19 research outputs found
A Novel Feature Selection and Extraction Technique for Classification
This paper presents a versatile technique for the purpose of feature
selection and extraction - Class Dependent Features (CDFs). We use CDFs to
improve the accuracy of classification and at the same time control
computational expense by tackling the curse of dimensionality. In order to
demonstrate the generality of this technique, it is applied to handwritten
digit recognition and text categorization.Comment: 2 pages, 2 tables, published at IEEE SMC 201
Chance Constraint Based Multi-objective Vendor Selection Using NSGAII
AbstractSuccess of a buying firm depends largely on the suitable selection of its vendors as it ensures timely delivery of goods to support the firm's output. The paper presents a Stochastic Vendor Selection Problem (SVSP) in the presence of uncertainties associated with operational risks. The problem is modeled using Chance constraint approach and solved using NSGA II. A case example is presented as an illustration
An Improved Classical Singular Value Transformation for Quantum Machine Learning
We study quantum speedups in quantum machine learning (QML) by analyzing the
quantum singular value transformation (QSVT) framework. QSVT, introduced by
[GSLW, STOC'19, arXiv:1806.01838], unifies all major types of quantum speedup;
in particular, a wide variety of QML proposals are applications of QSVT on
low-rank classical data. We challenge these proposals by providing a classical
algorithm that matches the performance of QSVT in this regime up to a small
polynomial overhead.
We show that, given a matrix , a vector , a bounded degree- polynomial , and linear-time
pre-processing, we can output a description of a vector such that in time. This improves upon the
best known classical algorithm [CGLLTW, STOC'20, arXiv:1910.06151], which
requires time, and narrows the gap with QSVT, which, after linear-time
pre-processing to load input into a quantum-accessible memory, can estimate the
magnitude of an entry to error in
time.
Our key insight is to combine the Clenshaw recurrence, an iterative method
for computing matrix polynomials, with sketching techniques to simulate QSVT
classically. We introduce several new classical techniques in this work,
including (a) a non-oblivious matrix sketch for approximately preserving
bi-linear forms, (b) a new stability analysis for the Clenshaw recurrence, and
(c) a new technique to bound arithmetic progressions of the coefficients
appearing in the Chebyshev series expansion of bounded functions, each of which
may be of independent interest.Comment: 62 pages, v3: fixed bug, runtime exponent now 11 instead of 9; v2:
revised abstract to clarify result
Weighted Maximum Independent Set of Geometric Objects in Turnstile Streams
We study the Maximum Independent Set problem for geometric objects given in
the data stream model. A set of geometric objects is said to be independent if
the objects are pairwise disjoint. We consider geometric objects in one and two
dimensions, i.e., intervals and disks. Let be the cardinality of the
largest independent set. Our goal is to estimate in a small amount of
space, given that the input is received as a one-pass stream. We also consider
a generalization of this problem by assigning weights to each object and
estimating , the largest value of a weighted independent set. We
initialize the study of this problem in the turnstile streaming model
(insertions and deletions) and provide the first algorithms for estimating
and .
For unit-length intervals, we obtain a -approximation to
and in poly space. We also show a
matching lower bound. Combined with the -approximation for insertion-only
streams by Cabello and Perez-Lanterno [CP15], our result implies a separation
between the insertion-only and turnstile model. For unit-radius disks, we
obtain a -approximation to and
in poly space, which is closely related to
the hexagonal circle packing constant.
We provide algorithms for estimating for arbitrary-length intervals
under a bounded intersection assumption and study the parameterized space
complexity of estimating and , where the parameter is the ratio
of maximum to minimum interval length.Comment: The lower bound for arbitrary length intervals in the previous
version contains a bug, we are updating the submission to reflect thi