10,935 research outputs found
Effective criteria for specific identifiability of tensors and forms
In applications where the tensor rank decomposition arises, one often relies
on its identifiability properties for interpreting the individual rank-
terms appearing in the decomposition. Several criteria for identifiability have
been proposed in the literature, however few results exist on how frequently
they are satisfied. We propose to call a criterion effective if it is satisfied
on a dense, open subset of the smallest semi-algebraic set enclosing the set of
rank- tensors. We analyze the effectiveness of Kruskal's criterion when it
is combined with reshaping. It is proved that this criterion is effective for
both real and complex tensors in its entire range of applicability, which is
usually much smaller than the smallest typical rank. Our proof explains when
reshaping-based algorithms for computing tensor rank decompositions may be
expected to recover the decomposition. Specializing the analysis to symmetric
tensors or forms reveals that the reshaped Kruskal criterion may even be
effective up to the smallest typical rank for some third, fourth and sixth
order symmetric tensors of small dimension as well as for binary forms of
degree at least three. We extended this result to symmetric tensors by analyzing the Hilbert function, resulting in a
criterion for symmetric identifiability that is effective up to symmetric rank
, which is optimal.Comment: 31 pages, 2 Macaulay2 code
Onion Curve: A Space Filling Curve with Near-Optimal Clustering
Space filling curves (SFCs) are widely used in the design of indexes for
spatial and temporal data. Clustering is a key metric for an SFC, that measures
how well the curve preserves locality in moving from higher dimensions to a
single dimension. We present the {\em onion curve}, an SFC whose clustering
performance is provably close to optimal for the cube and near-cube shaped
query sets, irrespective of the side length of the query. We show that in
contrast, the clustering performance of the widely used Hilbert curve can be
far from optimal, even for cube-shaped queries. Since the clustering
performance of an SFC is critical to the efficiency of multi-dimensional
indexes based on the SFC, the onion curve can deliver improved performance for
data structures involving multi-dimensional data.Comment: The short version is published in ICDE 1
Double Time Window Targeting Technique: Real time DMRG dynamics in the PPP model
We present a generalized adaptive time-dependent density matrix
renormalization group (DMRG) scheme, called the {\it double time window
targeting} (DTWT) technique, which gives accurate results with nominal
computational resources, within reasonable computational time. This procedure
originates from the amalgamation of the features of pace keeping DMRG
algorithm, first proposed by Luo {\it et. al}, [Phys.Rev. Lett. {\bf 91},
049701 (2003)], and the time-step targeting (TST) algorithm by Feiguin and
White [Phys. Rev. B {\bf 72}, 020404 (2005)]. Using the DTWT technique, we
study the phenomena of spin-charge separation in conjugated polymers (materials
for molecular electronics and spintronics), which have long-range
electron-electron interactions and belong to the class of strongly correlated
low-dimensional many-body systems. The issue of real time dynamics within the
Pariser-Parr-Pople (PPP) model which includes long-range electron correlations
has not been addressed in the literature so far. The present study on PPP
chains has revealed that, (i) long-range electron correlations enable both the
charge and spin degree of freedom of the electron, to propagate faster in the
PPP model compared to Hubbard model, (ii) for standard parameters of the PPP
model as applied to conjugated polymers, the charge velocity is almost twice
that of the spin velocity and, (iii) the simplistic interpretation of
long-range correlations by merely renormalizing the {\it U} value of the
Hubbard model fails to explain the dynamics of doped holes/electrons in the PPP
model.Comment: Final (published) version; 39 pages, 13 figures, 1 table; 2 new
references adde
Sparse Coding on Symmetric Positive Definite Manifolds using Bregman Divergences
This paper introduces sparse coding and dictionary learning for Symmetric
Positive Definite (SPD) matrices, which are often used in machine learning,
computer vision and related areas. Unlike traditional sparse coding schemes
that work in vector spaces, in this paper we discuss how SPD matrices can be
described by sparse combination of dictionary atoms, where the atoms are also
SPD matrices. We propose to seek sparse coding by embedding the space of SPD
matrices into Hilbert spaces through two types of Bregman matrix divergences.
This not only leads to an efficient way of performing sparse coding, but also
an online and iterative scheme for dictionary learning. We apply the proposed
methods to several computer vision tasks where images are represented by region
covariance matrices. Our proposed algorithms outperform state-of-the-art
methods on a wide range of classification tasks, including face recognition,
action recognition, material classification and texture categorization
Hybrid LSTM and Encoder-Decoder Architecture for Detection of Image Forgeries
With advanced image journaling tools, one can easily alter the semantic
meaning of an image by exploiting certain manipulation techniques such as
copy-clone, object splicing, and removal, which mislead the viewers. In
contrast, the identification of these manipulations becomes a very challenging
task as manipulated regions are not visually apparent. This paper proposes a
high-confidence manipulation localization architecture which utilizes
resampling features, Long-Short Term Memory (LSTM) cells, and encoder-decoder
network to segment out manipulated regions from non-manipulated ones.
Resampling features are used to capture artifacts like JPEG quality loss,
upsampling, downsampling, rotation, and shearing. The proposed network exploits
larger receptive fields (spatial maps) and frequency domain correlation to
analyze the discriminative characteristics between manipulated and
non-manipulated regions by incorporating encoder and LSTM network. Finally,
decoder network learns the mapping from low-resolution feature maps to
pixel-wise predictions for image tamper localization. With predicted mask
provided by final layer (softmax) of the proposed architecture, end-to-end
training is performed to learn the network parameters through back-propagation
using ground-truth masks. Furthermore, a large image splicing dataset is
introduced to guide the training process. The proposed method is capable of
localizing image manipulations at pixel level with high precision, which is
demonstrated through rigorous experimentation on three diverse datasets
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