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 $A \in \mathbb{C}^{m\times n}$, a vector $b \in \mathbb{C}^{n}$, a bounded degree-$d$ polynomial $p$, and linear-time pre-processing, we can output a description of a vector $v$ such that $\|v - p(A) b\| \leq \varepsilon\|b\|$ in $\widetilde{\mathcal{O}}(d^{11} \|A\|_{\mathrm{F}}^4 / (\varepsilon^2 \|A\|^4 ))$ time. This improves upon the best known classical algorithm [CGLLTW, STOC'20, arXiv:1910.06151], which requires $\widetilde{\mathcal{O}}(d^{22} \|A\|_{\mathrm{F}}^6 /(\varepsilon^6 \|A\|^6 ) )$ 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 $p(A)b$ to $\varepsilon\|b\|$ error in $\widetilde{\mathcal{O}}(d\|A\|_{\mathrm{F}}/(\varepsilon \|A\|))$ 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 $\alpha$ be the cardinality of the largest independent set. Our goal is to estimate $\alpha$ 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 $\beta$, 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 $\alpha$ and $\beta$. For unit-length intervals, we obtain a $(2+\epsilon)$-approximation to $\alpha$ and $\beta$ in poly$(\frac{\log(n)}{\epsilon})$ space. We also show a matching lower bound. Combined with the $3/2$-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 $\left(\frac{8\sqrt{3}}{\pi}\right)$-approximation to $\alpha$ and $\beta$ in poly$(\log(n), \epsilon^{-1})$ space, which is closely related to the hexagonal circle packing constant. We provide algorithms for estimating $\alpha$ for arbitrary-length intervals under a bounded intersection assumption and study the parameterized space complexity of estimating $\alpha$ and $\beta$, 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