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1 Introduction
In the last two decades internet has become a pervasive medium that has changed completely, and perhaps irreversibly, the way information and knowledge are transmitted and shared throughout the world.
All this new information now readily available represents a great opportunity to generate knowledge from direct observations. But, at the same time, its typically unstructured nature can exceed the capabilities of systems, without providing articulated knowledge to its actors.
In order to deal with the knowledge extraction from data obtained from several domains, data clustering could be applied. In an simplified way, the problem of data clustering may be defined as that of assigning each of N data items to one of K possible clusters.
This task consists of separating the available observations into well-defined subgroups, based on the set of selected features. If the task is successful, the clustering process reveals the characteristics of the different underlying classes in the domain of interest.
When the data comes from a well-known domain, it is possible to establish in advance a convenient number of classes to analyze the data. In many real-world cases, however, even the number of underlying groups into which existing observations can be classified is unknown.
Currently, there are large amounts of measurement records of all kinds from which the necessary information and knowledge can be extracted to respond in a timely manner to the demands of the environment.
But the volume, speed, and diversity with which this data continues to be generated makes it difficult to properly harness the insights hidden in data. The use of questionnaires and surveys is a very useful approach for obtaining data, particularly in the economic and social fields.
Currently, with the rise of computer systems, the Internet and social networks, the coverage that can be made of a domain by these means is virtually unlimited. On the other hand, the analysis of data collected in this way is often very challenging, especially in cases of ill-defined problems.
Furthermore, in many environments, the data often contains variables of different nature (numeric, boolean, multivalued, range, classification, categorical or open text) mixed in the same response, while most of the available methods and libraries are focused only on the processing of numerical data.
This paper presents an adaptation of the Isodata clustering method for the analysis of survey responses data. The 2021 StackOverflow Developers Survey has been selected as a test case. This database contains mixed data (numeric, multivalued, range and categorical), there are no predefined classes, it contains a lot of missing values in most of the variables, and yet the algorithm is able to generate sound data clustering.
The rest of the paper is organized as follows: First, in subsection 1.1, we provide a state of the art of the topic addressed in the paper; Section 3 presents an description of the Isodata/Isoclus method algorithms. In subsections 2.2, 2.3 and 2.4, the adaptation, that represents our contribution, to the Isodata method is detailed.
In section 3, a description of the dataset (the 2021 Stack Overflow Survey Data) and the data preparation stage used in the experiment of the paper is presented. In Section 4 the results of the experiment are addressed. Finally, section 5 concludes the study summarizing its findings.
2 Related Work
Although mixed data is a fairly common feature in a variety of contexts, there are very few methods that allow the processing of categorical data, particularly when it comes to discovering the underlying classes in real problems.
A common strategy for clustering data containing mixed values is to transform the qualitative data into some form of numerical representation and then use conventional clustering methods. Salem et al. [1], for example, perform a transformation on categorical variables, replacing linguistic values with their relative frequency in the attributes.
Subsequently, they use the conventional
Next, they also use the conventional
From this data transformation, they derive a clustering method based on the
Dinh et al. [4], for example, compute the value of the centroid using the arithmetic mean for numerical variables and a probabilistic value for categorical data. The distance of each sample from the centroid is calculated using the squared Euclidean distance for numerical features and an information-theoretic-based dissimilarity measure for categorical variables.
Other approaches for data clustering in the presence of categorical values are the use of genetic algorithms [8, 13, 14], the representation of data/prototypes by means of fuzzy sets [3, 12, 17], the use of linear programming techniques [10, 7, 16], methods derived from information theory [6, 11], etc.
3 ISODATA/ISOCLUS Method
ISODATA (Iterative Self-Organizing Data Analysis Techniques) is a partition-based clustering method, similar to
However, unlike
– Clusters with ”few elements” are eliminated.
– Clusters that are ”too close” to each other are merged.
– Clusters with ”high dispersion” are split.
The ISOCLUS algorithm is a variant of the Isodata method that optimizes the performance of the original method. The clustering method presented in this work is derived from this algorithm.
3.1 Isoclus Algorithm
The Isoclus algorithm uses the following parameters:
–
–
–
–
–
–
–
–
Additionally, and due to the high dispersion of the data in a survey responses, a new parameter is added to control the maximum dispersion allowed in each cluster:
–
The Isoclus algorithm follows the following steps [9]:
1. Define the values for
2. Select the initial centroids arbitrarily.
3. Assign each point in the data set to the cluster with the nearest centroid.
4. Eliminate those clusters with less than
5. Recalculate the centroids. If clusters were removed in step 4) the algorithm returns to step 3).
Note: In the original algorithm, this step is not performed. Instead, the points associated with the clusters removed in step 4 are ignored for the rest of the iteration.
However, due to the complexity of the data in the survey, each iteration is more expensive than it would be for data with only numeric values.
Thus, in this work it was decided to go back to step 3. This strategy has the risk of creating a loop, so a maximum of cluster reconstructions is performed in each iteration of the complete Isoclus algorithm.
6. Calculate the average distances
7. If this is the last iteration, terminate. Otherwise check if
-
8. Calculate, for each cluster
If these conditions are met, replace the cluster with two new clusters centers located around the current centroid of the cluster and separated by an amount and direction that depends on the maximum value in
If there was at least one cluster split, rebuild all clusters (and centroids).
Note: The original algorithm, as described in [9], uses a stricter split rule regarding the spread of values in the cluster: If the maximum standard deviation, among all variables in the feature vector, exceeds
However, in the case of survey data, such as that from Stack Overflow, the dispersion of values is usually very high, so the rule has been softened so that only those clusters with high dispersion in several variables (
-
9. Compute the matrix of distances between centroids. Select the
If these conditions are met, replace the two clusters by a new cluster whose centroid is the midpoint of the original centroids. If there was at least one cluster merge, rebuild all clusters.
The Isoclus method has given very good results with numerical data and is widely used, particularly in the area of satellite image processing. However, to apply it to the case of mixed data, such as what we have in the survey database, adjustments need to be made to several steps, which are presented in the sections below.
3.2 Computing the Distance between Survey Answers
The central element in a clustering algorithm is the computation of the similarity between feature vectors. When working with numerical data, in real problems, the typical choice is the Euclidean distance.
To work with mixed data containing nominal values and numeric values, the typical choice is to use the Gower distance.
As mentioned above, the responses in the survey include not only numeric and nominal values, but also scale values (not used in the 2021 edition) and variable-length sets of nominal values, such as {Python, HTML /CSS, SQL, JavaScript, C++}, {java, C++, C#} or {Python}.
To deal with this type of data, a similarity measure based on Gower’s similarity [5] has been used. The Gower distance between two records,
where
being:
–
–
–
–
In this case, the maximum similarity is obtained when both vectors
On the other hand, the minimum similarity is obtained when the vectors have the same length, but all their elements are different. When the vectors share some elements, the similarity will be between 0 and 1:
where:
3.3 Computing the Clusters Centroids
Computing centroids for hybrid data also requires some special considerations. Let
being
– For the case of nominal variables, the approach used is the usual alternative of using the modal value as the representative value of the class, as is done in the
being
– In the case of multivalued variables, obtaining the value of the centroid requires special considerations. A straightforward option would be to get the modal value of all responses. However, this solution does not reflect the fact that responses often have multiple values.
Obtaining the most common set is also not a good option since now only the most common combinations would be highlighted, for example, the languages that are most frequently used together.
-
Therefore, in this case the centroid value has been defined as a combination of modal values, so that those answers including more modal values are most close to the class prototype. So, in this case, centroid component is computed as follows:
1. One of the characteristics of multiple value answers is the length of the list of values included in the response.
So the first step in defining the value of the centroid is to compute the average length of the lists of values in the answers,
2. Obtain, from the entire list of values used in the responses to the corresponding item in the elements of the cluster, the
So, the centroid value is give by:
3.4 Computing the Dispersion of the Data in the Cluster
– The calculation of the dispersion for the numerical variables is carried out using the square root of the mean absolute deviation (MAD), that is:
The MAD is the most robust measure of dispersion in data with outliers. Additionally, the use of the square root helps to further reduce the impact of outliers by emphasizing smaller spread values.
– For the case of nominal variables, the dispersion is calculated as:
where
where
4 Stack Overflow Survey Data
4.1 Stack Overflow Annual Developer Survey
The software developer community is made up of unique people dedicated to an activity that can be considered the newest in the history of mankind and which requires a special combination of skills.
The uniqueness of this community is reflected not only in aspects of personal image and social interaction (the most stereotyped aspects), but particularly in its motivators.
These characteristics of a group of professionals who represent the core of the new economy have led to the emergence of a new discipline in human resource management, the so-called Geek Management.
Understanding the points of view of this community, their daily activities and their personal development plans, can make it possible to optimize the development of the profession and opens up possibilities for defining very well-segmented markets.
Stack Overflow is a private website, dedicated to facilitating the solution of specific programming questions, based on peer advice, with more than 15 million registered users as of March 2021.
Since 2011, Stack Overflow has carried out a survey among developers, which covers various professional and anthropological aspects.
More than 83,000 developers from 181 countries around the world responded to the 2021 Stack Overflow Annual Developer Survey (hereinafter ”the survey”), conducted from May 25, 2021, to June 15, 2021. Survey data is available on the Stack Overflow sitefn.
Analyzing the survey is interesting, not only for the insight it can give on the developer community, but because it is a good example of a survey with mixed data, high levels of missing values, and prank responses. Additionally, it is a real survey, with a significant number of responses and which has been produced every year since 2011.
4.2 Original Data Description
Reading the survey data into a Pandas Dataframe object identifies 48 columns that correspond to the survey questions; 2 columns identified as float64, 1 column identified as int64, and 45 columns identified as object. The data contains 83,439 rows corresponding to the “qualified” responsesfn.
The questionnaires used in the different editions of the StackOverflow Developer Survey have combined questions with responses in nominal, numerical, multiple choice and scale variables, although the latter type was not used in the 2021 survey.
4.3 Data Preparation
For the analysis, the following variables were discarded:
– ResponseId: This variable is an index of the completed questionnaires.
– CompFreq, CompTotal and Currency: These variables are summarized in a computed variable called ConvertedCompYearly.
– UK_Country: This variable has 94.7% blank responses.
– US_State: This variable has 82.12% of blank responses.
As a result of discarding these variables, the final data set includes 42 variables A first stage of data cleaning was carried out, making imputations to missing values based on correlated variables.
Even after this cleaning step, the missing values were still considerable. Additionally, atypical data were observed, such as students from lower school levels with salaries greater than $45,000,000 USD per year.
Considering that these data were unreliable, those records in which the value of the ConvertedCompYearly variable exceeded the third quartile of the data by more than 3 times the Inter-Quartile Range were eliminated (
In this data cleaning step, 1,764 records were deleted (2.11% of the complete data), leaving 81,675 records in the database.
In the final data preparation step, the numerical variables were normalized and the nominal variables were recoded to make them more manageable.
5 Results
The proposed adaptation of the Isodata method was tested on the survey data, using different sets of parameter values. The results presented below were obtained using:
This experiment yielded a clustering of the survey data in 12 clusters. Below is a description of each cluster whose centroid value for the MainBranch dimension is ”I’m a developer by profession”fn:
Cluster 1. This cluster includes the answers of 9496 developers. The most common age range in this group is 18–24 years old (53.64%), with a standard deviation
The mean annual salary (ConvertedCompYearly) for developers in this group is $31,313.90 USD, with
The most frequent country of residence is India (29.43%,
Regarding the programming languages used by developers belonging to this group during 2021 (LanguageHaveWorkedWith), the most mentioned languages were: ’JavaScript’, ’HTML/CSS’, ’Node.js’, ’SQL’, ’Python’ and ’Type-Script’ (being the combination [’HTML/CSS’, ’JavaScript’, ’Node.js’, ’TypeScript’] the most frequent answer with 2.25%,
The operating system (OpSys) most used by these developers was some Linux-based (45.48%,
Cluster 9. (8500 members). Age: 25-34 years old (64.28%,
Cluster 0. (16354 members) Age: 25-34 years old (46.25%,
Cluster 5. (9004 members) Age: 25-34 years old (59.75%,
Cluster 2. (10159 members) Age: 25-34 years old (69.67%,
Cluster 4. (7127 members) Age: 35-44 years old (56.42%,
It can be seen that the group of programmers with the lowest salary is represented by young professionals, mostly from India, who carry out website development activities (speculating based on the programming languages used).
On the contrary, the best paid group is represented by older programmers, working in the USA and carrying out more complex activities (again, speculating based on the programming languages used).
In general, when analyzing the different class prototypes, it is observed that the results are consistent with the general knowledge about how the programming industry is distributed worldwide.
6 Conclusions
The present work is developed to satisfy two main purposes: On the one hand, and from a broad academic perspective, it seeks to develop tools that allow the analysis of the information that is collected through surveys and whose answers usually contain values that are not necessarily numerical.
On the other hand, from a more specific point of view, it seeks to make the most of the information obtained by the Stack Overflow network through its Annual Developer Survey, to achieve a better understanding of the international community of developers of computer solutions.
In this work, an adaptation of the Isodata method that allows analyzing data containing mixed numerical and categorical values is presented. Among other possible applications with mixed data, this extension of the Isodata method allows to analyze the information obtained through questionnaires to obtain a preliminary understanding of a system.
This method was tested by analyzing the responses to the 2021 Annual Stack Overflow Developer Survey. Although the data present serious quality problems (large number of blank values, presence of outliers, apparent confusion in the meaning of the questions, prank responses), the results obtained initially reveal a distribution of programmers in groups that reflect a priori knowledge of the software industry, such as the formation of labor poles.
Regarding the broad purpose of developing tools for survey analysis with mixed data, the preliminary results show that the presented method can take advantage of qualitative information together with numerical information to detect clusters that make sense.
In subsequent works, results will be shown when applying this method to other important surveys. Concerning the specific purpose of better understanding the formation of developer communities, the results show sound results, the use of the Isodata method is only exploratory: the goal is to obtain insights about the structure of the response groups.
These results now allow, for example, a better cleaning of the data by analyzing them by clusters. Descriptive analyzes can also be performed but separated by clusters.
More importantly, it is possible to analyze the structure of the questionnaire to adjust it to what is desired, detecting, for example, items that do not provide useful knowledge for the understanding of the industry.
Due to space restrictions, the results obtained in this project have hardly been described, however, the full results and further discussion are available on the site: https://github.com/.
