A Two-Parameter Fractional Tsallis Decision Tree

Decision trees are decision support data mining tools that create, as the name suggests, a tree-like model. The classical C4.5 decision tree, based on the Shannon entropy, is a simple algorithm to calculate the gain ratio and then split the attributes based on this entropy measure. Tsallis and Renyi entropies (instead of Shannon) can be employed to generate a decision tree with better results. In practice, the entropic index parameter of these entropies is tuned to outperform the classical decision trees. However, this process is carried out by testing a range of values for a given database, which is time-consuming and unfeasible for massive data. This paper introduces a decision tree based on a two-parameter fractional Tsallis entropy. We propose a constructionist approach to the representation of databases as complex networks that enable us an efficient computation of the parameters of this entropy using the box-covering algorithm and renormalization of the complex network. The experimental results support the conclusion that the two-parameter fractional Tsallis entropy is a more sensitive measure than parametric Renyi, Tsallis, and Gini index precedents for a decision tree classifier.

Introduction
Entropy is a measure of the unpredictability of the state in physical systems that would be needed to specify the degree of disorder in full micro-structure of them. Claude Elwood Shannon [1] defined a measure of entropy to measure the amount of information in a digital system in the context of theory communication that has been applied in a variety of fields such as information theory, complex networks, and data mining techniques.
The most widely used form of the Shannon entropy is given by where N is the number of possibilities p i and ∑ n k=1 p k = 1. Two celebrated generalizations of Shannon entropy are Renyi [2] and Tsallis entropies [3]. Alfred Renyi proposed a universal formula to define a family of entropy measures given by the expression [2] where q denotes the order of moments. Constantino Tsallis proposed the q-logarithm defined by to introduce a physical entropy given by [3] Tsallis entropy could be rewritten [4][5][6] as where D t q of a function f given by D t q f (t) = f (qt) − f (t) (q − 1)t , t = 0, stands for the Jackson [7] q-derivative, to reflect that it is an extension of Shannon entropy. Renyi and Tsallis entropy measures depend on the parameter q, which describes their deviations from the standard Shannon entropy. Both entropies converge to Shannon entropy in the limit q → 1. For complex network applications [8] and data mining techniques [9][10][11][12][13][14][15][16][17], the parameter q varies into a range of values. On the other hand, the computation of the entropic index q of the Tsallis entropy was implemented for physics applications in [18][19][20][21][22][23][24][25].
Shannon and Tsallis entropies can be obtained by the action of standard derivative or q-derivative, respectively, to the same generating function ∑ N i=1 p −t i with respect to variable t and then letting t → −1. This approach can be used to reveal different entropy measures based on the actions of appropriate fractional order differentiation operators [26][27][28][29][30][31][32].
The major goal of this work is to introduce a new decision tree based on a twoparameter fractional Tsallis entropy. This new kind of tree is tested on twelve databases for a classification task. The structure of the paper is as follows. Section 2 focuses attention on the notion of two-parameter fractional Tsallis entropy. In Section 3, two-parameter fractional Tsallis decision trees and a constructionist approach to the representation of the databases as a complex network are introduced. The basic facts on the box-covering algorithm of a complex network are reviewed. Finally, we compute an approximation set of parameters q, β, and α of the two-parameter fractional Tsallis entropy. Section 4 is concerned with the testing of two-parameter fractional Tsallis decision trees on twelve databases. Next, the approximations of q values are tested on Renyi and Tsallis entropies. Discussion of the findings of this study and concluding remarks are offered in Section 5.

Parametric Decision Trees
A decision tree is a supervised data mining technique that creates a tree-like structure, where the non-leaf node tests a given attribute [45]. The outcome gives us the path to reach a leaf node, where the classification label is found. For example, let (x = 3, y = 1) be a tuple to be classified by the decision tree of Figure 1. If we test x = 1, we must follow the left path to reach y = 1 and finally arrive at the leaf node with the classification label "a".
In general, the cornerstone of the construction process of decision trees is the evaluation of all attributes to find the best node and the best split condition on this node to classify the tuple with the lower error rate. This evaluation is carried out by information gain on each attribute a [45]: where I(D) is the entropy of the database after being partitioned by the condition c of a given attribute a and I c (D) is the entropy induced by c. The tree's construction needs to evaluate several partition conditions c on all attributes of the database, then chooses the pair of attribute-condition with the highest value. Once a pair is chosen, the process evaluates the partitioned database recursively using a different attribute-condition. The reader is referred to [45] for details on decision tree construction and computation of (14).

Two-Parameter Fractional Tsallis Decision Tree
Following a similar fashion, a two-parameter fractional decision tree can be induced by the information gain obtained by rewritten (14) using (13): An alternative informativeness measure for constructing decision trees is the Gini index, or Gini coefficient, which is calculated by The Gini index can be deduced from Tsallis entropy (4) using q = 2 [14]. On the other hand, the two-parameter fractional Tsallis entropy with q = 2, α = 1, β = 1 reduces to the Gini index. Hence, Gini decision trees are a particular case of both Tsallis and two-parameter fractional Tsallis trees.
The main issue with Renyi and Tsallis decision trees is the estimation of q-value to obtain a better classification than the one produced by the classical decision trees. Trial and error is the accepted approach for this purpose. It consists of testing several values in a given interval, usually [−10, 10], and comparing the classification rates. This approach becomes unfeasible in two-parameter fractional Tsallis decision trees as it is needed to tune q, α, and β. A representation of a database as a complex network is introduced to face this issue. This representation lets us compute α and β following the approach in [22], which is the basis for determining the fractional decision tree parameters.

Network's Construction
A network is a powerful tool to model the relationships among entities or parts of a system. When those relationships are complex, i.e., properties that cannot be found by examining single components, something emerges that is called a complex network. Thus, networks as a skeleton of complex systems [46] have attracted considerable attention in different areas of science [47][48][49][50][51]. Following this approach, a representation of the relationships among attributes (system entities) of a database (system) as a network is obtained.
The attribute's name will be concatenated before the value of a given row to distinguish the same value that might appear on different attributes. Consider the first record of the database shown on the top of Figure 2. The first node will be N AME.BruceDickinson, the second node will be PHONE.54 − 76 − 90, and the third node will be ZIP.08510. These nodes belong to the same record, so they must be connected; see dotted lines of the network in the middle of Figure 2. We next consider the second record; the nodes Name.MichaelKiske and PHONE.87 − 34 − 67 will be added to the network. Note that the node ZIP.08510 was added in the previous step. We may now add the links between these three nodes. This procedure is repeated for each record in the database. The outcome is a complex network that exhibits non-simple topological features [52], which cannot be predicted by analyzing single nodes as occurs in random graphs or lattices [53].

Computation of Two-Parameter Fractional Tsallis Decision Tree Parameters
By the technique introduced in [22], the parameters α and β-on the network representation of the database-of the two-parameter fractional Tsallis decision tree are defined to be where |G i | is the number of nodes in the box G i obtained by the box-covering algorithm [54], n is the number of nodes of the network, and innerdeg(G i ) is the average degree of the nodes of the G i box. Similarly, two values of β are computed as follows [22]: where l > 2 is the diameter of the box G i , ∆ is the diameter of the network, and outerdeg(G i ) is the number of links among the boxes G i . The computation of innerdeg and outerdeg will be explained later. Inspired by the right-hand term of (19) and (20) (named α ) with the fact that is a normalized measure of the number of boxes to cover the network [20], an approximation of the q-value for the two-parameter fractional decision tree is introduced: Similarly, from the right hand of (21) and (22) (named β ), a second approximation of the q-value is given by where N b (l) is the minimum number of boxes of diameter l to cover the network, n, ∆, The process to compute the minimum number of boxes N b of diameter l to cover the network G is shown in Figure 3. A dual network (G ) is created only with the nodes of the original network, Figure 3b. Then, the links in G are added following the rule: two nodes i, j, in the dual network, are connected if the distance between l ij is greater than or equal to l. In our example, l = 3, and node one is selected to start. Node one will be connected in G with nodes five and six since their distance is four and three. The procedure is repeated with the remaining nodes to obtain the dual network shown in Figure 3b. Next, the nodes will be colored as follows: two directly connected nodes in G must not have the same color. Finally, the nodes colored in G are mapped to G; see Figure 3c. The minimum number of boxes to cover the network given l equals the number of colors in G. In addition, the nodes in the same color belong to the same box. In practice, l = [1, ∆]; thus, N b (l) of the example are shown in Table 1. For details of the box-covering algorithm, the reader is referred to [54].  Now, we are ready to compute innerdeg. Two boxes were found following the previous example for for l = 3; see Figure 4a. The innerdeg(G 1 ) = 2 is the average link per node between the nodes of this box; for this reason, the link between nodes four and six is omitted in this computation. Similarly, innerdeg(G 2 ) = 1. The outerdeg is the degree of each node of the renormalized network; see the network of Figure 4b.
In our example, outerdeg(G 1 ) = outerdeg(G 2 ) = 1. The renormalization converts each box into a super node, preserving the connections between boxes. On the other hand, it is known that N b (1) = n, and N b (∆ + 1) = 1; in the first case, each box contains a node, and in the second one, there is one box to cover the network that contains all nodes. For this reason, the innerdeg and outerdeg are not defined for l = 1 and l = ∆ + 1, respectively. This force to l = [2, ∆] as was stated in (19)- (24). Additionally, note that the right hand of (19) and (20) (α ), (21) and (22) (β ) are "pseudo matrices", where each row has N b (l) values; see Table 1. Consequently, q α and q β are also "pseudo matrices". The network represents the relationships between attribute-value (nodes) of each record and the relationships between different database records. For example, the dotted lines in Figure 2 show the relationships between the first record's attribute value. Links of the node ZIP.08510 are the relationships between the three records, and the links of PHONE.54-76-90 are the relationships between the first and third one. The box-covering algorithm groups these relationships into boxes (network records). The network in the middle of Figure 2 shows that the three boxes (in orange, green, and blue) coincide with the number of records in the database. However, the attribute value of each box does not coincide entirely with records in the database since box-covering finds the minimum number of boxes with the maximum number of attributes where the boxes are mutually exclusive.
The nodes in each box (network record) are enough to differentiate the records in the database. For example, the first network record consists of name, phone, and zip values (nodes in orange). The second record in the database can be differentiated from the first by its name and phone (values of those attributes are the second network record in green). The third one can be distinguished from the two others by its name (the third network record in blue). The cost of differentiating the first network record (measured by innerdeg) is the highest; meanwhile, the lowest is for the third. Thus, α measures the local differentiation cost for the network records.
On the other hand, β measures the global differentiation cost (by outerdeg). For example, the global cost for the first network record is two, and one for the second and third; see the renormalized network (at the bottom of Figure 2). It means that the first network record needs to be differentiated from two network records, and the second and third only need to be distinguished from the first. Note that α , β for a given l relies on the topology network that captures the relationships of the records and their values. Finally, q α is the ratio between network records (normalized number of boxes δ) and the local differentiation cost; meanwhile, q β is the ratio between network records and the global differentiation cost.
The network can be obtained from a raw database or after being discretized. Since the classification-measured by the area under receiver operating characteristic curve (AU-ROC) and Matthews correlation coefficient (MCC)-was better using the approximations computed on the networks from discretized databases, these approximations are only reported. The attribute discretization of a database can be found in [56]. The discretization technique is unsupervised and uses equal-frequency binning. The discretized databases were only used to obtain the networks so that the classification task was carried out using the original databases. The networks obtained from the discretized and non-discretized databases turned out to be different; see Figure 5.  The classification task was performed by classical, Renyi, Tsallis, Gini, and the twoparameter fractional Tsallis decisions trees on each database. We used a 10-fold crossvalidation repeated ten times to calculate the AUROC and MCC. The best value of the AUROC and MCC, produced by one of the four sets of parameters-used to approximate q, α, and β-of fractional Tsallis decisions trees, was chosen and compared with the classical and Gini decision trees. In the same way, q α or q β was chosen for the q parameter of Renyi and Tsallis trees. Then, their AUROCs and MCCs were compared with those of the classical trees. It is known that decision trees could produce non-normal distributed AUROC and MCC measures [57]. Hence, the normality was verified by the Kolmogorov-Smirnov test. These measures were compared using a T or a U Mann-Whitney test, according to their normality [10,[57][58][59].

Applications
The approximations of q, α, and β parameters computed on discretized databases are shown in Table 3. Table 4 shows the AUROC and MCC of classical and two-parameter fractional Tsallis decisions trees and the result of the statistical compassion. In addition, the values of the parameters of fractional Tsallis decisions trees are reported.
The two-parameter fractional Tsallis decision tree outperforms the AUROC and MCC of the classical trees for eight databases. The statistical result of both measures disagrees with Car and Haberman. The AUROC of the two-parameter fractional Tsallis tree was equal to the classical trees for Car, Image, Vehicle, and Yeast; meanwhile, for Haberman, Image, Vehicle, and Yeast, the MCC of both trees showed no difference. Table 3. The parameters of the fractional Tsallis decision tree were obtained using the networks from discretized databases. Tsallis entropy is a non-extensive measure [60] as well as a two-parameter fractional Tsallis entropy [22]. On the contrary, Shannon entropy is extensive. The super-extensive property is given by q < 1, and sub-extensive property by q > 1. Note that the approximations of the q parameter for all the databases, see Table 3, are < 1 except for Yeast. Thus, they can be considered candidates for being named super-extensive databases. We say that a database is super-extensive if q < 1 and its value produces a better classification (AUROC, MCC, or another measure) than the classical trees (based on Shannon entropy). Similarly, a database is sub-extensive if q > 1 and its value produces a better classification. Otherwise, the database is extensive since, in this case, the Shannon entropy (the cornerstone of classical trees) is a less complex measure than the two-parameter fractional Tsallis entropy; hence Shannon entropy must be preferred. The two-parameter fractional Tsallis trees produce classifications equal to or better than the classical trees. Following those conditions, based on MCC, Breast Cancer, Car, Cmc, Glass, Hayes, Letter, Scale, and Wine are super-extensive. Meanwhile, Haberman, Image, Vehicle, and Yeast can be classified as extensive.
The AUROC and MCC of Renyi and Tsallis decision trees are compared with the baseline of the classical ones. The q α and q β were tested as the entropic index of both parametric decision trees. The parameters of Renyi (q r ) and Tsallis (q t ) that produce the better AUROCs and MCCs are reported in Table 5. The result shows that the AUROC of Renyi trees was better for Breast Cancer, Glass, Letter, and Yeast and worse for Cmc and Haberman than classical trees. The results are quite similar for MCC, where Car's classification outperforms the classical tree classification. On the contrary, the MCC of the Vehicle database was statistically less than that of the classical tree. The Tsallis AUROCs were better for Cmc, Glass, Haberman, Hayes, and Wine and worse for Yeast than those of classical trees. Additionally, the MCCs of Car, Cmc, Glass, and Scale were higher, and lower for Yeast, than the classical trees' MCCs. Based on MCC, Car, Cmc, Glass, and Scale are super-extensive, which is a subset of the classification obtained by two-parameter fractional Tsallis.  Finally, the Gini and the two-parameter fractional Tsallis decisions trees are compared using AUROC and MCC. The results are shown in Table 6. These results indicate that twoparameter fractional Tsallis trees outperform AUROC of Gini trees in six databases, and MCC in ten. It underpins that Gini trees are a particular case of two-parameter fractional Tsallis trees with q = 2. In summarizing, two-parameter fractional Tsallis trees have better classifications than classical and Gini trees. Table 6. AUROC and MCC of Gini decision trees (GT) and two-parameter fractional Tsallis decision trees (TFTT). + means that AUROC is statistically greater than AUROC or MCC of GT.

Conclusions
This paper introduces two-parameter fractional Tsallis decision trees underpinned by fractional-order entropies. The three parameters of this new decision tree need to be tuned to produce better classifications than the classical ones. The trial and error approach is the standard method to adjust the entropic index for Renyi and Tsallis decision trees. However, it is unfeasible for two-parameter fractional Tsallis trees. From a database representation as a complex network, it was possible to determine a set of values for parameters q, α, and β based on this network. The experimental results on twelve databases show that the proposed values yield better classifications (AUROC, MCC) for eight of them, and for the four remaining, the classification was equal to that produced by classical trees.
Moreover, two values (q al pha , q beta ) were tested in Renyi and Tsallis decision trees. The results show that Renyi outperforms the classical trees in four (AUROC) and five (MCC) out of twelve databases. Similarly, Tsallis decision trees produced better classification for five (AUROC) and four (MCC) databases. The classification was worse in almost three and one databases for Renyi and Tsallis, respectively. The overall results of both parametric decision trees suggest that both outperform the classical trees in seven databases. All of the above is less favorable than what happened in eight databases analyzed with the two-parameter fractional Tsallis decision trees. In addition, the databases with a better classification using Tsallis decision trees are a subset of those for which two-parameter fractional Tsallis trees produced a better classification. It supports the conjecture that two-parameter fractional Tsallis entropy is a finer measure than the parametric entropies such as Renyi and Tsallis.
The approximate technique for the tree parameters introduced here is a valuable alternative for practitioners. Furthermore, the network classification based on the nonextensive properties of Tsallis and two-parameter fractional Tsallis entropies reveals that the relationships between the records and their attribute values (modeled by a network) are complex. Such complex relationships are better measured by two-parameter fractional Tsallis entropy, the cornerstone of the proposed decision tree.
The results pave the way for using the two-parameter Tsallis fractional entropy in other data mining techniques such as K-means, generic MST, Kruskal MST, and algorithms for dimension reduction in the future. Our research has the limitation that the databases used in the experiments are not large enough to reveal the reduction in time compared with the trial-and-error approach to set the tree parameters. However, we may conjecture that our method works in large databases, which will be the scope of future research.


“I Can’t Keep It Up Anymore.” A Dataset from the Defunct Voat.co News Aggregator

Voat was a news aggregator website that shut down on December 25, 2020. The site had a troubled history and was known for hosting various banned subreddits. This paper presents a dataset with over 2 . 3 M submissions and 16 . 2 M comments posted from 113 K users in 7 . 1 K subverses (the equivalent of subreddit for Voat). Our dataset covers the whole lifetime of Voat, from its developing period starting on November 8, 2013, the day it was founded, April 2014, up until the day it shut down (December 25, 2020). This work presents the largest and most complete publicly available Voat dataset, to the best of our knowledge. We also present a preliminary analysis to cover posting activity and daily user and subverse registration on the platform so that researchers interested in our dataset can know what to ex-pect. Our data may prove helpful to false news dissemina-tion studies as we analyze the links users share on the platform, ﬁnding that many communities rely on alternative news press, like Breitbart and GatewayPundit, for their daily discussions. Last, we perform network analysis on user interactions ﬁnding that many users prefer not to interact with subverses outside their narrative interests, which could be helpful to researchers focusing on polarization and echo chambers. Also, since Voat was one of the platforms many Reddit users migrated to after a ban, we are conﬁdent that our dataset will motivate and assist researchers studying deplatforming. In addition, many hateful and conspiratorial communities seem to be very popular on Voat, which makes our work valuable for researchers focusing on toxicity, conspiracy theories, cross-platform studies of social networks, and natural language processing.

Introduction
Social networks are a primary tool in today's society. They offer countless opportunities for people around the world to connect in various ways, find jobs, entertain themselves, catch up on world happenings, etc. At the same time, social networks sometimes offer a "safe-house" for people that want, among other things, to connect to like-minded individuals towards sharing hate and toxicity [4,8], discussing controversial matters [27], and spreading misinformation and disinfor-mation [16].
Mainstream social networks suffer from users and communities that organize these conversations on their platforms. A common "solution" the administrators result to is to ban these users -deplatforming. The social network that is known to have taken this action many times so far is Reddit, which banned more than 7K subreddits [41] from its platform -the first one being in 2014 [1]. Research on deplatforming shows that users that had their communities banned met on other platforms and forums and even got more toxic than what they used to be [19]. Other than forums, users move to social networks that allow controversial discussions. One of the platforms that many banned Reddit communities decided to migrate to was Voat.
Voat was a Reddit-esque social network founded in April 2014 and shut down in December 2020 [37]. Similar to Reddit, discussions on Voat are divided into various channelssubverses -the equivalent of a subreddit. Users can subscribe to as many subverses they wish but cannot moderate more than ten to prevent users gaining undue influence on the platform. Registration of new users on Voat requires only a unique username and a password. Newcomers can upvote, downvote, and comment on existing submissions but cannot create new submissions under subverses until they achieve a certain amount of upvotes on all of their comments.
Since its foundation, Voat gradually gained popularity over the years, especially after every Reddit cleansing [34,22,18,36]. Overall, Voat is known for hosting banned extreme communities and users, providing a safe space for likeminded individuals to share their ideas "freely." Voat has attracted the interest of researchers before as it hosted communities like /v/fatpeoplehate, /v/CoonTown, and /v/Nigger [9], /v/TheRedPill [38], /v/GreatAwakening [25], etc. Data Release. In this work, we present, to the best of our knowledge, the largest and most complete dataset of Voat. Along with this paper, we release a dataset [43] that consists of over 18.6M posts from 113K users in 7K subverses over the lifetime of Voat (November 2013 -December 2020). Specifically, our dataset is four fold: -Title, body, and metadata of submissions; -content and metadata of comments; -user profile data; and -subverse profile data.
Relevance. Our dataset provides several opportunities to the research community. First, Voat was evidently the place many banned users and communities moved to after being banned on other platforms [26,9]. To this end, our dataset can assist researchers that focus on deplatforming and user migration. Also, our dataset may aid researchers deepen our understanding of how and when these communities choose their new "home" after being removed from their previous one. Second, our dataset covers numerous offline events like the 2016 and 2020 US Presidential Election and debate, Brexit, Epstein's arrest, and various terrorist attacks and unrest around the world that can prove helpful in further analysis of these events. Third, since Voat was a supporter of freedom of expression and online free speech for extreme and hateful communities, it contains a variety of slang language and toxic content that can be useful towards understanding hateful communities.
Paper organization. The rest of the paper is organized as follows. First, we briefly explain what Voat is and how it works in Section 2 before going through its history in Section 3. Then, we describe the process of parsing the Internet Archive Wayback Machine (IAWM) published data, along with the complimentary collection of additional user and subverse data in Section 4. We then describe the structure of our dataset in Section 5 and provide a statistical analysis of the dataset (Section 6), followed by reviewing related work (Section 7). The paper concludes with Section 8.

What was Voat?
Voat was a Reddit-esque news aggregator launched in April 2014. It was originally named "WhoaVerse" and renamed as "Voat" in December 2014. The mascot of Voat resembles an angry goat, which was designed and freely offered to the website by a user of the site.
Subverses. Discussions on Voat occur in specific groups of interests under the name of "subverses." Users could register new subverses on-demand before June 2020, when the administrators disabled this functionality. When a user registers a subverse, they become its owner. The owner of a subverse has complete authority over the subverse: they can deactivate the subverse and appoint other co-owners and moderators. The moderators can delete submissions and comments posted by users and even ban users from posting on the subverse. The owners and moderators can also allow users to post anonymously in their subverse, which replaces the poster username with a random multi-digit number. To prevent users from gaining extreme influence on the platform, Voat limits the number of subverses one can own or moderate [25].
Users. Voat was proclaiming itself as a free-speech platform that offered its users anonymity. When newcomers register a new account, Voat does not require any personal details to verify the account, like an email address or phone number. A user can insert a username and a password to register, but if they forget their password, there is no way to recover the account.
After registering a new account, users can subscribe to subverses of interest, comment, upvote, and downvote the comments and submissions but cannot post new submissions. To post a new submission, they first need to acquire ten Comment Contribution Points (CCP). When newcomers post comments on existing submissions, they can try and collect a net score of ten upvotes on all of their comments (one downvote cancels one upvote). The privilege of posting submissions is not guaranteed as users may lose it if their CCP falls below ten. Although this functionality may discourage users from being toxic to each other, it might also prevent users from expressing their honest opinions as others may disagree and downvote them. Voat users often refer to themselves as "goats" due to the platform's mascot. Submissions and voting system. Voat was a news aggregator platform, and hence users create a new submission by posting a title and a description accompanied by a link to a news source, although it is also possible to post without a link. If the poster provides a link, the submission's title becomes a hyperlink to the source website. The domain of the source website appears next to the submission's title, along with the poster's username and the date and time the submission was posted.
Similar to Reddit, Voat offers a hierarchical, tree-like commenting system: other users can comment on the submission and the comments of other users. As mentioned before, users can upvote or downvote the submission or other users' comments. In contrast with Reddit, Voat displays the total number of upvotes and downvotes a submission or a comment received. Also, the downvote functionality on Voat is not the same as Reddit's. Downvoted submissions and comments on Voat alert the moderators of spammy or illegal content so they can take action. This functionality enforces the establishment of echo chambers as users usually downvote content that does not align with their beliefs and usually results in the user that posted the downvoted post either losing their submission posting privilege or even being banned from the subverse.
Content visibility. Voat attempted to provide its users with some ephemerality without deleting its content, but hiding it instead. Voat subverses filter submissions under three tabs, namely, hot, new, and top. Each subverse has 500 active submissions in 20 pages (0 to 19). Hot submissions are the ones that are currently active and discussed, new submissions are the ones that were posted most recently, and top submissions are the most popular submissions of the subverse (many comments). Many subverses disabled the functionality of these tabs, and the submissions shown across all three tabs are the same, just in a different order.
When a user creates a new submission on a subverse, it would typically appear first on the new tab on page 0. At the same time, the last submission of page 19 is archived but not deleted. If one knows the direct link to that submission, they can still reach it but cannot comment or vote it.
Voat API. Voat supported a JSON API service for some time, but its maintenance stopped in October 2020. To collect the submissions of a subverse, one had to request the API of a specific page number (0 to 19) of a subverse's tab. The response of the API would be the 25 submissions of that page without their comments. To collect the comments, one needs to request them using the submission ID number, in which the API responds with 25 comments at a time.
Thus, to collect all the submissions from a subverse, one needs to request all 20 pages for the three tabs separately from the API. As explained by [25], the API does not list the archived subverses and does not respond to requests where the page is above 19.
However, if one knows the submission ID and the subverse it was posted in, they can request the API for that specific submission. Since submission IDs on Voat are incremental, one could theoretically collect all of Voat's submissions by requesting the API for each submission ID incrementally for more than 7.5K subverses; that is 7.5K requests, in the worst case, to collect a single submission. To the best of our knowledge, no study or work managed to collect the full Voat dataset.

SearchVoat.
A website named searchvoat.co used to collect the Voat submissions and comments. 1 This site is not associated with Voat, but one can browse and find Voat submissions there. The site does not support an API and does not allow web scraping. After Voat shut down, the website transformed into a news aggregator, similar to Voat. 2

Voat's Troubled History
In this section, we present Voat's history as we believe it highlights the significance of our dataset. WhoaVerse was the original name of the website that was founded in April 2014. The website was a hobby project of Atif Colo (Voat username @Atko). Justin Chastain later joined Colo (Voat username @PuttItOut). The owners advertised the website as Reddit's alternative with a focus on freedom of expression and speech, which satisfies its users' needs and wants. In December 2014, WhoaVerse changed its name to Voat and marked its mascot as an angry goat.
In June 2015, after Reddit banned various hateful subreddits [34], including /r/nigger and /r/fatpeoplehate, many Reddit users started registering accounts on Voat. The sudden influx of users overloaded the site, causing a lot of temporary down time [40].
On June 19, 2015, Voat's web hosting service, Host Europe, 3 canceled Voat's contract claiming that the site is publicizing abusive, insulting, youth-endangering content, along with illegal right-wing extremist content [39]. Some days later, PayPal froze Voat's payment processing services [28]. In response, Voat shut down four subverses, two of which hosted sexualized images of minors and the founders attributed the shutdown to political correctness [11]. The site moved to a different hosting provider and started accepting cryptocurrency donations.
In July 2015, Reddit banned a popular administrator that caused another influx of Reddit members registering with Voat, leading to more downtime. In an interview, Colo said that they "provide an alternative platform where users would not be censored and still say whatever they want" [29]. Voat was the target of a DDoS attack many times and experienced numerous downtime during its six years of operation. The most significant attack was in July 2015 [32]. Voat, Inc. became a registered corporation in the U.S. in August 2015. Although Voat was based in Switzerland, the U.S. seemed like the best option since "U.S. law with regards to free speech, by far beats every other candidate country we've researched" as explained by Colo in a post.
In November 2016, more users relocated to Voat after Reddit banned the /r/pizzagate conspiracy theory subreddit [22]. In January 2017, Colo resigned as CEO of Voat due to time availability restrictions and was replaced by Chastain. Chastain ran a fundraising campaign in May 2017 after announcing that Voat might have to shut down due to financial issues; Voat managed to stay online.
In November 2017, Reddit banned its incel community (/r/incel), and many of its followers reportedly moved to Voat [18]. About a year later, on September 12, 2018, Reddit banned numerous subreddits dedicated to the QAnon conspiracy theory, which again caused many QAnon adherents to migrate to Voat [25].
In April 2019, Voat's CEO Chastain asked Voat users to stop threatening people as he had been contacted by a "US agency" about the threats posted on the website. 4 Voat users were not pleased to hear that Voat was working with agencies to remove Voat content and "limiting" the site's free speech and freedom of expression. Specifically, the first comment on the submission was an anti-Semitic slur, calling for the extermination of Jews [13].
Last, on December 22, 2020, Voat announced again, now for the last time, that it would shut down due to lack of funding. 5 Chastain explained that he had been funding the site himself since March 2020 but had run out of money. On December 25, 2020, Voat shut down and its last submission was posted by Chastain, explaining "@Atko made the first post to Voat, so I am making the last." 6 In Table 1, we list some aforementioned Reddit bans that probably affected Voat's activity. Some of these bans previously captured researchers' interest. We use these bans in our analysis in Section 6 to show whether Voat's activity was indeed affected.

Data Parsing and Data Collection
This section details the methodology and tools employed for our data collection infrastructure. Submissions and Comments. Following Voat's shutdown on December 25, 2020, the Internet Archive Wayback Machine (IAWM) released all of Voat's snapshot captures in Web   ARChive (WARC) format [5]. These WARC captures include all the snapshots the IAWM captured over the lifetime of Voat. A WARC format file consists of single or multiple WARC records (snapshots), and it supports, among other things, the access and scraping of archived data. The files also hold revised and duplicated snapshots [12].
To parse these snapshots into structured data, we download them and set up a Python parser to collect the submissions and comments. In our case, every WARC file is a collection of various Voat snapshots the IAWM captured. To facilitate the smooth parsing of the WARC files, we use the warcio Python library. 7 This library offers a convenient and reliable way to read a WARC file by streaming every entry included in the file and automatically detecting the payload. The payload contains the capture itself, i.e., the HTML DOM tree code of the platform. Each WARC file includes the snapshot of the entire platform for a specific time and date, that is, millions of submission pages for thousands of submissions.
Our parser captures the HTML DOM tree code of all the pages included in all the WARC files serially. Then, it passes the HTML DOM tree code to a function that uses the beautifulsoup Python library to read and store in a JSON format the data and metadata of the submissions and comments, i.e., submission title and content, number of upvotes and downvotes, comments, etc. 8 We ensure that our parser only stores the latest submission version, as WARC files have duplicate data. User and subverse profiles. To complement our dataset, we also collected user and subverse profiles. A user profile con-  sists of user-related data like username and registration date, whereas a subverse profile consists of subverse creation date, description, and subscriber count. To collect this data, we built a crawler using the IAWM API, 9 along with beautifulsoup and HTML requests. 10 Every user and subverse profile URL is unique, but they all start the same way; voat.co/u for the former and voat.co/v for the latter. First, we request the IAWM API for all the snapshots whose URLs start like users or subverse URLs. We then collect the responses and parse them into JSON format, storing the latest snapshot the IAWM has in its database for every unique username and subverse profile URL.
The above process resulted in the dataset summarized in Table 2. We collect a dataset that consists of more than 2.3M submissions posted by 80K users in 7.6K subverses and over 15.7M comments posted by almost 154K users. Note that IAWM does not have the profile of about 500 subverses and hence we only manage to collect the profiles of 7.1K subverses (6.8% loss). In addition, we collect almost 108.5K unique user profiles. Data collected via Voat API In an attempt to complete our dataset, we incorporate to our dataset, the data that was collected for the [25] study. For that study we collected 176K submissions and 1.45M comments posted from 28K users in 241 subverses. For our data collection infrastructure, we used Voat's API between May 2020 and October 2020, when Voat stopped the maintenance of its API. We find 45.5K submissions and 532K comments that were missing from the IAWM archive and incorporate them in the released dataset.
Some subverses on Voat offered anonymity to their users by replacing their username with a random eight-digit number (not a unique number for every user). The total number of users that commented or posted a submission ( Table 2) does not include anonymous or deleted users. Hence, we assume that Voat's known user base is 155K users at least, based on the data we collect from the IAWM. It is impossible to know the exact Voat user base since Voat never shared the complete list of user profiles, even when it supported a data API service; to collect a user's profile, one needs to know the username. This means that we cannot acquire user profile data of "stalkers." Alas, assuming the total known number of usernames is 155K, we estimate that about 27.1% of the total users' profile data (41.6K) is either missing, or deleted users. However, [25] show that 13% of the 15K users being active in QAnon discussions consisted of deleted profiles. Considering that many usernames were deleted every day on Voat, we estimate that this dataset offers the best representation of Voat's user base to date. Incorporating [25] user data with ours, we find 5K additional user profiles and 1 subverse. The final dataset presented and released with this work is detailed in Table 3. Fair Principles. The data released and presented in this paper aligns with the FAIR guiding principles for scientific data, as described below: 11 9 https://pypi.org/project/waybackpy/ 10 https://pypi.org/project/requests-html/ 11 https://www.go-fair.org/fair-principles/ • Findable: We assign a unique constant digital object identifier (DOI) to our dataset [43]. 12 • Accessible: Our dataset is openly accessible.
• Interoperable: The dataset is stored using the standard JSON format that is widely used for storing data and can be used in various programming languages. We also provide a detailed description of our dataset's format in Section 5. • Reusable: We provide all the available metadata along with our dataset and we extensively document them in this paper, in Section 5.

Ethical Considerations
The data collected, presented, and released with this paper are available on the Wayback Machine and also used to be accessible (without the need of a registered account) on Voat before it went down. The collection and release of this dataset do not violate Voat's or Wayback Machine's Terms of Service. Although some subverses on Voat allowed users to post anonymously, the overwhelming majority did not offer this functionality. Hence, we detect and collect user profile data of 114K users. The only identification of these user profiles is the unique pseudo name, which is not personally identifiable information. Analysis of the activity generated on Voat to other services could potentially be used to de-anonymize users. We note that we followed standard ethical guidelines [31] and made no attempt to de-anonymize users.

Data Description
We now present the structure of our dataset, available at [43]. Our dataset consists of four parts, namely, submission, comment, user profile, and subverse profile data. We release our data in various newline-delimited JSON files (.ndjson). 13 Each line in a .ndjson file consists of a JSON object that holds various keys and values. Specifically, we release 7, 616 .ndjson files, one for every subverse, that hold the submission data. Similarly, we release 7, 515 .ndjson files that have comment data. We inspect our dataset for the missing 101 subverses' comments and find that these subverses had no comment activity, only a small number of submissions. Also, a single .ndjson file is released for user profile data, and another one for subverse profile data. In total, we release 15, 133 .ndjson files. Table 4 lists the keys, value data type, and description of our dataset files.
We choose to release the submission and comment data separately for every subverse as we believe it facilitates researchers that want to focus on specific communities. We also use JSON to release our dataset as it is among the most optimal ways to store and share data as it has extensive documentation and is supported by all popular programming languages. 14 12

Data Analysis
In this Section we provide some statistical analysis and visualization of our dataset.
Posting Activity. First, we show the overall posting activity on Voat. Figure 1 shows the number of submissions and comments per day on the platform. The vertical red dotted lines represent the events listed in Table 1 The date with the most submissions on the site is very close to the day Reddit banned many communities like /r/fatpeoplehate and /r/nigger [34]. Shortly after Reddit banned these communities, Voat experienced heavy traffic and  In addition, we show the overall activity on Voat in the top ten most subscribed subverses, namely, /v/AskVoat, /v/GreatAwakening, /v/QRV, /v/fatpeoplehate, /v/funny, /v/news, /v/politics, /v/theawakening, /v/videos, and /v/whatever, in Figure 2. We present this analysis to show how active the most popular subverses on Voat were since we believe that researchers interested in our dataset might consider these findings useful. The vertical red dotted lines on the figure indicate the bans listed in Table 1. When Reddit refugee crowd joined Voat (ban number 1, 3 and 4 from Table 1) many general discussion subverses like /v/AskVoat, /v/news, /v/politics, /v/videos, /v/funny, and /v/whatever became more active, indicating that this new influx of users bolstered the overall activity on the platform.
Interestingly, not all banned subreddits appeared on Voat as subverses shortly after a Reddit ban frenzy. The sub-verse /v/GreatAwakening was created on January 1, 2018, nine months before Reddit banned QAnon subreddits (ban no. 8 ). This subverse was the 10th most popular subverse when Voat shut down. QAnon discussion on the platform boomed when /v/theawakening and /v/QRV first appeared on Voat on September 12 and September 22, 2018, respectively, with approximately 200 submissions per day on /v/QRV alone. These three subverses turned out to be among the top 5 most active subverses on the platform, with /v/QRV being the most active in both daily submissions and comments on the whole Voat, within only ten days after being banned from Reddit [23].
The figures discussed in this subsection support the reports that Voat was among the main hubs for Reddit migrating communities. In addition, Figure 2 shows that other than general discussion subverses, the most subscribed subverses focused on hate speech (/v/fatpeoplehate) and conspiracy theories (/v/QRV, /v/theawakening, /v/TheGreatAwakening).
Submission Engagement. We set to discuss the engagement of the users on the platform. In Figure 3 we plot the Cumulative Distribution Functions (CDF) of the number of comments, upvotes, downvotes, and net votes (upvotes minus The most liked comment noted that "someone isn't happy that Voat is succeeding" and reached 1.5K upvotes on a submission posted by Atko that was discussing the DDoS attacks Voat was experiencing in July 2015. Last, the most disliked comment received 247 downvotes from a user that was asking @PuttItOut to reconsider the voting system of the site since they lost their submission posting privileges because of people downvoting them when posting their honest opinion. The user asks the CEOs: [...]ask yourself: Are you fine with a website that caters to some of the most dangerous people currently walking the planet? Take a look at how depraved Trump supporters are, and ask yourself if free speech is worth the cost:[...] User registration and Subverse creation. In Figure 4 we plot the number of daily user and subverse registrations on Voat. The vertical dotted lines mark the bans listed in Table 1. The first Reddit ban that seemed to have influenced Voat's user base is the one of /r/beatingwomen, on June 9, 2014 [2] (ban no. 1). Eleven days after the ban, on June 20, Voat had 145 new subverses in a single day. Specifically, the day with the most subverses ever created on the platform. On June 22, there were 112 new subverses.
Moving on to 2015, we find that July 7 is the date with the most users ever registered on Voat in a single day, 3, 175 registrations, followed by July 5 with 2, 854 registrations. These dates are close to the date Reddit banned various hate subreddits like /r/nigger and /r/fatpeoplehate (ban no. 3 and 4). Also, during summer of 2015, Reddit changed their free speech and content policy [33] and the founder noted that "Reddit was not created to be a bastion of free speech." On July 12 and 13, the platform marked two of the five days with the highest new subverses created, 125 and 112, respectively. The fifth top date with the most user registrations on Voat is September 13, 2018, with 2, 021 users, probably due to Reddit banning QAnon focused subreddits (ban no. 8).
This analysis provides a glance at Voat's user base and subverse changes over the years. It is apparent that Reddit influenced Voat activity and that the platform was among the preferred Reddit alternatives for banned users. Links. Since Voat is a news aggregator platform, we also analyze the domains the users posted on the site to show what kind of content the userbase of Voat consumed.
For each submission that redirects users to other domains, we retrieve the name of the subverse the submission is posted in and the external link it redirects to. We count how many times a domain is shared in a community, keeping only the subverse and domain pairs that are the most recurrent in the dataset. The results of this analysis are displayed in Figure 5, an alluvial diagram, where the line thickness represents the number of times the domain was shared on the subverse it points to.
Most of the links that redirect users to Reddit were posted in /v/MeanwhileOnReddit. The subverse focusing on bodyshaming, /v/fatpeoplehate, redirected users to Instagram, YouTube, and image sharing services; websites where users can upload images and share the link to that image on other platforms. The /v/news subverse linked YouTube, Voat, online press outlets, and archiving services links. It is known that users in alt-right social networks avoid sharing the direct link to a website and prefer an archive link instead to avoid monetizing the website [42]. The majority of the alternative news links (Breitbart, GatewayPundit, and Zero Hedge) are posted on /v/news and /v/WorldToday. Most of the Twitter links on the website were posted in /v/QRV and /v/GreatAwakening. Most of the tweets include Donald Trump's tweets and other political discussions on Twitter.
Overall, Voat users shared links to other social networks like 4chan, Twitter, and Instagram. News on the website was shared via legitimate online press outlets and other alternative news outlets, along with archiving services links. Most of the images on the platform were shared on /v/funny, /v/fatpeoplehate, and /v/whatever. Content Creators. We now take a deep look into Voat's user ecosystem. We attempt to show how users form clusters based on the subverses they most often engaged with (posted a submission or a comment) to show whether the userbase of Voat is homogeneous or not. Further analysis on Voat's user base may shed light on what content users prefer to see on Voat and whether all of Voat's subverses focused on hateful and politically incorrect content.
As shown from [25,17], some users are responsible for a large amount of content being shared in some communities, leading to imbalances, influencing the content users consume on the platform. By analyzing each user's interactions on Voat, we hope to obverse how all these various communities blended after a mass migration from Reddit, or if Voat was nothing more than an aggregate of small, selective echo chambers. This way, researchers interested in our paper can  know what to expect. In Figure 6 we plot a graph network where nodes represent users, and the edges symbolize their interactions. For example, users are linked together if they participated in the same conversation, i.e., they both commented on the same submission, or one of them is the submitter while the other one commented. The weight of the edge is given by the number of interactions shared by the same two users, and the color represents the subverse where the user participated the most.
The network is composed of a giant cluster, where most of the subverses are mixed together. This cluster includes /v/politics, /v/news, and /v/whatever, which makes sense since these are general discussion subverses, and it is expected that many users meet there for general discussion. However, some of the subverses are strongly isolated in the network. For example, the /v/NeoFAG (yellow) community shows that most users tend to only engage within that subverse. Similarly, /v/GreatAwakening (red) and /v/theawakening (dark blue) seem to be clustered together and somewhat interacting with /v/pizzagate (dark green). Some users that engage with these three subverses also engage in the general discussion subverses, which is aligned with the findings of [25]. Last, /v/fatpeoplehate (brown) users also seem to form their own cluster while infiltrating the general discussion subverses.
To measure the homophily of these communities, we used the EI homophily index, which is a metric that indicates how many members of a network favor in-group interactions rather than out-group ones. Given a specific node with E external edges, i.e., edges with nodes from the out-group, and I internal edges, i.e., edges with nodes from the in-group, the EI homophily index is given by the equation EI = (E−I)/(E+I).
An index EI = +1 indicates that the node only interacts with members of the out-group, whereas EI = −1 applies to nodes that only interact within their in-group. Table 5 lists the average EI homophily index of the members of the subverses highlighted in the legend of Figure 6.  Users who are very active on popular subverses such as /v/politics and /v/news have a high average EI homophily index, meaning they mostly interact with users from the out-group. The opposite can be said for subverses like /v/theawakening, /v/GreatAwakening, /v/pizzagate, and especially, /v/NeoFAG and /v/fatpeoplehate. These communities do not converse a lot outside of their social group. The EI index is almost zero for /v/theawakening, meaning users from this community interact as much with the out-group as with the in-group. By looking at the community, this can be explained by the fact that users from the communities gravitating around the QAnon narrative, i.e., /v/theawakening, and /v/GreatAwakening, are more connected than other communities. As a result, the external edges can be nothing more than crossovers between these two subverses. The userbases of /v/NeoFAG and /v/fatpeoplehate seem to be the ones that only prefer to interact with members of their community.
We present this analysis to motivate researchers studying user interactions and echo chambers. Further research using our dataset may shed light on whether Voat was a bastion of echo chambers or not, along with what narratives users within these communities exchanged.

Related Work
In this section, we present existing work focusing on Voat, and other dataset papers similar to ours. Voat attracted the interest of researchers over the past years, especially after Reddit started banning communities in 2015. Although some papers mention that their dataset is available upon request, these datasets only include data from a couple of subverses that cover a short period of time. To the best of our knowledge, our Voat dataset is 1) the only one to be openly and publicly available online, and 2) the most complete and largest one, covering the whole history of Voat, along with data of the users that ever posted a submission or a comment on the platform. Voat research. Newell et al. [21] collect data from various platforms, including Voat and Reddit and perform, among others, computational analysis to identify the primary motivations that drive users to move to other platforms. Chandrasekharan et al. [9] collect data from 4chan, Reddit, MetaFilter, and Voat and build a model to detect abusive content online. The Voat subverses used in this work include /v/CoonTown, /v/Nigger, and /v/fatpeoplehate, all focused on hate towards individuals of specific body or race characteristics, created on Voat shortly after the 2015 Reddit bans [34]. Similarly, Saleem et al. [38] collect data from Reddit, Voat, and three online forums to train a classifier that detects hateful speech. Their Voat dataset includes data from /v/CoonTown, /v/fatpeoplehate, and /v/TheRedPill. A study on deepfakes finds that pornographic deepfakes are mainly created for circulation within the community [30]. The study uses data from Voat's /v/DeepFake and the site mrdeepfakes.com, which both were created after Reddit banned the subreddit /r/DeepFakes in 2018 [35].
Khalid and Srinivasan [20] compare the features of 872K comments from /v/politics, /v/television, and /v/travel, to Reddit and 4chan comments building a classifier that predicts the origin of the comments based on its style and content. Papasavva et al. [25] collect 0.5M posts from /v/GreatAwakening, /v/news, /v/politics, /v/funny, and /v/AskVoat to provide an empirical exploratory analysis of the QAnon community on Voat. They find, among other things, that /v/GreatAwakening is not as toxic as the general discussion subverses. Last, Aliapoulios et al. [24] compare Voat's /v/GreatAwakening and /v/news posts to 4chan, 8kun, Reddit, and Q drops (posts posted by "Q," the mastermind behind the QAnon conspiracy theory) on a large scale study on QAnon. They find that Voat posts are as threatening as Q drops and that content creators on Reddit and Voat only consist of a small portion of the total community.
Other datasets. One of the largest Reddit datasets is the one of Baumgartner et al. [6], which presents an archiving platform that collects Reddit data and makes them available to researchers since 2015. The same platform also published over 27.8K channels and 317M messages from 2.2M users from Telegram [7]. Fair and Wesslen [14] release a dataset of 37M posts, 24.5M comments, and 819K user profiles collected from Gab. Aliapoulios et al. [3] published a dataset consisting of 183M posts and 13.25M user profiles from Parler, a Twitter alternative. Last, Papasavva et al. [26] present a dataset with over 3.3M threads and 134.5M posts from the Politically Incorrect board (/pol/) of the imageboard forum 4chan.

Conclusion
In this work, we present and release a Voat dataset comprising more than 2.38M submissions and 16.2M comments posted from 113K users in over 7K Voat subverses. We combine data collected from Voat API and IAWM released archives to complete the dataset to the best of our ability. Voat shut down on December 25, 2020, and its data are now otherwise inaccessible. In this work we also perform a preliminary analysis of the released dataset so researchers interested in it can know what to expect.
Overall, we hope this work further motivates and assists researchers focusing on deplatforming and how users organize massive immigration to other platfroms. In addition, our dataset could also help answer numerous questions about how 'free-speech' sites operated, e.g., do moderators ban users that express opinions other than the ones aligned with the narratives of a subverse? How do other users vote and how toxic are they towards such content? Do sites like these incentivize users to form echo chambers? What kind of content users in this communities consume, etc.? Also, our dataset could assist multi-platform studies to understand similarities and differences of different communities. Last, since Voat was a bastion of free-speech, we are confident that access to our dataset could assist researchers towards training algorithms in natural language processing and detecting hate speech, fake news dissemination, conspiracy theories, etc. Finally, other than quantitative work, we hope that the data can also be used in qualitative work studying specific events, social theories, and communities.