Exploratory Data Analysis for Airline Disruption Management ¹¹1This article represents one full chapter from the corresponding author’s completed doctoral dissertation.

While there have been consistent improvements to the existing decision support systems used by human controllers in the Airline Operations Control Center (AOCC), two factors have continued to limit the performance of the disruption resolutions that are applied. First, the decision support systems do not explicitly proffer solutions to specific schedule disruptions. As such, human controllers in the AOCC are required to be reactive in addressing disruptions by using their best judgement based upon their prior experience from resolving the same (or similar) disruption. Second, majority of the decision support (computer) systems used by multiple departments (including the AOCC) in an airline and other air transportation stakeholders (e.g. airports) are not designed or developed at the same time nor by the same vendor (Nathans, 2015). As such, information and data are required to be entered into multiple computer systems thereby exposing human controllers in the AOCC to data input problems and errors. Therefore, information entered into a decision support system for disruption management may be out of sync with other systems and yield incorrect decisions due to lack of data integrity.

Furthermore, extant literature on the adoption of machine learning for decision support systems have only focused on addressing irregular operations for system-wide disruption management in the national airspace system as a whole. In other words, existing literature address irregular operations for system-wide disruption management by exploiting airport data from multiple airlines in the air transportation system. For instance, Liu et al. (2019) used machine learning to analyze air traffic management actions for incidences of ground delay programs across major airports in the United States. The authors employed a two-stage framework, such that the first stage used support vector machines to correlate incidences of ground delay programs with regional convective (weather) activity while the second stage trained logistic regression and random forest models by using a weather score obtained from the first stage. In addition, Ye et al. (2020) presented an approach for estimating aggregate flight departure delay at airports in China through supervised learning models. They applied four separate types of airport-related aggregate characteristics (including weather) to predict expected departure delays at a major airport in China, by employing linear regression, support vector machines, randomized trees, and LightGBM. While the models presented in both research studies provided acceptable predictive capacity for disruption management at the airport level in the respective air transportation networks, they (i.e. the models) do not describe the disruption management proclivities of a decision support system commissioned by a specific airline in the air transportation network.

In the bid to improve data integrity and fidelity for existing decision support systems, airlines have significantly invested in creating better localized data collection platforms within their respective organizations, which can amass information from different sources within and outside the organization that is easily accessible through a centralized data server (Amadeus IT Group, 2016). As such, there is a need to fully leverage the ubiquity and accessibility of information (data) collected by existing platforms in the AOCC to enhance agile decision-making capabilities of the AOCC during airline disruption management. To that effect, this paper provides a comprehensive discussion on exploratory analysis administered on historical scheduling and operations recovery data supplied by a major airline in the United States. This exploratory analysis serves as the basis for the development of credible predictive and prescriptive models for airline disruption management.

To the best of our knowledge, we provide the first literature that strictly employs the statistics of big data and machine learning to demonstrate the characterization and evaluation of a functional role (i.e. domain) in the AOCC of a major U.S. airline for disruption management. Thus, in contrast and complement to existing literature, our work provides research on irregular operations and disruption management accustomed to a specific U.S. airline based upon data provided by the airline. To achieve the aforementioned objectives, this paper enhances prior research and literature on irregular operations and airline disruption management through the following contributions:

1. 1.

   We introduce and explore several abstraction methods for applying, enhancing, and sequestering raw features and labels in a historical data set on airline scheduling and operations recovery from a major U.S. airline, to readily identify relevant cognitive patterns for key drivers during airline disruption management.

2. 2.

   We investigate the application of appropriate machine learning techniques for revealing patterns, pertinence, and properties of abstracted data features, which provide necessary a priori information (i.e. beliefs) for Bayesian and pseudo-Bayesian methods. These methods are subsequently employed in future work for developing functional models in an intelligent multi-agent system for airline disruption management.

The next section in this paper provides an overview of the elements of historical scheduling and operations recovery data retrieved from a major U.S. airline, followed by a section that expansively discuses several relevant and interrelated processes for exploratory data analysis. We conclude with a summary of pertinent findings and areas for further research in Section 4.

Feature abstraction (often referred to as data abstraction) is an effective technique for accommodating semantic relationships between features in a database (Ramakrishnan & Ullman, 1995). Feature abstraction ensures that features that define specific properties of fundamental tenets of flight scheduling and operations (embedded in each flight schedule from the raw data set) is generalized into abstract values (Huh et al., 2000). As such, a specific property can be viewed as a specialized quality of an abstract value. The properties describing the tenets of flight scheduling and operations are described by two separate principles of abstraction that represent a knowledge abstraction (Abbott, 1987; Liskov, 1988; Huh et al., 2000). These related feature abstraction principles exist for creating semantic associations among data features for airline scheduling and disruption management and are namely: event abstraction and uncertainty abstraction.

• •

  Event abstraction: Event abstraction serves two primary purposes. First, it characterizes the importance of planned airline activities and resources associated with a specific flight schedule, and how their importance can be subject to change prior to (or on) day of operation due to the risk of disruption from passenger-boarding at a departure station to aircraft gate-parking at an arrival station. Second, event abstraction defines the manner in which planned airline activities for a specific flight schedule varies during schedule execution based upon the impact of irregular operations. As such, the event abstraction principle is synonymous to flight operation value abstraction, wherein the specific value (or profit) that a particular flight schedule in the airline route network provides is appraised by how effectively the flight schedule features estimated prior to schedule execution align with flight schedule features that are realized during and after schedule execution. To that effect, flight schedule features that are determined prior to schedule execution represent low-value features for event abstraction, and flight schedule features estimated during and after schedule execution represent high-value features for event abstraction.

• •

  Uncertainty abstraction: From an airline planning perspective, the uncertainty abstraction principle, also analogous to a functional domain planning abstraction, defines the manner in which the uncertainty for the risk of irregular operations during schedule planning and execution is quantified and propagated via various features in the data set. Most airlines, including Southwest Airlines, adopt a perspective on the scheduling process that accentuates the internal planning approach of different planning departments as an iterative cycle of flight schedule development and assessment over a timeline horizon, such that the flight schedule is continually adjusted and optimized until a suitable schedule is obtained or the planning period is over (Grosche, 2009a). Thus, the primary purpose of uncertainty abstraction is to express the relationships among flight schedule features that are representative of the transitions through three iterative and interconnected airline planning phases namely: strategic planning, tactical planning and operational planning respectively (Grosche, 2009b). Strategic planning, otherwise known as “future scheduling”, focuses on long-term decision-making for the subsequent tactical and operational planning phases, such that a generic service plan consisting of essential and viable sets of serviceable routes without specific aircraft and crew assignments and tentative departure and arrival times are determined. Tactical planning or “current scheduling” focuses on creating a refined schedule of operations for the service plan based upon the resources that are actually expected to be available to the airline over a definitive time period. Lastly, the operational planning phase focuses on adjusting the schedule generated in the tactical planning phase with respect to changes in demand for air travel prior to executing the flight schedule, and also on executing the schedule with minimal penalty (cost) in the event of unexpected disruptions on the day of operation (i.e. rescheduling for disruption management) (Mathaisel, 1997).

By applying the event and uncertainty abstraction principles, we identify three separate classes of features in the raw data that can be used to enable robust airline disruption management and are described as follows:

1. 1.

   Determinate aleatoric features: These represent flight schedule features that are determined during the strategic planning phase of airline planning and are required to remain unchanged during schedule execution on the day of operation. Examples of determinate aleatoric features include flight date, origin (departure) station, destination (arrival) station, route originator indicator, route distance, etc. With respect to disruption management, determinate aleatoric features represent flight schedule features whose alternatives do not differ considerably each time the AOCC invokes a disruption management initiative. Thus, from a statistical perspective, determinate aleatoric features are flight schedule features that are subject to the least possible uncertainty for the risk of reassessment (or alteration) during irregular operations for disruption management, based upon inherent randomness of disruption events. For instance, airport identifiers and exact longitude and latitude coordinates that provide specific information for origin and destination stations are always assumed to remain unchanged, by the AOCC, during the recovery of a delayed flight schedule. However, if a human specialist in the AOCC chooses to divert the same delayed flight to another airport during schedule execution, then the airport information for the destination station changes to that of the airport where the flight is to be diverted. It is important to note that this scenario is unlikely, based upon our research scope, because we consider irregular operations for delayed flight schedules only.

2. 2.

   Indeterminate aleatoric features: These are separate data features from flight schedule features that represent disruption types for different functional domains, which occur randomly during schedule execution on day of operation. Examples of indeterminate aleatoric features include delay codes for uncontrollable inclement weather and controllable maintenance inspections. From a disruption management perspective, indeterminate aleatoric features represent triggers for the need of the AOCC to address a specific disruption. As such, indeterminate aleatoric features are data features that can create the most uncertain responses in disruption management initiatives employed by the AOCC during schedule execution. From a statistical perspective, indeterminate aleatoric features are data features that are subject to the most possible uncertainty for the risk of occurrence (or instantiation) of irregular operations during schedule execution, due to inherent randomness of disruption events. For example, inclement weather at a particular airport may require a human specialist in the AOCC to delay the departure of a specific flight at the (origin) airport and reassign some or all of its passengers to another flight with a later departure, while also reallocating the arrival of the original delayed flight to a different gate at the destination airport.

3. 3.

   Epistemic features: These represent flight schedule features that are determined during the tactical and operational phases of airline planning and can be subject to change during schedule execution on day of operation. Examples of epistemic features include specific departure and arrival times during the day, aircraft type, delay periods, actual turnaround and block time periods. With regards to disruption management, epistemic features represent flight schedule features with considerable amount of alternatives for every time the AOCC initiates a disruption management plan. As such, from a statistical standpoint, epistemic features are flight schedule features that are subject to the most possible uncertainty for the risk of alteration during irregular operations for disruption management, due to lack of knowledge of the exact impact of their alteration. For instance, following a specific disruption like late arrival of flight crew for a scheduled flight, a human specialist in the AOCC may choose to delay the departure of the flight by a specific period of time after the original departure time. However, most times, the human specialist can not guarantee that the decision on applying a particular delay duration after scheduled departure will produce a specific recovery plan, due to the cascading effect of disruptions in large airline networks.

Fig. 2 shows a generic knowledge abstraction for airline disruption management based upon some specific flight schedule features. The horizontal axis in Fig. 2 represents event abstraction for defining the value of flight operations management based upon the perishable nature of a flight service during schedule execution, while the vertical axis represents uncertainty abstraction for defining the risk of disruption instances and schedule alteration during flight schedule planning.

While the abstraction of raw flight schedule data features provides an excellent avenue for effectively representing latent planning capabilities in airline operations control, the quality of the knowledge extracted from the raw data can be enhanced through transformation to enable discernible representation and interpretation for machine learning algorithms (Liu & Motoda, 1998; Kusiak, 2001). These algorithms provide efficient means for easily recognizing useful patterns and relationships amongst flight schedule features in a data set. To this end, feature transformation is the process of converting flight schedule and disruption features in raw historical airline scheduling and operations data into relevant mathematical properties (or functions) that can be readily understood by machine learning algorithms. Every direct flight schedule in the raw data set is defined by forty separate data features (or attributes) that describe different resources, behaviors, and performance indicators that are observable during airline scheduling and disruption management. As such, raw flight schedule features can be separated into four distinct categories namely: geographical features, temporal features, categorical features, and continuous features.

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  Geographical features: These are flight schedule features which represent resources, behaviors, or performance indicators that require or enable the perception and property of geographic location (or position) during airline disruption management. Examples of geographical features in the raw data set are International Air Transport Association (IATA) codes for departure and arrival airport stations, and the identifier for the origin of the first departure flight of the day.

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  Temporal features: These are flight schedule features that describe and enable the perception and property of time during airline scheduling and disruption management. Temporal features are conceptualized by four different types of time (Shurkhovetskyy et al., 2018) namely:

  1. 1.

     ordinal time: This represents time points that occur one after another on day of operation. Examples of flight schedule features defined by ordinal time are time-of-day events such as aircraft pushback time, takeoff time, landing time, and aircraft gate-parking time.

  2. 2.

     interval time: This represents time events that are measured on an interval scale with a specific duration (or length). Examples of flight schedule features characterized by interval time include the duration between aircraft pushback and aircraft gate-parking otherwise known as blocktime, the duration for boarding passengers and loading cargo unto an aircraft also known as turnaround, and the duration of any form of delay in airline operations during schedule execution.

  3. 3.

     cyclic time: This describes cyclic or repeatable processes wherein the application of an ordered relation is inane. Flight date is an example of a flight schedule feature characterized by cyclic time.

  4. 4.

     branching time: This represents time points that can occur in different branches or alternatives to describe several scenarios or processes. Thus, all temporal flight schedule features in the raw data set are defined by branching time.

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  Categorical features: These are flight schedule features that represent fields in the raw data defined by discrete values which belong to a finite set of categories or classes. Categorical features can be text or numeric, and are separated into two classes namely nominal and ordinal, based upon the perception of ordering.

  1. 1.

     nominal: Nominal categorical features represent flight schedule features for which there is no concept of ordering among different values of each feature. An example of a nominal categorical feature is A0, which is a binary number (i.e. 0 or 1) indicating whether or not a flight schedule arrives exactly on time.

  2. 2.

     ordinal: Ordinal categorical features represent flight schedule features for which there is a strict adherence to the concept of ordering among different values of each feature. An example of an ordinal categorical feature in flight schedule data is aircraft type, which effectively characterizes the relevance of size and seat capacity for aircraft performance.

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  Continuous features: These are flight schedule features that represent fields in the raw data, which have infinitely many alternatives between any two values. Examples of continuous features in raw flight schedule data include digital timestamps for different time-of-day events (such as takeoff time) during schedule execution.

Fig 3 reveals a two-layer data transformation process of raw flight schedule data features for airline disruption management. The first layer, known as feature engineering, enables the creation of additional data features from mathematical functions that characterize rudimentary properties of the airline operations control center. Next, these data features are combined with extant low-level data features in the raw data set and normalized by using fundamental statistical parameters in the second layer through a process called feature scaling.

1. (i)

   Feature engineering represents a first-degree transformation of raw flight schedule data that defines the augmentation of properties associated with daily routines of functional roles in the AOCC by using mathematical principles. Thus, flight schedule features representing geographic locations (i.e. geographical features) such as departure and arrival stations are first transformed into spherical directional vectors based upon the longitude and latitude coordinates of their corresponding airport stations, and subsequently transformed into the distance between the departure and arrival airports on an oblate spheroid Earth via the Vincenty geodesic equation (T. Vincenty, 1975). Ordinal temporal flight schedule features (such as departure and arrival times) are transformed into two separate periodic (i.e. sine and/or cosine) vectors of different amplitudes, based upon a 24-hr clock period and the percentage of 8-hr work shift completed (at the time of departure or arrival) by human specialists in the AOCC, respectively. The work shift characterization of time-of-day events, via a periodic vector, is intended to capture and represent daily disruption resolution proclivities of human specialists, which can be induced by how much time the specialists have to address a disruption before their work shift is complete. Cyclic temporal flight schedule features defined by Gregorian dates are transformed into four separate periodic vectors, whose periods are based upon the season of the year, month of the year, day of the week, and day of the year respectively.

   Lastly, most categorical flight schedule features defined by texts are transformed into binary numbers by one-hot encoding (Seger, 2018), wherein all $n$ feature values are represented as a $n$-dimensional sparse vector with zero entries except for one of the dimensions for which the entry is one. However, categorical flight schedule feature values for aircraft type, which are defined by aircraft model codes, are transformed into discrete numbers based upon the total number of available seats in the aircraft. A secondary objective of feature engineering is to provide a precursor for continuous feature representation by ensuring that all data features are in numeric form. As such, feature engineering may not be applicable to flight schedule features that are already in continuous form in a raw data set.

2. (ii)

   Feature Scaling represents a second-degree transformation of raw numeric data features that include additional features created from feature engineering, such that a uniform statistical grounding basis is used to transform values for all data fields (i.e. flight schedule features) in the raw data set into bounded continuous values that describe a differentiable function. We explore three different approaches for enabling feature normalization (Pedregosa et al., 2011) namely: Standard scaling, Range scaling, and Power scaling.

   1. (a)

      Standard scaling: Standard scaling or standardization normalizes values for each flight schedule feature in the data set by removing the mean of the values and scaling to a unit variance, thus resulting in a standard score for each value. The standard score, $z_{i}$, of an arbitrary sample (i.e data feature value), $x_{i}$, in the data set is calculated as follows:

      $\displaystyle z_{i}=\frac{(x_{i}-u)}{s}$

      (1)

      where $u$ and $s$ represent the mean and standard deviation, respectively, of all values for each flight schedule feature in the data set. As such, standardization provides a platform to ensure that each flight schedule feature in the data set follows a Gaussian distribution with zero mean and a variance of one.

   2. (b)

      Range scaling: Range scaling, otherwise known as min-max normalization, transforms each flight schedule feature in the data set by scaling the values of each feature by the difference between the maximum value and the minimum value (i.e. range). This results in adjusted values of a range (or distance) between zero and one for each flight schedule feature. The adjusted (range-scaled) value, $y_{i}$, of a characteristic flight schedule feature in the data set is calculated as follows:

      $\displaystyle y_{i}=\frac{x_{i}-\min(X)}{\max{(X)}-\min{(X)}}$

      (2)

      where $x_{i}$ and $X$ represent an original value and set of all original values, respectively, for a flight schedule feature.

   3. (c)

      Power scaling: Power scaling involves adapting a family of parametric and monotonic transformations to convert flight schedule data values from any distribution to the closest possible representation of Gaussian distribution, so as to reduce variance and skewness in data. An appropriate power transformation of flight schedule and disruption features is the Yeo-Johnson transform (Weisberg, 2001), because it can be applied to all forms of numeric data just like standard and range scaling transforms. The Yeo-Johnson transform is given by:

      $\displaystyle x_{i}^{(\lambda)}=\begin{cases}[(x_{i}+1)^{\lambda}-1]/\lambda&\quad\text{if}\quad\lambda\neq 0,x_{i}\geq 0,\\ \ln{(x_{i}+1)}&\quad\text{ if}\quad\lambda=0,x_{i}\geq 0,\\ -[(-x_{i}+1)^{2-\lambda}-1]/(2-\lambda)&\quad\text{ if}\quad\lambda\neq 2,x_{i}<0,\\ -\ln{(-x_{i}+1)}&\quad\text{ if}\quad\lambda=2,x_{i}<0\\ \end{cases}$

      (3)

      where $x_{i}$ and $\lambda$ represent an original data value and an arbitrary parameter that is determined through maximum likelihood estimation (Glas, 2017), respectively.

Completion of the feature transformation process shown in Fig. 3 results in a refined, continuous data set that can be readily comprehensible by suitable machine learning estimators.

The efficacy of constructing and applying relevant machine learning algorithms for identifying and acknowledging high-level properties from data features (such as flight schedule and disruption data features) is dependent on the form in which the data values are presented. To this end, feature transformation has a strong propensity to increase the number of elements in the flight schedule and disruption feature space that constitutes the problem dimensions for airline disruption management. As such, the intrinsic dimensionality of the refined data appropriated for airline disruption management is defined by the least number of flight schedule and disruption features required to delineate observed behavioral properties from AOCC routines. Hence, dimensionality reduction is the process of mitigating the curse of dimensionality (Verleysen & François, 2005) and other unwanted properties of high-dimensional feature space through classification, visualization, and compression of high dimensional data obtained as a result of feature transformation (Van Der Maaten & Hinton, 2008). In essence, dimensionality reduction aims to provide a rudimentary means to attain and observe the latent feature space of a refined data set for airline disruption management.

From a mathematical perspective, we assume that the refined flight schedule and disruption data set is represented in a $n\times m$ matrix X, which consists of $n$ feature vectors $\textbf{x}_{i}(i\in\{1,2,...,n\})$ with dimensionality $m$. Furthermore, we assume that the refined data set has an intrinsic dimensionality $d$, such that $d<m$ and often $d||m$. The intrinsic dimensionality property refers to points in the refined data set X, which lie near a manifold with dimensionality $d$ that is embedded in the $m$-dimensional feature space. To that effect, dimensionality reduction techniques transmute the refined flight schedule and disruption data set X with dimensionality $m$ into a new data set Y with dimensionality $d$, while maintaining the geometry of the refined data set X as much as possible. Typically, the intrinsic dimensionality $d$ and the geometry of the manifold of the new data set Y are unknown, and as such, most dimensionality reduction techniques require that certain assumptions about the properties (like intrinsic dimensionality) of the refined data set be made a priori. For the remainder of this section, we denote a high dimensional data instance for flight schedule and disruption (i.e. datapoint) by $\textbf{x}_{i}$, such that $\textbf{x}_{i}$ is the $i^{th}$ row of the refined $m$-dimensional data set X. In complement, the low-dimensional equivalent of $\textbf{x}_{i}$ is expressed by $\textbf{y}_{i}$, where $\textbf{y}_{i}$ is the $i^{th}$ row of the new $d$-dimensional matrix Y.

To demonstrate the usefulness of dimensionality reduction on refined flight schedule and operations data, we investigate two separate techniques that employ linear and nonlinear principles nicknamed PCA and t-SNE, respectively, by utilizing delayed flight schedule and disruption instances for the Weather functional domain in SWA-NOC between September 2016 and September 2017. It is important to note that the flight schedule data for the Weather functional domain constitutes a subset (with 12,659 delayed flight schedule instances) of the full refined data set. For validation, we adopt min-max normalization for scaling all feature values in the refined data set because both dimensionality reduction techniques strongly depend on Euclidean distances between refined high-dimensional datapoints $\textbf{x}_{i}$ and $\textbf{x}_{j}$ to obtain and simplify the gradient of their respective cost functions (Van Der Maaten & Hinton, 2008; Van Der Maaten et al., 2009).

Although dimensionality reduction techniques provide an effective means to readily (i.e. visually) discern high-level patterns and properties associated with a data set, they are ineffectual in revealing detailed information on the specific importance of flight schedule and disruption features in a data set and their corresponding relationships (Koller & Sahami, 1996). To this end, feature selection presents simple fundamental methods for efficiently selecting and investigating pertinent associations among data features in a refined data set, which can provide insightful knowledge (or a priori information) for developing useful data-driven models for robust airline disruption management. In essence, feature selection methods aim to proactively enhance model prediction performances by increasing generalization (i.e. minimize data overfitting) and decreasing model runtimes (Moran & Gordon, 2019). There are three major categories of feature selection methods namely: wrapper, filter, and embedded methods.

Wrapper methods involve algorithms that search the feature space for plausible subsets of features by assessing each subset after running a specific model. Typically, the model is validated on a test data set to estimate the model’s error rate, before a score is registered for each feature subset and the feature subset with the best score is ultimately selected. Unlike computationally intensive wrapper methods, filter methods do not consider a model when searching the feature space for relevant subsets of the feature space, and rely on general statistical measures such as Pearson correlation coefficient (Benesty et al., 2009) and mutual information (Jiang et al., 2010). In this manner, filter methods are somewhat analogous to dimensionality reduction techniques, such that they are not customized to a particular type of predictive model and consume significantly less computational resources than wrapper methods. Embedded methods involve feature selection methods that are entrenched in a specific learning algorithm that performs classification (or regression) and feature selection concurrently. As such, embedded methods deliver the advantages of both wrapper and filter methods with medium computational expense.

To demonstrate the relevance of feature selection on refined flight scheduling and operations data, we apply two specific types of feature selection that belong to the filter and embedded categories, respectively, to identify flight schedule features that are pertinent for disruption management during turnaround. Turnaround is an airline process (or time period) primarily representative of loading, unloading and occasional servicing of aircraft, and is crucial for minimizing overall flight schedule delays. In addition to reducing overall flight delay, most airlines typically aim to expedite the turnaround process as much as possible in order to avoid causing discomfort to passengers, stemming from long waits in the aircraft on the ground, thus invariably minimizing loss of passenger goodwill.

In that regard, the filter method that we apply is defined by mutual information and the embedded method is defined by a Gaussian process, such that actual turnaround duration is set as the target flight schedule feature. We do not consider wrapper methods in our discussion because of the significant computational expense required as compared to filter and embedded methods. Similar to the dimensionality reduction analysis discussed in Section 3.3, we utilize delayed flight schedule and disruption instances for the Weather functional domain in SWA-NOC between September 2016 and September 2017 for our analysis. For validation, we adopt standardization for the second-degree transformation (i.e. scaling) of all feature (i.e label and target) values in the refined data set, because the algorithms for both filter and embedded methods perform best with a zero-mean Gaussian distribution as prior instantiation for each feature space in the refined data set (C. E. Rasmussen & Williams, 2006; Jiang et al., 2010; Ross, 2014).