**1. Introduction**

Cultural heritage preservation has been a persistent topic in most societies. Computer games can contribute by offering unhindered access to cultural content in a fun and vivid way [1]. Games promoting cultural heritage preservation rely on affective learning, namely the human ability to understand and internalize complex concepts through intense emotions and joyful activities, to successfully introduce its player base to cultural content. The latter may well include famed monuments, works of art such as paintings and films, and even anecdotal stories and myths. Each of these cultural items, material or not, cause positive or even negative sentimental reactions. It has has long been the objective of numerous private and public research initiatives to create such games [2]. The gaming industry has also been involved. One recent example is Assassin's Creed Origins which takes place in Egypt near the end of the Ptolemaic period (BC 49-44) and represents this era with great historical accuracy and making it accessible to a much greater audience.

There has been a trend towards the development of more complex, serious games, which are informed by both pedagogical and game-like, fun elements. Under this framework, the ANTIKLEIA project introduces the implementation of a specific gamified module application [3] applied on real-life

content mostly collected from the Europeana repository [4]. More specifically, the interactive platform of ANTIKLEIA employs a collection of cultural content files [5] in order to be further modified by individual users, as well as groups of users, through its software components, while making them directly available to the general public. Furthermore, metadata from existing files and related collections support a cultural gamified experience, allowing large collections to be restored and managed through coordinated individual or collective efforts. This kind of (semi-)automatic enrichment can be beneficial for activating recovery, even across many languages, and adding a conceptual framework to the resources that will be accessible through its platform.

In order to keep player interest unabated, cultural games often depend on eliciting affective responses from players on two distinct levels. Low-level activity relates to simple decisions such as using in-game items. In contrast, high-level activity relies heavily on the outcome of conscious strategic decisions ranging from behavior in in-game tournaments to how game connections to the real word are exploited. Since both attributes ultimately describe player behavior from different perspectives, it makes perfect sense to combine them in player profiles. Once such profiles are created, the game player base can be better understood under Bartle taxonomy or any other player classification for that matter. To achieve that, profiles have to be clustered, as ground truth regarding player types is typically unavailable. This is essentially the principal motivation behind this work.

The primary research objective of this article is twofold. First, a template Simon–Ando iterative scheme for clustering the player profiles of a cultural game based on the Bartle player taxonomy is developed. Second, the effect of including user annotations about in-game items or player activity to the above scheme is evaluated. As a secondary objective, practical recommendations for selecting game elements based on maximizing the affective potential are given. The above were implemented in Julia and differentiate this work from previous ones. Moreover, the core of the proposed methodology will be incorporated in the aforementioned ANTIKLEIA project framework.

The remainder of this work is structured as follows. The recent scientific literature is briefly reviewed in Section 2. In Section 3, the Bartle player taxonomy and the low- and high-level attributes are presented. The proposed tensor based methodology is the focus of Section 4. The experimental setup, the results, and their analysis are given in Section 5, while the recommendations coming from this analysis are discussed in Section 6. Section 7 concludes this article by recapitulating the main findings and delineating future research directions. Tensors are represented by capital calligraphic, matrices by boldface capital, and vectors by boldface small letters. Each technical abbreviation is defined the first time it is met in the text. Finally, the notation of this article is summarized in Table 1.


**Table 1.** Notation of this article.

#### **2. Previous Work**

Games have been proven to be excellent tools for recreation and learning [6,7]. Their design is based on properties such as immersion and engagement [8]. To this end, the elements of points, leaderboard, and badges (collectively known as PBL) take advantage of the player engagement loop [9,10]. Games designed for cultural heritage preservation are explored in [11,12]. The Bartle taxonomy is examined in [13]. The mechanisms behind leaderboard operation based on personality traits are explored in [14], whereas personality patterns can be discovered through gaming [11,15]. Affective learning can be applied to gaming [12,16] in conjunction with big data [17] and machine learning (ML) techniques [18,19]. Clustering can be applied to emotional and physiological states [20]. Finally, if properly processed, voice can be a major indicator of human emotional state [21].

Tensor algebra extends linear algebra beyond two dimensions as explained in [22]. Tensor operations such as Tucker decomposition [23], Kruskal factorization [24], and higher order singular value decomposition (HOSVD) [25] naturally discover the multilinear interplay between a number of factors in the same way the singular value decomposition (SVD) can reveal linear dependencies between two vector spaces [26]. Tensor stack networks (TSNs) rely on neural network stacking in order to perform classification tasks [27], evaluate graph resiliency [28] and discover higher-order graph structures [29], and learn large vocabularies [30,31]. TSNs have also been applied to image compression as shown in [32] and in discovering geo-linguistic communities in Twitter [33]. TensorFlow is an open source low level framework for tensor operations including tensor eigenvectors and higher order SVD (HOSVD) [34,35]. Finally, in [36], a toolkit with extensive TSN functionality is described.

#### **3. Players**

#### *3.1. Bartle Taxonomy*

Bartle taxonomy describes four fundamental player types according to their objectives and how they accomplish them, the interactions with other players, and their relationship with the in-game world [13]. The four fundamental player types according to the Bartle taxonomy and potential factors behind the interest of each such type in cultural games are the following:


The above qualitative taxonomy can be seen from another view. This is comprised of two axes, each with two points representing the two possible options in a fundamental decision, namely:


Figure 1 shows how each player category fits in this two dimensional (2D) space set forth by the above axes. This representation contains more semantic content in comparison to a single categorical scale. According to this systematic view, there exists the following two pairs of opposite categories:

• **Achievers and socializers**: Achievers are highly competitive players since they often race against both the clock and other achievers of comparable or even superior skills to fulfill a set of objectives. On the contrary, socializers are very cooperative and seek harmonic and mutually beneficial coexistence with other players usually in a more relaxed style.

*Big Data Cogn. Comput.* **2020**, *4*, 39

• **Killers and explorers**: Explorers aim at learning whatever is possible to be known about the game and even some more. In that sense, they are the least invasive player category as they tend to observe and not act upon the game world. On the other hand, killers do change the game world, especially if they act en masse, in numerous ways.

**Figure 1.** Bartle taxonomy in two dimensions (Source: Authors).

When designing game mechanics, the behavior of the player types and their expectations from the game should should be taken into consideration in order for their interest to remain unabated. Player categorization is not static. Instead, changes occur for one or more of the following reasons:


Detecting player categorization changes can be done with an LMS-like algorithm monitoring tensor gradient [37]. Such a scheme tracks separately each factor of the higher-order dynamics of the player profile. This is impossible for a matrix method, as it mixes these factors in a gradient vector.
