Pattern Search Problem Research Articles

Small Candidate Set for Translational Pattern Search

In this paper, we study the following pattern search problem: Given a pair of point sets A and B in fixed dimensional space \(\mathbb {R}^d\), with \(|B| = n,|A| = m\) and \(n \ge m\), the pattern search problem is to find the translations \(\mathcal {T}\)’s of A such that each of the identified translations induces a matching between \(\mathcal {T}(A)\) and a subset \(B'\) of B with cost no more than some given threshold, where the cost is defined as the minimum bipartite matching cost of \(\mathcal {T}(A)\) and \(B'\). We present a novel algorithm to produce a small set of candidate translations for the pattern search problem. For any \(B' \subseteq B\) with \(|B'| = |A|\), there exists at least one translation \(\mathcal {T}\) in the candidate set such that the minimum bipartite matching cost between \(\mathcal {T}(A)\) and \(B'\) is no larger than \((1+\epsilon )\) times the minimum bipartite matching cost between A and \(B'\) under any translation (i.e., the optimal translational matching cost). We also show that there exists an alternative solution to this problem, which constructs a candidate set of size \(O_{d,\epsilon }(n \log ^2 n)\) in \(O_{d,\epsilon }(n \log ^2 n)\) time with high probability of success. As a by-product of our construction, we obtain a weak \(\epsilon \)-net for hypercube ranges, which significantly improves the construction time and the size of the candidate set. Our technique can be applied to a number of applications, including the translational pattern matching problem.

Searching cosmic strings network in the CMB

The CMB stochastic field provides us with a unique opportunity to search for the predicted imprints of various cosmological theories. In this work, we explore the detectability of the cosmic string (CS) network traces in the pixel-space through its gravitational impact on the CMB anisotropies, i.e. the Gott–Kaiser–Stebbins effect. First, in a classical approach, we use a series of multi-scale edge-detection algorithms followed by certain critical and excursion sets measures on the CMB simulated data (with different levels of contributions from the CSs). With this pipeline the minimum value of detectable CS’s tension for noiseless maps with a resolution of [Formula: see text] is found to be [Formula: see text]. Calling for the help the power of the machine learning algorithms with our proposed feature vectors, decreases the above lower bound to [Formula: see text]. The methods developed and used in this work are quite general and applicable to a wide variety of pattern search problems in the various stochastic fields ranging from cosmological random fields to other natural and artificial complex systems.

Generative RNNs for OOV Keyword Search

The modeling of text queries as sequences of embeddings for conducting similarity matching based search within speech features has been recently shown to improve keyword search (KWS) performance, especially for the out-of-vocabulary (OOV) terms. This technique uses a dynamic time warping based search methodology, converting the KWS problem into a pattern search problem by artificially modeling the text queries as pronunciation-based embedding sequences. This query modeling is done by concatenating and repeating frame representations for each phoneme in the keyword's pronunciation. In this letter, we propose a query model that incorporates temporal context information using recurrent neural networks (RNN) trained to generate realistic query representations. With experiments conducted on the IARPA Babel Program's Turkish and Zulu datasets, we show that the proposed RNN-based query generation yields significant improvements over the statistical query models of earlier work, and yields a comparable performance to the state-of-the-art techniques for OOV KWS.

A Spiking Neural Model of HT3D for Corner Detection

Obtaining good quality image features is of remarkable importance for most computer vision tasks. It has been demonstrated that the first layers of the human visual cortex are devoted to feature detection. The need for these features has made line, segment, and corner detection one of the most studied topics in computer vision. HT3D is a recent variant of the Hough transform for the combined detection of corners and line segments in images. It uses a 3D parameter space that enables the detection of segments instead of whole lines. This space also encloses canonical configurations of image corners, transforming corner detection into a pattern search problem. Spiking neural networks (SNN) have previously been proposed for multiple image processing tasks, including corner and line detection using the Hough transform. Following these ideas, this paper presents and describes in detail a model to implement HT3D as a Spiking Neural Network for corner detection. The results obtained from a thorough testing of its implementation using real images evince the correctness of the Spiking Neural Network HT3D implementation. Such results are comparable to those obtained with the regular HT3D implementation, which are in turn superior to other corner detection algorithms.

Error repair and knowledge acquisition via case-based reasoning

To cope with the knowledge acquisition bottleneck, the authors propose a new architecture combining rule-based reasoning (RBR), case-based reasoning (CBR) and knowledge acquisition technology in a system which solves pattern search problems. The RBR part searches for specified patterns in a large space represented by a network structure such as an LSI circuit diagram, which contains a great number of patterns and variations. It then carries out specified actions, such as fault diagnosis, on the patterns that are found. The outputs of the RBR part are transferred to the CBR part. The user of the system detects and repairs a few pattern detection errors caused by the RBR part. The CBR part detects and repairs all remaining errors which can be estimated from the user detected ones. The repaired results are sent back to the RBR part to recover the RBR output. The repaired results are also stored automatically in the case base. Similar cases are grouped in a same case family. The knowledge acquisition part relates each case family to an incomplete rule in the RBR knowledge base and proposes modifying the rule. Eventually, the system can obtain refined rules with the cooperation of domain experts. Thus, the problem solving process and knowledge acquisition process are performed cyclically. The architecture was successfully applied to a pair condition extraction problem for an analog LSI circuit layout system.

Implementation of the three-dimensional-pattern search problem on Hopfield-like neural networks.

The three-dimensional (3D)-pattern search problem can be summarized as finding, in a molecule, the subset of atoms that have the most similar spatial arrangement as those of a given 3D pattern. For this NP-complete combinatorial optimization problem we propose, by analogy to the travelling salesman problem, a new method taking advantage of the capability of Hopfield-like neural networks to carry out combinatorial optimization of an objective function. This objective function is built from the sum of the differences of interatomic distances in the pattern and the molecule. Here we present the implementation we have found of the 3D-pattern search problem on Hopfield-like neural networks. Initial tests indicate that this approach not only successfully retrieves a given pattern, but can also suggest partial solutions having one or two atoms less than the given pattern, an interesting feature in the case of local conformational flexibility of the molecule. The distributed representation of the problem on Hopfield-like neural networks offers a good perspective for parallel implementation.