26,377 research outputs found
Efficient weight vectors from pairwise comparison matrices
Pairwise comparison matrices are frequently applied in multi-criteria
decision making. A weight vector is called efficient if no other weight vector
is at least as good in approximating the elements of the pairwise comparison
matrix, and strictly better in at least one position. A weight vector is weakly
efficient if the pairwise ratios cannot be improved in all non-diagonal
positions. We show that the principal eigenvector is always weakly efficient,
but numerical examples show that it can be inefficient. The linear programs
proposed test whether a given weight vector is (weakly) efficient, and in case
of (strong) inefficiency, an efficient (strongly) dominating weight vector is
calculated. The proposed algorithms are implemented in Pairwise Comparison
Matrix Calculator, available at pcmc.online.Comment: 19 page
Unsupervised Representation Learning with Minimax Distance Measures
We investigate the use of Minimax distances to extract in a nonparametric way
the features that capture the unknown underlying patterns and structures in the
data. We develop a general-purpose and computationally efficient framework to
employ Minimax distances with many machine learning methods that perform on
numerical data. We study both computing the pairwise Minimax distances for all
pairs of objects and as well as computing the Minimax distances of all the
objects to/from a fixed (test) object.
We first efficiently compute the pairwise Minimax distances between the
objects, using the equivalence of Minimax distances over a graph and over a
minimum spanning tree constructed on that. Then, we perform an embedding of the
pairwise Minimax distances into a new vector space, such that their squared
Euclidean distances in the new space equal to the pairwise Minimax distances in
the original space. We also study the case of having multiple pairwise Minimax
matrices, instead of a single one. Thereby, we propose an embedding via first
summing up the centered matrices and then performing an eigenvalue
decomposition to obtain the relevant features.
In the following, we study computing Minimax distances from a fixed (test)
object which can be used for instance in K-nearest neighbor search. Similar to
the case of all-pair pairwise Minimax distances, we develop an efficient and
general-purpose algorithm that is applicable with any arbitrary base distance
measure. Moreover, we investigate in detail the edges selected by the Minimax
distances and thereby explore the ability of Minimax distances in detecting
outlier objects.
Finally, for each setting, we perform several experiments to demonstrate the
effectiveness of our framework.Comment: 32 page
Pattern vectors from algebraic graph theory
Graphstructures have proven computationally cumbersome for pattern analysis. The reason for this is that, before graphs can be converted to pattern vectors, correspondences must be established between the nodes of structures which are potentially of different size. To overcome this problem, in this paper, we turn to the spectral decomposition of the Laplacian matrix. We show how the elements of the spectral matrix for the Laplacian can be used to construct symmetric polynomials that are permutation invariants. The coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner. We extend this representation to graphs in which there are unary attributes on the nodes and binary attributes on the edges by using the spectral decomposition of a Hermitian property matrix that can be viewed as a complex analogue of the Laplacian. To embed the graphs in a pattern space, we explore whether the vectors of invariants can be embedded in a low- dimensional space using a number of alternative strategies, including principal components analysis ( PCA), multidimensional scaling ( MDS), and locality preserving projection ( LPP). Experimentally, we demonstrate that the embeddings result in well- defined graph clusters. Our experiments with the spectral representation involve both synthetic and real- world data. The experiments with synthetic data demonstrate that the distances between spectral feature vectors can be used to discriminate between graphs on the basis of their structure. The real- world experiments show that the method can be used to locate clusters of graphs
End-to-End Cross-Modality Retrieval with CCA Projections and Pairwise Ranking Loss
Cross-modality retrieval encompasses retrieval tasks where the fetched items
are of a different type than the search query, e.g., retrieving pictures
relevant to a given text query. The state-of-the-art approach to cross-modality
retrieval relies on learning a joint embedding space of the two modalities,
where items from either modality are retrieved using nearest-neighbor search.
In this work, we introduce a neural network layer based on Canonical
Correlation Analysis (CCA) that learns better embedding spaces by analytically
computing projections that maximize correlation. In contrast to previous
approaches, the CCA Layer (CCAL) allows us to combine existing objectives for
embedding space learning, such as pairwise ranking losses, with the optimal
projections of CCA. We show the effectiveness of our approach for
cross-modality retrieval on three different scenarios (text-to-image,
audio-sheet-music and zero-shot retrieval), surpassing both Deep CCA and a
multi-view network using freely learned projections optimized by a pairwise
ranking loss, especially when little training data is available (the code for
all three methods is released at: https://github.com/CPJKU/cca_layer).Comment: Preliminary version of a paper published in the International Journal
of Multimedia Information Retrieva
Pairwise comparison matrices and the error-free property of the decision maker
Pairwise comparison is a popular assessment method either for deriving criteria-weights or for evaluating alternatives according to a given criterion. In real-world applications consistency of the comparisons rarely happens: intransitivity can occur. The aim of the paper is to discuss the relationship between the consistency of the decision maker—described with the error-free property—and the consistency of the pairwise comparison matrix (PCM). The concept of error-free matrix is used to demonstrate that consistency of the PCM is not a sufficient condition of the error-free property of the decision maker. Informed and uninformed decision makers are defined. In the first stage of an assessment method a consistent or near-consistent matrix should be achieved: detecting, measuring and improving consistency are part of any procedure with both types of decision makers. In the second stage additional information are needed to reveal the decision maker’s real preferences. Interactive questioning procedures are recommended to reach that goal
Environmental, human health and socio-economic effects of cement powders: The multicriteria analysis as decisional methodology
The attention to sustainability-related issues has grown fast in recent decades. The experience gained with these themes reveals the importance of considering this topic in the construction industry, which represents an important sector throughout the world. This work consists on conducting a multicriteria analysis of four cement powders, with the objective of calculating and analysing the environmental, human health and socio-economic effects of their production processes. The economic, technical, environmental and safety performances of the examined powders result from official, both internal and public, documents prepared by the producers. The Analytic Hierarchy Process permitted to consider several indicators (i.e., environmental, human health related and socio-economic parameters) and to conduct comprehensive and unbiased analyses which gave the best, most sustainable cement powder. As assumed in this study, the contribution of each considered parameter to the overall sustainability has a different incidence, therefore the procedure could be used to support on-going sustainability efforts under different conditions. The results also prove that it is not appropriate to regard only one parameter to identify the ‘best’ cement powder, but several impact categories should be considered and analysed if there is an interest for pursuing different, often conflicting interests
Multimodal Network Alignment
A multimodal network encodes relationships between the same set of nodes in
multiple settings, and network alignment is a powerful tool for transferring
information and insight between a pair of networks. We propose a method for
multimodal network alignment that computes a matrix which indicates the
alignment, but produces the result as a low-rank factorization directly. We
then propose new methods to compute approximate maximum weight matchings of
low-rank matrices to produce an alignment. We evaluate our approach by applying
it on synthetic networks and use it to de-anonymize a multimodal transportation
network.Comment: 14 pages, 6 figures, Siam Data Mining 201
Nonlinear Matroid Optimization and Experimental Design
We study the problem of optimizing nonlinear objective functions over
matroids presented by oracles or explicitly. Such functions can be interpreted
as the balancing of multi-criteria optimization. We provide a combinatorial
polynomial time algorithm for arbitrary oracle-presented matroids, that makes
repeated use of matroid intersection, and an algebraic algorithm for vectorial
matroids.
Our work is partly motivated by applications to minimum-aberration
model-fitting in experimental design in statistics, which we discuss and
demonstrate in detail
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