Manuel Rubio-Sánchez

Axis Calibration for Improving Data Attribute Estimation in Star Coordinates Plots

Star coordinates is a well-known multivariate visualization method that produces linear dimensionality reduction mappings through a set of radial axes defined by vectors in an observable space. One of its main drawbacks concerns the difficulty to recover attributes of data samples accurately, which typically lie in the [0], [1] interval, given the locations of the low-dimensional embeddings and the vectors. In this paper we show that centering the data can considerably increase attribute estimation accuracy, where data values can be read off approximately by projecting embedded points onto calibrated (i.e., labeled) axes, similarly to classical statistical biplots. In addition, this idea can be coupled with a recently developed orthonormalization process on the axis vectors that prevents unnecessary distortions. We demonstrate that the combination of both approaches not only enhances the estimates, but also provides more faithful representations of the data.

Exploring recursion with fibonacci numbers

This paper addresses the relationship between recursion and combinatorial problems, which may benefit teaching recursion in CS1/2 courses. Problems whose solutions are related to Fibonacci numbers are particularly interesting, since some can be decomposed by using different strategies, which may be based on the numerous Fibonacci identities or even on the concept of mutual recursion.

GRASP with path relinking for the single row facility layout problem

The single row facility layout problem (SRFLP) is an NP -hard problem that consists of finding an optimal arrangement of a set of rectangular facilities (with equal height and different lengths), placing them next to each other along a line. The SRFLP has practical applications in contexts such as arranging rooms along corridors, setting books on shelves, allocating information on magnetic disks, storing items in warehouses, or designing layouts for machines in manufacturing systems. This paper combines the greedy randomized adaptive search procedure (GRASP) methodology, and path relinking (PR) in order to efficiently search for high-quality solutions for the SRFLP. In particular, we introduce: (i) several construction procedures, (ii) a new fast local search strategy, and (iii) an approach related to the Ulam distance in order to construct short path relinking trajectories. We also present a new set of large challenging instances, since previous sets do not allow to determine significant differences among advanced metaheuristics. Experiments show that our procedure outperforms state-of-the-art methods in all of the scenarios we considered. Firstly, the GRASP with PR finds the best known solutions for previous instances used in the literature, but employing considerably less computing time than its competitors. Secondly, our method outperforms the current state-of-the-art methods in 38 out of 40 new instances when running for the same amount of computing time. Finally, nonparametric tests for detecting differences between algorithms report p-values below 10 - 11 , which supports the superiority of our approach.

Adaptable Radial Axes Plots for Improved Multivariate Data Visualization

Radial axes plots are multivariate visualization techniques that extend scatterplots in order to represent high‐dimensional data as points on an observable display. Well‐known methods include star coordinates or principal component biplots, which represent data attributes as vectors that define axes, and produce linear dimensionality reduction mappings. In this paper we propose a hybrid approach that bridges the gap between star coordinates and principal component biplots, which we denominate “adaptable radial axes plots”. It is based on solving convex optimization problems where users can: (a) update the axis vectors interactively, as in star coordinates, while producing mappings that enable to estimate attribute values optimally through labeled axes, similarly to principal component biplots; (b) use different norms in order to explore additional nonlinear mappings of the data; and (c) include weights and constraints in the optimization problems for sorting the data along one axis. The result is a flexible technique that complements, extends, and enhances current radial methods for data analysis.

Tail recursion by using function generalization

The design of tail recursive algorithms may require thinking about iteration rather than recursion. This paper provides a methodology for deriving tail recursive functions that is based on declarative programming and the concept of function generalization, which allow to avoid iterative thinking.

An introduction to problem equivalence with combinatorics

This paper proposes the use of several classes of simple combinatorial problems that share the same solution for teaching problem equivalence and recursion. Our focus is on counting problems that involve Fibonacci numbers. While these problems have simple recursive solutions, we propose that - for teaching purposes - they can also be solved by finding other isomorphic problems for which the solution is known.

On the Use of Decision Trees Based on Diagnosis and Drug Codes for Analyzing Chronic Patients

Diabetes mellitus (DM) and essential hypertension (EH) are chronic diseases more prevalent every year, both independently and jointly. To gain insights about the particularities of these chronic conditions, we study the use of decision trees as a tool for selecting discriminative features and making predictive analyses of the health status of this kind of chronic patients. We considered gender, age, ICD9 codes for diagnosis and ATC codes for drugs associated with the diabetic and/or hypertensive population linked to the University Hospital of Fuenlabrada (Madrid, Spain) during 2012. Results show a relationship among DM/EH and diseases/drugs related to the respiratory system, mental disorders, or the musculoskeletal system. We conclude that drugs are quite informative, collecting information about the disease when the diagnosis code is not registered. Regarding predictive analyses, when discriminating patients with EH-DM and just one of these chronic conditions, better accuracy is obtained for EH (85.4%) versus DM (80.1%).

Scaled radial axes for interactive visual feature selection: A case study for analyzing chronic conditions

Abstract In statistics, machine learning, and related fields, feature selection is the process of choosing a smaller subset of features to work with. This is an important topic since selecting a subset of features can help analysts to interpret models and data, and to decrease computational runtimes. While many techniques are purely automatic, the data visualization community has produced a number of interactive approaches where users can make decisions taking into account their domain knowledge. In this paper we propose a new visualization technique based on radial axes that allows analysts to perform feature selection effectively, in contrast to previous radial axes methods. This is achieved by employing alternative scaled axes that provide insight regarding the features that have a smaller contribution to the visualizations. Therefore, analysts can use the technique to carry out interactive backwards feature elimination, by discarding the least relevant features according to the information on the plots and their expertise. Our approach can be coupled with any linear dimensionality reduction method, and can be used when performing analyses of cluster structure, correlations, class separability, etc. Specifically, in this paper we focus on combining the proposed technique with methods designed for classification. Lastly, we illustrate the effectiveness of our proposal through a case study analyzing high-dimensional medical chronic conditions data. In particular, clinicians have used the technique for determining the most important features that discriminate between patients with diabetes and high blood pressure.

Student-centered design of a parser visualization tool

There exist many visualizations tools which visualize some aspect of the compiling process. They can be separated in two groups. On the one hand there are the ones which have a clear educational aim e.g. JFlap [3]. On the other hand, there are tools which display some aspects of the parsers generated with a particular generation tool e.g. ANTLRworks. The limitations of these tools are that they depend on a particular generation tool and they offer a partial view of the parsing process. In this situation when a student/teacher needs to visualize a different aspect, has to change both, the generation and visualization tool, adapting to the new syntax notation and graphical representations. We have developed VAST [1], an educational tool to display the syntax tree and its construction process within the compiling process. One of the main advantages of VAST is its independence from the parsing technique and the parser generator. We have used VAST with: LL parsers developed with ANTLR and LALR parsers developed with CUP. VAST has passed educational and usability evaluations. Although the results of the last evaluation [2] were positive, we realized that, due to the generic approach of VAST, the user has to perform many intermediate steps until he/she produces the visualizations.