The paper describes the task of identifying of homogeneous groups of software projects with similar behavior of metrics of software development processes. This is necessary for analysis, understanding and improving the practice of software development, for planning, detection of numerical relationships between key metrics of the development process and the quality and cost of the project; it is also necessary to identify where efforts are made, where defects occur; to identify the impact of technological, process, and organizational aspects on the result. To solve this task the FBC-approach (Fuzzy Behavior Clustering) based on combination of three types of time series clustering is applied to group the software projects taking in account similar behavior of their development processes. Two experiments on the set of metrics from open projects repositories showed the availability of the proposed FBCapproach to identify homogeneous groups of software projects with similar behavior of key software metrics.
The beginning of the 21st century is characterized by the entry of mankind into the "information" era,
information becomes the main resource, tool and output of production. At the same time, the software
engineering reaches industrial scales, software projects are becoming increasingly complex. According
to the statistics of software projects success around the world, more than half of them are controversial
or disastrous [
Among the tasks to be performed when analyzing data from a repository based on clustering, we will distinguish the following tasks:
Search for the causes of anomalies and how to remove them;
Prediction of software defects (it was revealed in the work [
A review of the literature on the repository data analysis is given in [
Clustering data allows us to split the objects of the software development process into homogeneous
groups. In the work [
The work of Chintakindi Srinivasa, Vangipuram Radhakrishnab and Dr.CVGuru Rao [
Many works are devoted to the prediction of software errors based on data from a repository,
reviews on this topic are given in [
In the works of T. Zimmermann et al. [
In the work of James W. Tunnell [
Based on the results of a review of works in the field of clustering in the software development processes analysis, it can be concluded that the use of only static metrics does not fully allow analysis of the development process status. Existing approaches to the software development projects analysis do not provide for clustering by dynamic process metrics. For a deeper analysis of software development, it is necessary to investigate metrics not only of the program code (static), but also the dynamic metrics of the software development processes (grouping of processes with similar dynamics, revealing the degree of proximity of processes, comparing groups of linguistic estimates reflecting qualitative metrics and processes are necessary).
Time series (TS) are often used to represent and study the dynamics of processes in complex systems, so the clustering of time series is relevant and in demand and is considered an important step in the analysis of processes that allows homogeneous groups of data to form.
A review of the time series clustering is given in [
Clustering of raw data (point-based, time-frequency metrics), upon that, the same length,
scope, close regions of time series values are necessary; the problem becomes the significant
effect of noises on the clustering result;
Clustering based on density and based on a quantum grid, the limitation of which is the loss of
individual features of objects, the loss of perception of time series as a chronological
sequence, the nature of time series behavior (increase, decrease, etc.) is not taken into account;
Clustering based on models or machine learning: statistical and artificial neural networks.
They are characterized by dependence on idealization in the construction of a model, by the
loss of individual features of objects when they are replaced by generalized metrics; moreover,
there is no correction for a time series behavior, that are fuzzy in nature [
Basic limitations of the considered above approaches for clustering of software metrics are the
requirements of the same length and scope of the time series [
Therefore in [
In this paper, the application of FBC-approach (Fuzzy Behavior Clustering) [
Let us consider the informational model of the software projects in the form
D {dijt } where i is a number of the project (i 1..m) , j is a number of the key metric ( j 1..n) , t is a the time moment for the key metric (t 1..T ) .
The task is to analyze software projects for key metrics using model D {dijt } with a view to identify groups of similar projects Clk that is the clusters of software projects,
k 1..Q . When i const , diconst,i,t is a set of time series characterizing temporal (dynamical) changes of project metrics. If j const , then di, jconst,t is the set of time series describing the temporal changes of the metric for different projects, such as, the number of commits, the number of branches, the number of developers, the average time between commits, the development time of the project, (1) etc. In the case t const , di, j,tconst are tabular data, with text, numeric and binary values, and static project metrics at a given time.
The problem is to group the software projects by temporal metrics (1) with similar structures and changes as well.
Then the clustering of software projects metrics is considered as the task of grouping of the time series di, jconst,t , obtained from the repository D {dijt } , and of deriving k clusters CDynamic similar on k time series behavior and on their density:
D jconst CDynamic k (1)
In this paper similarity on time series behavior will be considered using the fuzzy sets in the form of general tendencies from the term set {"fall", "stability", "growth" and "fluctuation"}. Similarity on time series density will be determined based on Euclidean measure. Parameter k should be calculated in dependence of data. The task in the form (2) will be named as dynamic clustering (for short ) in the paper further.
The task (2) is a machine learning task and the its results are needed to better understand of software development processes. The obtained clusters allow to extract information from repositories about groups of objects, such as tasks, projects and developers in temporal space. This knowledge is useful in software management to make decisions on improving development process in the future.
To cluster the software projects in the form (2), it is proposed to apply Fuzzy Behavior Clustering
(FBC) approach described in the work [
The scheme of the proposed dynamic clustering in the form (2) is shown in figure 1. The input data are extracted from the software repository D. The input could be presented by: commit hash No, branch name, author's login commit, commit date. Then data are pre-processed to obtain a set of statistical project metrics from the repository: the number of commits, the number of branches, the number of developers, the average time between commits, the project development time, etc. With the help of data pre-processing, time series of these metrics are obtained for developers, years, months, days, hours. Then FBC-approach of time series of these metrics is then applied. As a result, k clusters CDynamic are obtained being the outputs of dynamic clustering of software projects by temporal metrics. k of i const or j const , dijt are time series of different dimensions, diapason, scope, and different trends of behavior.
Below we briefly recall the algorithm of FBC-approach of time series, proposed in the paper [
Let’s i const or j const for D {dijt } . Then we obtain the input data in the form of a set of time series which we denote {X s} , where X s dis, j,t (s 1..m) or X s di, js,t (s 1..n) These time series could be of different dimension, diapason, scope and different trends of behavior. Output data of the FBC-approach are the clusters CkDynamic of time series X s corresponding to software development process metrics.
Since FBC-approach uses the representation of the behavior of time series at three levels of the
hierarchy (general trends, trend component, fluctuation components) [
The adopted technique of FBC-approach to software metrics in respect to expression (2) includes the following steps.
First step. The transformation that puts time series X s in line with the linguistic term of the general
tendencies from the set of linguistic terms of the general time series trend GT= {"fall", "stability",
"growth" and "fluctuation"}, according to the algorithm given in the work [
X s gts , gts GT , X s Y . (2)
Second step. Clustering of the gts by the general trends using the equivalent in the form of a linguistic term of the general trend from the set GT= {"fall", "stability", "growth" and "fluctuation "}. In this case, the set of corresponding time series Y {X s } is divided into subsets, or clusters of main trends:
Third step. The numerical clustering of time series X s from the clusters of Yfall , Ygrowth , Ystab , Yfluct based on the transformation of each time series X s Y into the parameter vector Z s .
A) Obtaining the parameter vector Z s for each X s Y . Grouping values of each initial time series X s on N1 clusters. Then barycentres of clusters, which are considered as parameters of time series, are calculated. Then the time series of parameters Z s is built from the barycentres sorted in chronological order. Upon that, the set Z {Zs} of vectors composed of the obtained parameters is divided into (3) clusters of main trends
(5) corresponding to the original time series from the sets Yfall , Ygrowth , Ystab , Yfluct in accordance with the partition of the set Y to the subsets from step 2.
B) Clustering of the vectors Z s from the sets Z fall , Z growth , Zstab , Z fluct to N 2 clusters. Output is the clusters CkDynamic which elements are time series X s , where N 2 k 4 * N 2 . Note that the values of N1 and N 2 are set by users. This setting is made due to the N 2 parameter. The values of N 2 8 correspond to the super-high intra-cluster similarity of time series requirement, up to full visual correspondence at the level of local trends. Values N2 0,1, 2,.., 4 – meet the requirement of low intracluster similarity of time series.
FBC-clustering algorithm has a high level of modularity, any numeric clustering methods can be used for 3rd step of clustering, including fuzzy ones. The proposed solution of the clustering problem for software development processes based on FBC-approach makes it possible to cluster software development processes for time series of different dimensions, scope and diapason; it also increases the information content of time series clustering in comparison with numerical methods, as it extracts knowledge about types of time series behavior.
The main purpose of the experimental study of the proposed approach is to show its usefulness for
clustering the software development metrics using the FBC-approach [
Experiment 1. The goal of the Experiment 1 was to obtain clusters of software development processes based on FBC-approach of time series by metrics represented in the form of a number of commits for various projects and their versions from Git repositories to identify homogeneous groups of projects with similar dynamics, giving to groups of linguistic assessments used to plan and manage software development processes.
The experiment uses data from 142 time series of daily commits for various projects and their versions from Git repositories of 3 projects: MongoDB (10 years of development, [https://github.com/mongodb/mongo.git]); Libvideo - 3 years of development [https://github.com/i3arnon/libvideo.git]; ProjectUD - 10 days of development [https://github.com/Anton7393/ProjectUD.git].
Commits of the form (Hesh Commit No, the name of the branch, the author of the commit, the date of the commit, for example, “2d700d9 | 1.8 | Anton 7393 | 2016-07-08 13:36:01 +0400 | ^)” have been received from Git repositories. Based on that data, a set of static metrics for projects from the Git repository was obtained by preprocessing: the number of commits, the number of branches, the number of developers, the average time between commits, the time of project development, etc. With the help of pre-processing the data, time series were obtained for employees, years, months, days, hours. These time series extracted from the specified sources, have different lengths and different main trends.
Application of the first step of FBC-approach ensured separation of 142 time series of commits to different projects into 4 groups of time series according to their main trends: "chaos" with 63 time series, "fluctuation" with 32 time series, "fall" with 33 time series, "growth" with 14 time series. At the second step of FBC-approach, further decomposition of each group of time series into the number of clusters equal to one-third of the total number in the corresponding group was carried out. Clustering was carried out for normalized time series using the centroid method, the single connection method, and the Ward method. Figure 2 shows examples of clusters of time series obtained with the help of FBC-approach. The OX axis shows the normalized number of days, and the OY axis shows the normalized number of commits per day.
FBC-approach with the use of the Ward method gave within each cluster of trends from 3 to 4 clusters of non-unit size, examples of which are shown in figure 2, and several single clusters. Namely, with the general trends "fall" were formed 4 single clusters and 4 clusters with 7, 4, 3 and 15 time series (figure 2a). In the cluster of "growth" trends 3 clusters with 3, 4 and 6 time series were found (figure 2b). The cluster of "chaos" trends consists of 15 single clusters and 3 clusters with 7, 9 and 32 time series (figure 2c). The cluster of "fluctuation" trends involves 4 single clusters and 4 clusters with of 7, 6, 4 and 15 time series (figure 2d).
So, in terms of the time series of daily commits, the following knowledge about change of software projects in accordance to main tendency were obtained using proposed clustering with Ward method: 44% of the projects tends to be "chaos", 23% of projects has the trend "fluctuation", 23% of projects are characterized by the trend "fall", only 10% of projects are developed in direction of "growth".
When FBC-approach was used with the centroid method or the single-linkage method, one cluster collects most of the time series, a plurality of clusters of unit capacity is also obtained, and one or two clusters collect from 2 to 3 time series. As the number of clusters increases single clusters continue to be outlay from the total mass. That is, these methods are good for detecting abnormal time series far from the main group. Single clusters require management attention as being abnormal. They can be used to search for software projects with atypical development process.
Another findings is that FBC-approach with the use of the centroid method, the single-linkage and the Ward method formed different clusters of time series with intersections. It is customary to select the static clustering method for a researcher's task in the practice of applying methods of clustering. Moreover, the Ward method is used to obtain spherical embedded clusters. The centroid method is good for finding anomalies. In our experiment 1, the method of single-linkage gave better results if the task was to identify time series that are similar to accuracy of compression, stretching, shifts, and symmetry of sections.
Experiment 2. The goal of the Experiment 2 is to obtain clusters of software development processes based on FBC-clustering of time series by metrics represented by the number of commits of individual developer in software projects from mention above Git repositories. We hoped to identify homogeneous groups of developers with similar dynamics in the work, giving to project teams of linguistic estimates used for planning and management of software development processes.
The initial data of the experiment are: 34 developers, 34 time series, 11 clusters, the length of time series is different and is a term of participation in the projects. One value of time series is the number of commits per day (axis OY is the normalized number of commits, and axis OX is the normalized number of days).
Figure 3 shows some results of FBC-clustering with the single-linkage clustering. The result of the application of FBC-clustering with dividing time series by behavior and density allows us to extract the following knowledge:
Five software developers decrease their activity. Two clusters C1 and C2 with a falling trend containing 2 and 3 time series of software project metrics (see figure 3a).
Five software developers increase their activity. Two clusters with a general trend of "growth" (with 4 and 1 time series) were obtained (cluster C3 with 4 time series is depicted on the figure 3b).
The activity of fifteen software developers characterized by non-regular fluctuations. Four clusters of the "chaos" trend for 9, 4, 1 and 1 time series (cluster 4 with 9 time series and cluster C5 with 4 time series are depicted on the figure 3c).
Nine software developers characterized by regular fluctuations. Three clusters with the trend "fluctuation", including 7, 1 and 1 time series (figure 3d shows the cluster D6 with 7 time series). By assigning to software developers the tasks suitable for this cluster, it is possible to stimulate professional growth if the developer's parameters are below the average ones for the cluster or decreasing. We can form a development vector to go to another cluster, if the parameters are higher than the average ones for the cluster. Clustering methods are used to search for anomalous objects (in this experiment, they are clusters of unit capacity), which, in particular, is suitable for "searching for talents".
Table 1 shows the inter-cluster distances (Euclidean distances between the centers of the clusters were used).
C1 C2 707 1148
0 860 698 736 860 0 Table 1 characterizes the mutual distance and scattering of cluster centers by data sets.
Inter-cluster distances are not homogeneous, what allows us to suggest, in the case of clusters, similarity of sets of control actions. The use of the first step of FBC-approach with division by general trends clusters made it possible to obtain clusters slightly different in their inter-cluster distances, but differing in the general trend of behavior.
Evaluation of the FBC-clustering results effectiveness was carried out using such indexes for
clustering results evaluation as “The Ball-Hall index” and “Calinski-Harabasz index” [
The FBC-approach application for the software projects analysis has shown the availability of the proposed grouping tools which allow us to identify on the basis of metrics from the software repository, homogeneous groups of software projects with similar behavior of key metrics. The FBCapproach can be used by software project managers, lead programmers, system administrators to improve the quality of project planning based on the extracted information.
In this paper the machine learning task of software project clustering is considered, described and solved using FBC-approach. The scheme and the adopted technique of FBC-approach are provided for clustering of temporal software metrics? Which could be of different length, behavior and diapason. The advantage of the FBC-approach is that it allows us to identify, on the basis of data from the repository, homogeneous groups with similar dynamics of key software metrics. The proposed approach showed their performance capabilities and efficiency in the clustering of software development processes according to the repository metrics presented by time series. The clustering of software development processes based on the repository metrics presented by time series describing the state and behavior of a system, will allow solving tasks on improving the practice of software development, planning, revealing numerical relationships of quality, cost of the project based on key metrics of the development process; identification of where efforts are made, where defects occur; revealing the influence of technological, process, and organizational aspects on the result. Grouping of dynamically changing key software development metrics allows us to identify groups of related processes, assign labels to classes, use results in order to search for anomalies and defects, and to build forecasts, what will be used in making managerial decisions.
The Future work will be focused on the study of using the domain knowledge in the form of domain ontology to produce the linguistic summarization of proposed machine learning results.
The authors acknowledge that this paper was partially supported by the Russian Foundation of Basic Research, projects № 16-07-00535 and № 16-47-730715.