Parallel Coordinate Plots

Abstrak— Salah satu upaya dalam meningkatkan kualitas pendidikan matematika adalah melalui peningkatan kualitas guru dan calon guru matematika. Banyak program yang telah dilaksanakan baik oleh pemerintah maupun LPTK untuk meningkatkan kualitas guru matematika, namun peningkatan kualitas calon guru matematika belum mendapat perhatian yang cukup. Isu yang berkembang dalam proses peningkatan kualitas mahasiswa calon guru matematika banyak terkait dengan kurikulum yang secara khusus mengacu pada kemampuan pedagogis dan kemampuan didaktis yang harus dikuasai oleh para calon guru matematika. Terkait dengan kemampuan didaktis, perdebatan tentang konsep-konsep matematika yang perlu dipelajari calon guru masih menjadi topik yang menarik untuk dikaji. Suatu ide tentang konsep matematika non-konvensional akan dikaji dalam tulisan ini. Analisis dan argumentasi tentang konsep matematika non-konvensional dengan topik koordinat paralel dipaparkan. Urgensi dari konsep koordinat paralel untuk para calon guru matematika dikemukakan berdasarkan hasil kajian literatur yang komprehensif. Selain itu, analisis tentang peranan konsep matematika non-konvensional, khususnya koordinat paralel, dalam mengembangkan proses abstraksi matematis juga dibahas. Pada akhirnya diperoleh kesimpulan bahwa  konsep koordinat paralel sebagai salah satu konsep matematika non-konvensional jika ditinjau dari perspektif pengembangan kurikulum di lembaga penghasil guru matematika, dapat disisipkan pada mata kuliah geometri analitik atau kalkulus guna mengembangkan proses abstraksi matematis mahasiswa calon guru matematika.

Kata kunci: konsep non-konvensional, koordinat paralel, proses abstraksi

Parallel Coordinates are a widely used visualization method for multivariate data analysis tasks. In this paper we discuss the techniques that aim to enhance the representation of categorical data in Parallel Coordinates. We propose Parallel Bubbles, a method that improves the graphical perception of categorical dimensions in Parallel Coordinates by adding a visual encoding of frequency. Our main contribution consists in a user study that compares the performance of three variants of Parallel Coordinates, with similarity and frequency tasks. We base our design choices on the literature review, and on the research guidelines provided by Johansson and Forsell (2016). Parallel Bubbles are a good trade-off between Parallel Coordinates and Parallel Sets in terms of performance for both types of tasks. Adding a visual encoding of frequency leads to a significant difference in performance for a frequency-based task consisting in assessing the most represented category. This study is the first of a series that will aim at testing the three visualization methods in tasks centered on the continuous axis, and where we assume that the performance of Parallel Sets will be worse.

Monte Carlo simulations combined with regionalized sensitivity analysis provide the means to explore a vast, multivariate design space in building design. Typically, sensitivity analysis shows how the variability of model output relates to the uncertainties in models inputs. This reveals which simulation inputs are most important and which have negligible influence on the model output. Popular sensitivity methods include the Morris method, variance-based methods (e.g. Sobol’s), and regression methods (e.g. SRC). However, such methods only address one output at a time, which makes it difficult to prioritize and fixate inputs when considering multiple outputs. In this work, the primary outcome is a novel sensitivity method denoted TOM, which relies on Kolmogorov-Smirnov two-sample (KS2) statistics to rank inputs due to their influence on multiple outputs. A secondary method, denoted TOR, provides a real-time sensitivity measure when exploring data with the interactive parallel coordinate plot (PCP). The latter is an effective tool to explore stochastic simulations and to find high-performing building designs. The proposed methods help decision makers to focus their attention to the most important design parameters. As case study, we consider building performance simulations of a 15.000 m² educational centre with respect to energy demand, thermal comfort, and daylight.