2,306 research outputs found
Multidimensional Scaling on Multiple Input Distance Matrices
Multidimensional Scaling (MDS) is a classic technique that seeks vectorial
representations for data points, given the pairwise distances between them.
However, in recent years, data are usually collected from diverse sources or
have multiple heterogeneous representations. How to do multidimensional scaling
on multiple input distance matrices is still unsolved to our best knowledge. In
this paper, we first define this new task formally. Then, we propose a new
algorithm called Multi-View Multidimensional Scaling (MVMDS) by considering
each input distance matrix as one view. Our algorithm is able to learn the
weights of views (i.e., distance matrices) automatically by exploring the
consensus information and complementary nature of views. Experimental results
on synthetic as well as real datasets demonstrate the effectiveness of MVMDS.
We hope that our work encourages a wider consideration in many domains where
MDS is needed
Euclidean Distance Matrices: Essential Theory, Algorithms and Applications
Euclidean distance matrices (EDM) are matrices of squared distances between
points. The definition is deceivingly simple: thanks to their many useful
properties they have found applications in psychometrics, crystallography,
machine learning, wireless sensor networks, acoustics, and more. Despite the
usefulness of EDMs, they seem to be insufficiently known in the signal
processing community. Our goal is to rectify this mishap in a concise tutorial.
We review the fundamental properties of EDMs, such as rank or
(non)definiteness. We show how various EDM properties can be used to design
algorithms for completing and denoising distance data. Along the way, we
demonstrate applications to microphone position calibration, ultrasound
tomography, room reconstruction from echoes and phase retrieval. By spelling
out the essential algorithms, we hope to fast-track the readers in applying
EDMs to their own problems. Matlab code for all the described algorithms, and
to generate the figures in the paper, is available online. Finally, we suggest
directions for further research.Comment: - 17 pages, 12 figures, to appear in IEEE Signal Processing Magazine
- change of title in the last revisio
Social Network Analysis with sna
Modern social network analysis---the analysis of relational data arising from social systems---is a computationally intensive area of research. Here, we provide an overview of a software package which provides support for a range of network analytic functionality within the R statistical computing environment. General categories of currently supported functionality are described, and brief examples of package syntax and usage are shown.
On the Construction of Near-MDS Matrices
The optimal branch number of MDS matrices makes them a preferred choice for
designing diffusion layers in many block ciphers and hash functions. However,
in lightweight cryptography, Near-MDS (NMDS) matrices with sub-optimal branch
numbers offer a better balance between security and efficiency as a diffusion
layer, compared to MDS matrices. In this paper, we study NMDS matrices,
exploring their construction in both recursive and nonrecursive settings. We
provide several theoretical results and explore the hardware efficiency of the
construction of NMDS matrices. Additionally, we make comparisons between the
results of NMDS and MDS matrices whenever possible. For the recursive approach,
we study the DLS matrices and provide some theoretical results on their use.
Some of the results are used to restrict the search space of the DLS matrices.
We also show that over a field of characteristic 2, any sparse matrix of order
with fixed XOR value of 1 cannot be an NMDS when raised to a power of
. Following that, we use the generalized DLS (GDLS) matrices to
provide some lightweight recursive NMDS matrices of several orders that perform
better than the existing matrices in terms of hardware cost or the number of
iterations. For the nonrecursive construction of NMDS matrices, we study
various structures, such as circulant and left-circulant matrices, and their
generalizations: Toeplitz and Hankel matrices. In addition, we prove that
Toeplitz matrices of order cannot be simultaneously NMDS and involutory
over a field of characteristic 2. Finally, we use GDLS matrices to provide some
lightweight NMDS matrices that can be computed in one clock cycle. The proposed
nonrecursive NMDS matrices of orders 4, 5, 6, 7, and 8 can be implemented with
24, 50, 65, 96, and 108 XORs over , respectively
Getting Things in Order: An Introduction to the R Package seriation
Seriation, i.e., finding a suitable linear order for a set of objects given data and a loss or merit function, is a basic problem in data analysis. Caused by the problem's combinatorial nature, it is hard to solve for all but very small sets. Nevertheless, both exact solution methods and heuristics are available. In this paper we present the package seriation which provides an infrastructure for seriation with R. The infrastructure comprises data structures to represent linear orders as permutation vectors, a wide array of seriation methods using a consistent interface, a method to calculate the value of various loss and merit functions, and several visualization techniques which build on seriation. To illustrate how easily the package can be applied for a variety of applications, a comprehensive collection of examples is presented.
О построении циркулянтных матриц, связанных с MDS-матрицами
The objective of this paper is to suggest a method of the construction of circulant ma-trices, which are appropriate for being MDS (Maximum Distance Separable) matrices utilising in cryptography. Thus, we focus on designing so-called bi-regular circulant matrices, and furthermore, impose additional restraints on matrices in order that they have the maximal number of some element occurrences and the minimal number of distinct elements. The reason to construct bi-regular matrices is that any MDS matrix is necessarily the bi-regular one, and two additional restraints on matrix elements grant that matrix-vector multiplication for the samples constructed may be performed effciently. The results obtained include an upper bound on the number of some ele-ment occurrences for which the circulant matrix is bi-regular. Furthermore, necessary and sucient conditions for the circulant matrix bi-regularity are derived. On the ba-sis of these conditions, we developed an effcient bi-regularity verication procedure. Additionally, several bi-regular circulant matrix layouts of order up to 31 with the maximal number of some element occurrences are listed. In particular, it appeared that there are no layouts of order 32 with more than 5 occurrences of any element which yield a bi-regular matrix (and hence an MDS matrix)
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