38,803 research outputs found
On Axiomatization of Inconsistency Indicators for Pairwise Comparisons
We examine the notion of inconsistency in pairwise comparisons and propose an
axiomatization which is independent of any method of approximation or the
inconsistency indicator definition (e.g., Analytic Hierarchy Process, AHP). It
has been proven that the eigenvalue-based inconsistency (proposed as a part of
AHP) is incorrect.Comment: Enhanced text, with 21 pages and 3 figures, proves that arbitrarily
inaccurate pairwise matrices are considered acceptable by theories with a
inconsistency based on the principal eigenvalue (e.g., AHP). CPC (corner
pairwise comparisons) matrix is the crucial part of this study as it
invalidates any eigenvalue-based inconsistency. All comments are highly
appreciate
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
Notes on the existence of solutions in the pairwise comparisons method using the Heuristic Rating Estimation approach
Pairwise comparisons are a well-known method for modelling of the subjective
preferences of a decision maker. A popular implementation of the method is
based on solving an eigenvalue problem for M - the matrix of pairwise
comparisons. This does not take into account the actual values of preference.
The Heuristic Rating Estimation (HRE) approach is a modification of this method
in which allows modelling of the reference values. To determine the relative
order of preferences is to solve a certain linear equation system defined by
the matrix A and the constant term vector b (both derived from M). The article
explores the properties of these equation systems. In particular, it is proven
that for some small data inconsistency the A matrix is an M-matrix, hence the
equation proposed by the HRE approach has a unique strictly positive solution.Comment: 8 page
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