15,652 research outputs found
Surface Comparison with Mass Transportation
We use mass-transportation as a tool to compare surfaces (2-manifolds). In
particular, we determine the "similarity" of two given surfaces by solving a
mass-transportation problem between their conformal densities. This mass
transportation problem differs from the standard case in that we require the
solution to be invariant under global M\"obius transformations. Our approach
provides a constructive way of defining a metric in the abstract space of
simply-connected smooth surfaces with boundary (i.e. surfaces of disk-type);
this metric can also be used to define meaningful intrinsic distances between
pairs of "patches" in the two surfaces, which allows automatic alignment of the
surfaces. We provide numerical experiments on "real-life" surfaces to
demonstrate possible applications in natural sciences
Supervised classification and mathematical optimization
Data Mining techniques often ask for the resolution of optimization problems. Supervised Classification, and, in particular, Support Vector Machines, can be seen as a paradigmatic instance. In this paper, some links between Mathematical Optimization methods and Supervised Classification are emphasized. It is shown that many different areas of Mathematical Optimization play a central role in off-the-shelf Supervised Classification methods. Moreover, Mathematical Optimization turns out to be extremely
useful to address important issues in Classification, such as identifying relevant variables, improving the interpretability of classifiers or dealing with vagueness/noise in the data.Ministerio de Ciencia e InnovaciónJunta de Andalucí
Supervised Classification and Mathematical Optimization
Data Mining techniques often ask for the resolution of optimization problems. Supervised Classification, and, in particular, Support Vector Machines, can be seen as a paradigmatic instance. In this paper, some links between Mathematical Optimization methods and Supervised Classification are emphasized. It is shown that many different areas of Mathematical Optimization play a central role in off-the-shelf Supervised Classification methods. Moreover, Mathematical Optimization turns out to be extremely useful to address important issues in Classification, such as identifying relevant variables, improving the interpretability of classifiers or dealing with vagueness/noise in the data
Learning and Interpreting Multi-Multi-Instance Learning Networks
We introduce an extension of the multi-instance learning problem where
examples are organized as nested bags of instances (e.g., a document could be
represented as a bag of sentences, which in turn are bags of words). This
framework can be useful in various scenarios, such as text and image
classification, but also supervised learning over graphs. As a further
advantage, multi-multi instance learning enables a particular way of
interpreting predictions and the decision function. Our approach is based on a
special neural network layer, called bag-layer, whose units aggregate bags of
inputs of arbitrary size. We prove theoretically that the associated class of
functions contains all Boolean functions over sets of sets of instances and we
provide empirical evidence that functions of this kind can be actually learned
on semi-synthetic datasets. We finally present experiments on text
classification, on citation graphs, and social graph data, which show that our
model obtains competitive results with respect to accuracy when compared to
other approaches such as convolutional networks on graphs, while at the same
time it supports a general approach to interpret the learnt model, as well as
explain individual predictions.Comment: JML
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Gait recognition using HMMs and dual discriminative observations for sub-dynamics analysis
This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.We propose a new gait recognition method that combines holistic and model-based features. Both types of features are extracted automatically from gait silhouette sequences and their combination takes place by means of a pair of hidden Markov models. In the proposed system, the holistic features are initially used for capturing general gait dynamics whereas, subsequently, the model-based features are deployed for capturing more detailed sub-dynamics by refining upon the preceding general dynamics. Furthermore, the holistic and model-based features are suitably processed in order to improve the discriminatory capacity of the final system. The experimental results show that the proposed method exhibits performance advantages in comparison with popular existing methods
Stem-Like Adaptive Aneuploidy and Cancer Quasispecies
We analyze and reinterpret experimental evidence from the literature to argue
for an ability of tumor cells to self-regulate their aneuploidy rate. We
conjecture that this ability is mediated by a diversification factor that
exploits molecular mechanisms common to embryo stem cells and, to a lesser
extent, adult stem cells, that is eventually reactivated in tumor cells.
Moreover, we propose a direct use of the quasispecies model to cancer cells
based on their significant genomic instability (i.e. aneuploidy rate), by
defining master sequences lengths as the sum of all copy numbers of physically
distinct whole and fragmented chromosomes. We compute an approximate error
threshold such that any aneuploidy rate larger than the threshold would lead to
a loss of fitness of a tumor population, and we confirm that highly aneuploid
cancer populations already function with aneuploidy rates close to the
estimated threshold
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