missing values individually by fitting a model on the rest of the data. The iterations continue until auser-defined condition is met. MIDA was developed in [11] and it is based on a type of artificial neuralnetworks called Denoising autoencoders (DAEs). Autoencoders consist of two artificial neural networks:
an encoder and a decoder. The encoder take some input and map it to an intermediate representation;
then, the decoder maps this representation back to its original domain. The main assumption is that
this intermediate representation captures the coordinates along the main factors of variation. GAIN,
developed in [12], adapts the well-known Generative Adversarial Nets (GAN) framework to the data
imputation domain. In this work the generator observes some components of a real data vector andimputes the missing ones. The discriminator then takes this completed vector and attempts to determine
which components were actually observed and which were imputed.
3. Methodology
We study how different imputation methods behave for different scenarios. Our process consists ofdifferent steps explained as follows:First, we define the data information shown in Table 1. For the vessel data information, we define two
scenarios, ALL (all columns: 217) and IMP (important columns: 57), based on the importance of thecolumns referring to causalities for the use case of machinery predictive maintenance. For the scheme, we
use three missing values mechanisms: Missing completely at random (MCAR), Missing not at random(MNAR), and Missing at random (MAR). We use the missing values settings from [13].
From the data information, we can obtain the subset of datasets. Then, we remove the missing rows
to get the original complete data. Next, we synthetically remove some cells based on the scheme andmissing rates defined in the data information. The visualization can be seen in Figure 1.
We then divided the process into the input and target generations. Input features are the measurementthat is obtained easily from the dataset characteristics. To generate suitable features, we emphasize
missing data-related features and follow some references [5, 14, 15]. The input features we used canbe seen in Table 1. To obtain the features, we first artificially removed some values from the originalcomplete data for particular data information. In total, we selected 17 input features from the data to test.
Target feature generation consists of three main steps: data imputation, best method selection, andgeneration. In the data imputation step, each data information will be imputed with eight imputation
methods: interpolation, mean, mode, median, miceforest, KNN, GAIN, and MissForest. Each method willrecord the RMSE, MAE, and time. Then the process continued to the second step: best method selection.
For each data information, the recorded RMSE, MAE, and time will be used to calculate the score using
Equation 1. The best method for particular data information is selected based on the lowest score.

Table 1. Data information, input, and target features.
Category

Component
Data
Scenario
SchemeData
Duration
Information
Year
Months

Input
Features

Missing rate
A: Missing rate
B: Number of incomplete rows
C: Percentage of incomplete rows
D: Number of complete rows
E: Percentage of complete rows
F: Number of incomplete columns
G: Percentage of incomplete columns
H: Number of complete columns
I: Percentage of complete columns
J: Average missing cells per row
K: Average missing cells per column
L: Number of all null features
M: Number of uniform features
N: Number of rows
O: Number of columns
P: Number of missing cells
Q: Number of maximum consecutive NaNs

Target FeaBest Methodtures

Description
The dataset name[ALL, IMP][MCAR, MNAR, MAR][3, 6, 12, 24][2020,2021,2020-2021][3: Jan-Mar, Apr-Jun, Jul-Sep, Oct-Dec, 6: Jan-Jun,
Jul-Dec, 12: Jan-Dec, 24: Jan 2020-Dec 2021][0.1, 0.2, 0.3, 0.4, 0.5, real]

The values were taken from the properties of thedata.

The values were taken from the best imputation
method for each data information.

Table 2. The statistics of the datasets.
DatasetPure Car Carrier (Vessel A)
LPG Tanker (Vessel B)
Ro-Ro Cargo Ship (Vessel C)
Container Vessel (Vessel D)
Oil Tanker (Vessel E)
Ro-Ro Cargo Ship (Vessel F)
LPG Tanker (Vessel G)
Ro-Ro Cargo Ship (Vessel H)
Oil Tanker (Vessel I)

Number ofsamples
171164165261
17489817398716034310213817391
175056
17517

Number ofcolumns
127
127
127
127
127
127
127
127
127

4. Experimental Setup
We applied the proposed method to the real vessel datasets. We use an IoT sensor time series dataset ofcommercial ocean-going vessels of various sizes and types. Datasets for all vessels were collected for two
years periods with 6 minutes sampling frequency. Statistics of the datasets are outlined in Table 2. For moredetails, summary statistics of selected columns from Vessel A can be seen in Table A1 of Appendix A.
Focusing on the vessel data, we found two common missing patterns for vessel IoT data, as shownby Table 3. The two vessels in the table have distinctly different missing patterns, MCAR and MNAR,
respectively (see Figure 2 for the illustration). If we process these missing data using only the deletion

Table 3. Characteristic of missing pattern for vessel data.
Characteristics
Vessel A
Built year
1999
LoA (m)199.94
Breadth (m)
32.2
DWT
21547
Design draft (m)8.75Main Engine
Mitsubishi 8UEC60LS
Number of Main Engine Cylinders
8
Data collection frequency
every 6 minutes
Duration of collected data
2020-2021
Missing by Rows
Total rows
171164Complete rows0
Incomplete rows
171164
Missing by Cell
Total cells
16431744
Missing cells
1999295
Avg missing cells (columns)
20826
Avg missing cells (rows)
12
Common missing pattern
MCAR (Figure 2a)(a) MCAR

Vessel C
2018
179.9427
6100
6.5
MAN 9S50ME
9every 6 minutes
2020-2021
1748984517485321862250
7649336120
4
MNAR (Figure 2b)(b) MNAR

Figure 2. Illustration of missing pattern.
method, it is natural to have fewer data to perform advanced analytics. In some cases, leave 0% of thedata available for modeling as shown by Figure 3.
We conducted two types of data preprocessing: data cleaning and data transformation. Data cleaning
consists of removing unnecessary space, changing the empty string into NaN, removing empty columns,
and removing columns with the same values in all rows. Data transformation consists of transforming alldata into numerical data.
To measure the quality of the imputation methods, we utilized three metrics: mean absolute error(MAE), root mean square error (RMSE), and normalized execution time (t). Those three measurements
were combined into one (see Equation 1) to discover a more resounding conclusion and avoid misleading.
The MAE and RMSE are the main metrics. The time metric is supplementary and not too important;
therefore, we add a weight of 0.1. Upon calculating the metrics, we transform the data within the samerange between 0 and 1 using the Min-Max Scaling.

Incomplete

Complete

100%

75%

50%

25%

0%
Vessel A Vessel B Vessel C Vessel D Vessel E Vessel F Vessel G Vessel H Vessel I

Figure 3. Percentage of leftover data for analysis when performing imputation by deletion method.
Table 4. Target class ratio of all imputation methods.
MethodRatio

Mean
0 (0.00%)Mode
0 (0.00%)

Median3 (0.08%)

Interpolation
1527 (39.57%)

KNN
30 (0.78%)

miceforest
57 (1.48%)

GAIN
0 (0.00%)

MissForest
2242 (58.10%)

Note: The values in the table represent the total and percentage (in the bracket)

score = (RM SE + M AE) ∗ (1 + (0.1 ∗ t))(1)

where t is the Min-Max normalized execution time.
5. Results and Discussion
From the features generation, we extract 3859 dataset samples. All samples consist of 17 input featuresand 1 target feature. We begin our discussion by assessing the performance of the imputation methods.
The first observation is that, in all cases, MissForest and interpolation dominated the overall best methods(Table 4).
Even though GAIN is considered the best-performing imputation method [16], it cannot outperform
interpolation and MissForest. One possible explanation is that GAIN is ineffective in imputing timeseries [17]. Comparing the performance, we can conclude that the simple classical methods outperform
advanced imputation methods.
We assume that the domination of interpolation and MissForest in performance is possible because of
the nature of both methods that are appropriate for the time series dataset. For interpolation, when data ofa column is missing at a particular time, it is natural to fill the missing data with a straight line between
the two points of time. Meanwhile, MissForest has been proven to be a reliable imputation method fortime series datasets with complex interactions and nonlinear relations [18, 19].
To investigate the difference between both methods more deeply, we had compared the number ofmaximum consecutive NaNs as shown in Figure 4. It is shown that most of the data samples that favorinterpolation as the best method has lower numbers of maximum consecutive NaNs than the data samplesof MissForest. It indicates that the missing gap is an important part of method selection. Interpolation
works best with smaller gaps between consecutive records. When the gap is high, the prediction ability

Number of max consecutive NaNs

500
400
300
200
100
0

0.0

0.2
0.4
Missing rate (Interpolation)

0.0

0.2
0.4
Missing rate (MissForest)

Figure 4. Number of max consecutive NaNs for all methods.
MissForest
GAIN

Methodmiceforest
KNN
INTERPOLATIONMEDIAN
MODE
MEAN
02000 4000 6000 8000 10000
Execution Time (s)Figure 5. Execution time analysis.

becomes limited as the interpolation fits a gap between the last and next observation data [20]. Meanwhile,
MissForest seems to perform well regardless of the gap size.
The boxplot of overall execution time (Figure 5) shows that although all the methods impute the same
number of missing cells, the execution time is different. The boxplot demonstrates two conclusions: (1)All statistical methods, mean, mode, median, and interpolation, only need a lower time to impute all
missing values, and (2) the other advanced methods need a higher execution time.
The XGBoost shows that the generated dataset can be successfully used to select the best imputation
method, as the weighted F1-Scores is 92.6%. Moreover, our approach significantly improves the average
imputation score. In a no-recommendation scenario, in which the same imputation method was used
for all datasets, the obtained average scores per method were 0.115, 0.504, 0.671, 0.514, 0.127, 0.233,
0.295, and 0.101 for interpolation, mean, mode, median, miceforest, KNN, GAIN, and MissForest,
respectively. However, with the employment of our approach, the average score was reduced to 0.096. The
best theoretical possible value for this measurement, i.e. the average score in a perfect recommendation
scenario, is 0.095. Our obtained value is notably close to this theoretical value, evidencing the effectivenessof our proposed method.
6. Conclusion and Future Remarks
In this paper, we present a systematic imputation method selection based on dataset characteristics. We
conduct experiments using nine real-world vessel datasets. We obtained 3859 dataset samples with 17
input and 1 target features. Interpolation and MissForest were found to be the dominant imputation
methods. The testing results showed that our approach was able to reach 92.6% of the weighted F1Score using XGBoost. Compared with the results without our approach, the highest and lowest average
imputation score improvement were 86% and 5%, respectively.
The current version of the algorithm only recommends the whole data. However, in some cases, it isbetter to make a mixed imputation, in which we perform imputation for subsets of the data using differentmethodologies. By incorporating domain knowledge, we will adapt the algorithm for future work to use asubset of columns instead of the whole data.
Acknowledgement
The authors wish to express their gratitude to MTI Co., Ltd. for providing the vessel datasets.
References[1] Fekade B, Maksymyuk T, Kyryk M and Jo M 2018 IEEE Internet of Things Journal 5 2282–2292[2] Khan S I and Hoque A S M L 2020 Journal of Big Data 7 ISSN 2196-1115[3] Bansal P, Deshpande P and Sarawagi S 2021 CoRR abs/2103.01600 (Preprint 2103.01600) URL https://arxiv.
org/abs/2103.01600[4] Velasco-Gallego C and Lazakis I 2021 RINA Maritime Innovation and Emerging Technologies Online Conference 2021
Proceedings (United Kingdom: Royal Institution of Naval Architects) royal Institution of Naval Architects Maritime
Innovation and Emerging Technologies Online Conference 2021, RINA Maritime Innovation and Emerging Technologies
Online Conference 2021 ; Conference date: 17-03-2021 Through 18-03-2021 URL https://www.rina.org.uk/
Maritime_innovation_2021.html[5] Liu Q and Hauswirth M 2020 2020 11th IEEE Annual Ubiquitous Computing, Electronics & Mobile Communication
Conference (UEMCON) pp 0349–0358[6] Stekhoven D J and Bühlmann P 2011 Bioinformatics 28 112–118 ISSN 1367-4803 (Preprint https://academic.oup.
com/bioinformatics/article-pdf/28/1/112/583703/btr597.pdf) URL https://doi.org/
10.1093/bioinformatics/btr597[7] Wothke W 2000 Modeling longitudinal and multilevel data: Practical issues, applied approaches, and specific examples(Lawrence Erlbaum Associates Publishers) pp 219–240[8] Graham J W 2009 Annual Review of Psychology 60 549–576 ISSN 0066-4308 URL https://www.annualreviews.
org/doi/10.1146/annurev.psych.58.110405.085530[9] Zhang S 2012 Journal of Systems and Software 85 2541–2552 ISSN 0164-1212 URL https://www.sciencedirect.
com/science/article/pii/S0164121212001586[10] White I R, Royston P and Wood A M 2011 Statistics in Medicine 30 377–399 ISSN 02776715 URL https://onlinelibrary.wiley.com/doi/10.1002/sim.4067[11] Gondara L and Wang K 2018 Advances in Knowledge Discovery and Data Mining (Springer International Publishing) pp
260–272 URL https://doi.org/10.1007%2F978-3-319-93040-4_21[12] Yoon J, Jordon J and van der Schaar M 2018 Proceedings of the 35th International Conference on Machine Learning(Proceedings of Machine Learning Research vol 80) ed Dy J and Krause A (PMLR) pp 5689–5698 URL https://proceedings.mlr.press/v80/yoon18a.html[13] Muzellec B, Josse J, Boyer C and Cuturi M 2020 Proceedings of the 37-th International Conference on Machine Learning(Vienna, Austria: arXiv) URL https://arxiv.org/abs/2002.03860[14] Zou Y, An A and Huang X 2005 2005 IEEE International Conference on Granular Computing vol 2 pp 728–733 Vol. 2[15] Sim J, Lee J S and Kwon O 2015 Mathematical Problems in Engineering 2015 ISSN 15635147[16] Awan S E, Bennamoun M, Sohel F, Sanfilippo F and Dwivedi G 2021 Neurocomputing 453 164–171 ISSN 0925-2312
URL https://www.sciencedirect.com/science/article/pii/S0925231221005282[17] Luo Y, Zhang Y, Cai X and Yuan X 2019 (International Joint Conferences on Artificial Intelligence Organization) pp
3094–3100 ISBN 978-0-9992411-4-1[18] Zhang S, Gong L, Zeng Q, Li W, Xiao F and Lei J 2021 Remote Sensing 13(12) ISSN 20724292[19] Arriagada P, Karelovic B and Link O 2021 Journal of Hydrology 598 126454 ISSN 0022-1694 URL https://www.sciencedirect.com/science/article/pii/S0022169421005011[20] Adhikari D, Jiang W, Zhan J, Rawat D B, Aickelin U and Khorshidi H A 2022 ACM Computing Surveys ISSN 0360-0300

Appendix A.
Table A1. Summary statistics of selected columns from Vessel A.
ColumnM/E RPM (rpm)
M/E LOAD (%)
LOG SPEED (AVERAGE) (knot)
OG SPEED (AVERAGE) (knot)
M/E NO.1 CYL EXH GAS OUT T (C)M/E NO.1 CYL SCAV AIR T (C)M/E NO.1 CYL JACKET COOLING FRESH WATER OUT T (C)M/E NO.1 CYL PCO OUT T (C)M/E FO IN P (MPa)M/E FO IN T (C)M/E MAIN LO IN P (MPa)M/E MAIN LO IN T (C)M/E SCAV AIR IN P (MPa)M/E SCAV AIR IN T (C)M/E NO.1 T/C TACHOMETER (x100 rpm)
M/E NO.1 T/C EXH GAS IN T (C)M/E NO.1 T/C EXH GAS OUT T (C)ROLL (AVERAGE) (deg)PITCH (AVERAGE) (deg)YAW (AVERAGE) (deg)HEADING (deg)RUDDER ANGLE (AVERAGE) (deg)RELATIVE WIND DIRECTION (deg)RELATIVE WIND (m/s)

Mean
46.07
27.87
6.00
6.64
230.06
54.41
77.67
47.55
0.53
98.99
0.26
44.95
0.04
41.95
52.80
270.60234.81
9.73
0.96
-4.57
198.00NaN
NaN
NaN

St.Dev.
38.92
26.77
6.76
6.48
141.11
6.64
10.06
6.13
0.10
24.47
0.09
3.81
0.04
4.81
48.54
170.24146.520.85
0.24
102.80
95.96
NaN
NaN
NaN

Min.
-120.00
0.00
0.00
0.00
17.00
31.00
32.00
21.00
0.00
23.00
0.00
24.00
0.00
25.00
0.00
22.00
18.00
6.23
-0.17
-179.38
0.00
NaN
NaN
NaN

25%
0.00
0.57
0.00
0.88
48.00
51.00
76.00
42.00
0.51
98.00
0.26
43.00
0.00
39.00
0.00
52.00
43.00
9.26
0.80
-95.95132.06
NaN
NaN
NaN

50%
59.00
21.03
0.38
2.32
311.00
54.00
81.00
48.00
0.54
106.00
0.27
44.00
0.02
43.00
47.50
358.00333.00
9.75
0.97
-8.94
197.37
NaN
NaN
NaN

75%
85.00
56.79
11.87
12.34
352.00
58.00
83.00
53.00
0.57
113.00
0.31
47.00
0.08
45.00
105.60426.00357.00
10.25
1.13
86.67
283.25
NaN
NaN
NaN

Max.
97.00
81.93
17.86
20.00
402.00
72.00
94.00
60.00
0.72
139.00
0.33
63.00
0.17
62.00
139.60463.00401.0013.26
1.92
179.24360.00NaN
NaN
NaN