157,547 research outputs found
View subspaces for indexing and retrieval of 3D models
View-based indexing schemes for 3D object retrieval are gaining popularity
since they provide good retrieval results. These schemes are coherent with the
theory that humans recognize objects based on their 2D appearances. The
viewbased techniques also allow users to search with various queries such as
binary images, range images and even 2D sketches. The previous view-based
techniques use classical 2D shape descriptors such as Fourier invariants,
Zernike moments, Scale Invariant Feature Transform-based local features and 2D
Digital Fourier Transform coefficients. These methods describe each object
independent of others. In this work, we explore data driven subspace models,
such as Principal Component Analysis, Independent Component Analysis and
Nonnegative Matrix Factorization to describe the shape information of the
views. We treat the depth images obtained from various points of the view
sphere as 2D intensity images and train a subspace to extract the inherent
structure of the views within a database. We also show the benefit of
categorizing shapes according to their eigenvalue spread. Both the shape
categorization and data-driven feature set conjectures are tested on the PSB
database and compared with the competitor view-based 3D shape retrieval
algorithmsComment: Three-Dimensional Image Processing (3DIP) and Applications
(Proceedings Volume) Proceedings of SPIE Volume: 7526 Editor(s): Atilla M.
Baskurt ISBN: 9780819479198 Date: 2 February 201
Efficient Gauss Elimination for Near-Quadratic Matrices with One Short Random Block per Row, with Applications
In this paper we identify a new class of sparse near-quadratic random Boolean matrices that have full row rank over F_2 = {0,1} with high probability and can be transformed into echelon form in almost linear time by a simple version of Gauss elimination. The random matrix with dimensions n(1-epsilon) x n is generated as follows: In each row, identify a block of length L = O((log n)/epsilon) at a random position. The entries outside the block are 0, the entries inside the block are given by fair coin tosses. Sorting the rows according to the positions of the blocks transforms the matrix into a kind of band matrix, on which, as it turns out, Gauss elimination works very efficiently with high probability. For the proof, the effects of Gauss elimination are interpreted as a ("coin-flipping") variant of Robin Hood hashing, whose behaviour can be captured in terms of a simple Markov model from queuing theory. Bounds for expected construction time and high success probability follow from results in this area. They readily extend to larger finite fields in place of F_2.
By employing hashing, this matrix family leads to a new implementation of a retrieval data structure, which represents an arbitrary function f: S -> {0,1} for some set S of m = (1-epsilon)n keys. It requires m/(1-epsilon) bits of space, construction takes O(m/epsilon^2) expected time on a word RAM, while queries take O(1/epsilon) time and access only one contiguous segment of O((log m)/epsilon) bits in the representation (O(1/epsilon) consecutive words on a word RAM). The method is readily implemented and highly practical, and it is competitive with state-of-the-art methods. In a more theoretical variant, which works only for unrealistically large S, we can even achieve construction time O(m/epsilon) and query time O(1), accessing O(1) contiguous memory words for a query. By well-established methods the retrieval data structure leads to efficient constructions of (static) perfect hash functions and (static) Bloom filters with almost optimal space and very local storage access patterns for queries
Oracle Complexity Classes and Local Measurements on Physical Hamiltonians
The canonical problem for the class Quantum Merlin-Arthur (QMA) is that of
estimating ground state energies of local Hamiltonians. Perhaps surprisingly,
[Ambainis, CCC 2014] showed that the related, but arguably more natural,
problem of simulating local measurements on ground states of local Hamiltonians
(APX-SIM) is likely harder than QMA. Indeed, [Ambainis, CCC 2014] showed that
APX-SIM is P^QMA[log]-complete, for P^QMA[log] the class of languages decidable
by a P machine making a logarithmic number of adaptive queries to a QMA oracle.
In this work, we show that APX-SIM is P^QMA[log]-complete even when restricted
to more physical Hamiltonians, obtaining as intermediate steps a variety of
related complexity-theoretic results.
We first give a sequence of results which together yield P^QMA[log]-hardness
for APX-SIM on well-motivated Hamiltonians: (1) We show that for NP, StoqMA,
and QMA oracles, a logarithmic number of adaptive queries is equivalent to
polynomially many parallel queries. These equalities simplify the proofs of our
subsequent results. (2) Next, we show that the hardness of APX-SIM is preserved
under Hamiltonian simulations (a la [Cubitt, Montanaro, Piddock, 2017]). As a
byproduct, we obtain a full complexity classification of APX-SIM, showing it is
complete for P, P^||NP, P^||StoqMA, or P^||QMA depending on the Hamiltonians
employed. (3) Leveraging the above, we show that APX-SIM is P^QMA[log]-complete
for any family of Hamiltonians which can efficiently simulate spatially sparse
Hamiltonians, including physically motivated models such as the 2D Heisenberg
model.
Our second focus considers 1D systems: We show that APX-SIM remains
P^QMA[log]-complete even for local Hamiltonians on a 1D line of 8-dimensional
qudits. This uses a number of ideas from above, along with replacing the "query
Hamiltonian" of [Ambainis, CCC 2014] with a new "sifter" construction.Comment: 38 pages, 3 figure
A Robust Logical and Computational Characterisation of Peer-to-Peer Database Systems
In this paper we give a robust logical and computational characterisation of peer-to-peer (p2p) database systems. We first define a precise model-theoretic semantics of a p2p system, which allows for local inconsistency handling. We then characterise the general computational properties for the problem of answering queries to such a p2p system. Finally, we devise tight complexity bounds and distributed procedures for the problem of answering queries in few relevant special cases
What Can We Learn Privately?
Learning problems form an important category of computational tasks that
generalizes many of the computations researchers apply to large real-life data
sets. We ask: what concept classes can be learned privately, namely, by an
algorithm whose output does not depend too heavily on any one input or specific
training example? More precisely, we investigate learning algorithms that
satisfy differential privacy, a notion that provides strong confidentiality
guarantees in contexts where aggregate information is released about a database
containing sensitive information about individuals. We demonstrate that,
ignoring computational constraints, it is possible to privately agnostically
learn any concept class using a sample size approximately logarithmic in the
cardinality of the concept class. Therefore, almost anything learnable is
learnable privately: specifically, if a concept class is learnable by a
(non-private) algorithm with polynomial sample complexity and output size, then
it can be learned privately using a polynomial number of samples. We also
present a computationally efficient private PAC learner for the class of parity
functions. Local (or randomized response) algorithms are a practical class of
private algorithms that have received extensive investigation. We provide a
precise characterization of local private learning algorithms. We show that a
concept class is learnable by a local algorithm if and only if it is learnable
in the statistical query (SQ) model. Finally, we present a separation between
the power of interactive and noninteractive local learning algorithms.Comment: 35 pages, 2 figure
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