Archive for the ‘Multidimensional’ Category

circlize implements and enhances circular visualization in R

Wednesday, July 2nd, 2014

circlize implements and enhances circular visualization in R by Zuguang Gu, et al.


Summary: Circular layout is an efficient way for the visualization of huge amounts of genomic information. Here we present the circlize package, which provides an implementation of circular layout generation in R as well as an enhancement of available software. The flexibility of this package is based on the usage of low-level graphics functions such that self-defined high-level graphics can be easily implemented by users for specific purposes. Together with the seamless connection between the powerful computational and visual environment in R, circlize gives users more convenience and freedom to design figures for better understanding genomic patterns behind multi-dimensional data.

Availability and implementation: circlize is available at the Comprehensive R Archive Network (CRAN):

The article is behind a paywall but fortunately, the R code is not!

I suspect I know which one will get more “hits.” 😉

Useful for exploring multidimensional data as well as presenting multidimensional data encoded using a topic map.

Sometimes displaying information as nodes and edges isn’t the best display.

Remember the map of Napoleon’s invasion of Russia?

napoleon - russia

You could display the same information with nodes (topics) and associations (edges) but it would not be nearly as compelling.

Although, you could make the same map a “cover” for the topics (read people) associated with segments of the map, enabling a reader to take in the whole map and then drill down to the detail for any location or individual.

It would still be a topic map, even though its primary rendering would not be as nodes and edges.

“You Know Because I Know”

Friday, May 31st, 2013

“You Know Because I Know”: a Multidimensional Network Approach to Human Resources Problem by Michele Coscia, Giulio Rossetti, Diego Pennacchioli, Damiano Ceccarelli, Fosca Giannotti.


Finding talents, often among the people already hired, is an endemic challenge for organizations. The social networking revolution, with online tools like Linkedin, made possible to make explicit and accessible what we perceived, but not used, for thousands of years: the exact position and ranking of a person in a network of professional and personal connections. To search and mine where and how an employee is positioned on a global skill network will enable organizations to find unpredictable sources of knowledge, innovation and know-how. This data richness and hidden knowledge demands for a multidimensional and multiskill approach to the network ranking problem. Multidimensional networks are networks with multiple kinds of relations. To the best of our knowledge, no network-based ranking algorithm is able to handle multidimensional networks and multiple rankings over multiple attributes at the same time. In this paper we propose such an algorithm, whose aim is to address the node multi-ranking problem in multidimensional networks. We test our algorithm over several real world networks, extracted from DBLP and the Enron email corpus, and we show its usefulness in providing less trivial and more flexible rankings than the current state of the art algorithms.

Although framed in a human resources context, it isn’t much of a jump to see this work as applicable to other multidimensional networks.

Including multidimensional networks of properties that define subject identities.

An Indexing Structure for Dynamic Multidimensional Data in Vector Space

Saturday, September 1st, 2012

An Indexing Structure for Dynamic Multidimensional Data in Vector Space by Elena Mikhaylova, Boris Novikov and Anton Volokhov. (Advances in Databases and Information Systems, Advances in Intelligent Systems and Computing, 2013, Volume 186, 185-193, DOI: 10.1007/978-3-642-32741-4_17)


The multidimensional k – NN (k nearest neighbors) query problem is relevant to a large variety of database applications, including information retrieval, natural language processing, and data mining. To solve it efficiently, the database needs an indexing structure that provides this kind of search. However, attempts to find an exact solution are hardly feasible in multidimensional space. In this paper, a novel indexing technique for the approximate solution of k – NN problem is described and analyzed. The construction of the indexing tree is based on clustering. Indexing structure is implemented on top of high-performance industrial DBMS.

The review of recent work is helpful but when the paper reaches the algorithm for indexing “…dynamic multidimensional data…,” it slips away from me.

Where is the dynamic nature of the data that is being overcome by the indexing?

I ask because we are human observers are untroubled by the curse of dimensionality, even when data is dynamically changing.

Although those are two important aspects when we process it by machine:

  • The number of dimensions of data, and
  • The rate at which the data is changing.

Optimal simultaneous superpositioning of multiple structures with missing data

Friday, July 20th, 2012

Optimal simultaneous superpositioning of multiple structures with missing data (Douglas L. Theobald and Phillip A. Steindel Optimal simultaneous superpositioning of multiple structures with missing data Bioinformatics 2012 28: 1972-1979. )


Motivation: Superpositioning is an essential technique in structural biology that facilitates the comparison and analysis of conformational differences among topologically similar structures. Performing a superposition requires a one-to-one correspondence, or alignment, of the point sets in the different structures. However, in practice, some points are usually ‘missing’ from several structures, for example, when the alignment contains gaps. Current superposition methods deal with missing data simply by superpositioning a subset of points that are shared among all the structures. This practice is inefficient, as it ignores important data, and it fails to satisfy the common least-squares criterion. In the extreme, disregarding missing positions prohibits the calculation of a superposition altogether.

Results: Here, we present a general solution for determining an optimal superposition when some of the data are missing. We use the expectation–maximization algorithm, a classic statistical technique for dealing with incomplete data, to find both maximum-likelihood solutions and the optimal least-squares solution as a special case.

Availability and implementation: The methods presented here are implemented in THESEUS 2.0, a program for superpositioning macromolecular structures. ANSI C source code and selected compiled binaries for various computing platforms are freely available under the GNU open source license from


Supplementary information: Supplementary data are available at Bioinformatics online.

From the introduction:

How should we properly compare and contrast the 3D conformations of similar structures? This fundamental problem in structural biology is commonly addressed by performing a superposition, which removes arbitrary differences in translation and rotation so that a set of structures is oriented in a common reference frame (Flower, 1999). For instance, the conventional solution to the superpositioning problem uses the least-squares optimality criterion, which orients the structures in space so as to minimize the sum of the squared distances between all corresponding points in the different structures. Superpositioning problems, also known as Procrustes problems, arise frequently in many scientific fields, including anthropology, archaeology, astronomy, computer vision, economics, evolutionary biology, geology, image analysis, medicine, morphometrics, paleontology, psychology and molecular biology (Dryden and Mardia, 1998; Gower and Dijksterhuis, 2004; Lele and Richtsmeier, 2001). A particular case we consider here is the superpositioning of multiple 3D macromolecular coordinate sets, where the points to be superpositioned correspond to atoms. Although our analysis specifically concerns the conformations of macromolecules, the methods developed herein are generally applicable to any entity that can be represented as a set of Cartesian points in a multidimensional space, whether the particular structures under study are proteins, skulls, MRI scans or geological strata.

We draw an important distinction here between a structural ‘alignment’ and a ‘superposition.’ An alignment is a discrete mapping between the residues of two or more structures. One of the most common ways to represent an alignment is using the familiar row and column matrix format of sequence alignments using the single letter abbreviations for residues (Fig. 1). An alignment may be based on sequence information or on structural information (or on both). A superposition, on the other hand, is a particular orientation of structures in 3D space. [emphasis added]

I have deep reservations about the representations of semantics using Cartesian metrics but in fact that happens quite frequently. And allegedly, usefully.

Leaving my doubts to one side, this superpositioning technique could prove to be a useful exploration technique.

If you experiment with this technique, a report of your experiences would be appreciated.


Saturday, April 9th, 2011


Jack Park forwarded this to my attention.

I am puzzling over:

At its core, the Globals database is powered by an extremely efficient multidimensional data engine. The exposed interface support access to the multidimensional structures – providing the highest performance and greatest range of storage possibilities. A multitude of applications can be implemented entirely using this data engine directly.

There is no data dictionary, and thus no data definitions, for the multidimensional data engine.

I “get” the part about extremely efficient multidimensional data engine (they say it often enough) but am curious why there is no data dictionary? Or at least why is that a claim to put up front?

Granting that I don’t consider data dictionaries to be self-describing but then neither are multidimensional arrays. Necessarily.

This database apparently lies at the core of a commercial application or line of commercial applications by Intersystems Corporation.