Criteria for choosing the number of dimensions in a principal component analysis: An empirical assessment

Principal component analysis (PCA) is an efficient model for the optimization problem of finding d' axes of a subspace Rd' ⊆ Rd so that the mean squared distances from a given set R of points to the axes are minimal. Despite being steadily employed since 1901 in different scenarios, e.g., mechanics, PCA has become an important link in machine learning chained tasks, such as feature learning and AutoML designs. A frequent yet open issue that arises from supervised-based problems is how many PCA axes are required for the performance of machine learning constructs to be tuned. Accordingly, we investigate the behavior of six independent and uncoupled criteria for estimating the number of PCA axes, namely Scree-Plot %, Scree Plot Gap, Kaiser-Guttman, Broken-Stick, p-Score, and 2D. In total, we evaluate the performance of those approaches in 20 high dimensional datasets by using (i) four different classifiers, and (ii) a hypothesis test upon the reported F-Measures. Results indicate Broken-Stick and Scree-Plot % criteria consistently outperformed the competitors regarding supervised-based tasks, whereas estimators Kaiser-Guttman and Scree-Plot Gap delivered poor performances in the same scenarios.

Graph-Based Software Process Management

Software process dynamics challenge the capabilities of process-centered software engineering environments. Dynamic task nets represent evolving software processes by hierarchically organized nets of tasks which are connected by control, data, and feedback flows. Project managers operate on dynamic task nets in order to assess the current status of a project, trace its history, perform impact analysis, handle feedback, adapt the project plan to changed product structures, etc. Developers are supported through task agendas and provision of tools and documents. Chained tasks may be executed in parallel (simultaneous engineering), and cooperation is controlled through releases of document versions. Dynamic task nets are formally specified by a programmed graph rewriting system. Operations on task nets are specified declaratively by graph rewrite rules at a high level of abstraction. Furthermore, editing, analysis, and execution steps on a dynamic task net, which may be interleaved seamlessly, are described in a uniform formalism.