Lanczos subspace filter diagonalization: Homogeneous recursive filtering and a low-storage method for the calculation of matrix elements

We develop a new iterative filter diagonalization (FD) scheme based on Lanczos subspaces and demonstrate its application to the calculation of bound-state and resonance eigenvalues. The new scheme combines the Lanczos three-term vector recursion for the generation of a tridiagonal representation of the Hamiltonian with a three-term scalar recursion to generate filtered states within the Lanczos representation. Eigenstates in the energy windows of interest can then be obtained by solving a small generalized eigenvalue problem in the subspace spanned by the filtered states. The scalar filtering recursion is based on the homogeneous eigenvalue equation of the tridiagonal representation of the Hamiltonian, and is simpler and more efficient than our previous quasi-minimum-residual filter diagonalization (QMRFD) scheme (H. G. Yu and S. C. Smith, Chem. Phys. Lett., 1998, 283, 69), which was based on solving for the action of the Green operator via an inhomogeneous equation. A low-storage method for the construction of Hamiltonian and overlap matrix elements in the filtered-basis representation is devised, in which contributions to the matrix elements are computed simultaneously as the recursion proceeds, allowing coefficients of the filtered states to be discarded once their contribution has been evaluated. Application to the HO2 system shows that the new scheme is highly efficient and can generate eigenvalues with the same numerical accuracy as the basic Lanczos algorithm.

Recursive filtering of images with symmetric extension

Recursive filters are widely used in image analysis due to their efficiency and simple implementation. However these filters have an initialisation problem which either produces unusable results near the image boundaries or requires costly approximate solutions such as extending the boundary manually. In this paper, we describe a method for the recursive filtering of symmetrically extended images for filters with symmetric denominator. We begin with an analysis of symmetric extensions and their effect on non-recursive filtering operators. Based on the non-recursive case, we derive a formulation of recursive filtering on symmetric domains as a linear but spatially varying implicit operator. We then give an efficient method for decomposing and solving the linear implicit system, along with a proof that this decomposition always exists. This decomposition needs to be performed only once for each dimension of the image. This yields a filtering which is both stable and consistent with the ideal infinite extension. The filter is efficient, requiring less computation than the standard recursive filtering. We give experimental evidence to verify these claims. (c) 2005 Elsevier B.V. All rights reserved.

Minimum-order stable recursive filter design via the genetic algorithm approach

In this paper, the minimum-order stable recursive filter design problem is proposed and investigated. This problem is playing an important role in pipeline implementation sin signal processing. Here, the existence of a high-order stable recursive filter is proved theoretically, in which the upper bound for the highest order of stable filters is given. Then the minimum-order stable linear predictor is obtained via solving an optimization problem. In this paper, the popular genetic algorithm approach is adopted since it is a heuristic probabilistic optimization technique and has been widely used in engineering designs. Finally, an illustrative example is sued to show the effectiveness of the proposed algorithm.

Fast-convergent iterative scheme for filtering velocity signals and finding Kolmogorov scales

The present fundamental knowledge of fluid turbulence has been established primarily from hot- and cold-wire measurements. Unfortunately, however, these measurements necessarily suffer from contamination by noise since no certain method has previously been available to optimally filter noise from the measured signals. This limitation has impeded our progress of understanding turbulence profoundly. We address this limitation by presenting a simple, fast-convergent iterative scheme to digitally filter signals optimally and find Kolmogorov scales definitely. The great efficacy of the scheme is demonstrated by its application to the instantaneous velocity measured in a turbulent jet.

The effect of high-pass filtering on TEOAE in 2-month-old infants

The aim of the present study was to investigate the effect of high-pass filtering on TEOAE obtained from 2-month-old infants as a function of filter cut-off frequency, activity states and pass/fail status of infants. Two experiments were performed. In Experiment 1, 100 2-month-old infants (200 ears) in five activity states (asleep, awake but peaceful, sucking a pacifier, feeding, restless) were tested by use of TEOAE technology. Five different filter conditions were applied to the TEOAE responses post hoc. The filter conditions were set at 781 Hz (default setting), 1.0, 1.2, 1.4 and 1.6 kHz. Results from this experiment showed that TEOAE parameters, such as whole-wave reproducibility (WR) and signal-to-noise ratio (SNR) at 0.8 kHz and 1.6 kHz, changed as a function of the cut-off frequency. The findings suggest that the 1.6 kHz and 1.2 kHz filter conditions are optimal for WR and SNR pass/fail criteria, respectively. Although all infant recordings appeared to benefit from the filtering, infants in the noisy states seemed to benefit the most. In Experiment 2, the high-pass filtering technique was applied to 23 infants (35 ears) who apparently failed the TEOAE tests on initial screening but were subsequently awarded a pass status based on the results from a follow-up auditory brainstem response (ABR) assessment. The findings showed a significant decrease in noise contamination of the TEOAE with a corresponding significant increase in WR. With high-pass filtering at 1.6 kHz, 21/35 ears could be reclassified into the pass category.

Tyre-force estimation by Kalman inverse filtering: applications to off-highway mining trucks

Kalman inverse filtering is used to develop a methodology for real-time estimation of forces acting at the interface between tyre and road on large off-highway mining trucks. The system model formulated is capable of estimating the three components of tyre-force at each wheel of the truck using a practical set of measurements and inputs. Good tracking is obtained by the estimated tyre-forces when compared with those simulated by an ADAMS virtual-truck model. A sensitivity analysis determines the susceptibility of the tyre-force estimates to uncertainties in the truck's parameters.

Incremental learning for interactive e-mail filtering

In this article, we propose a framework, namely, Prediction-Learning-Distillation (PLD) for interactive document classification and distilling misclassified documents. Whenever a user points out misclassified documents, the PLD learns from the mistakes and identifies the same mistakes from all other classified documents. The PLD then enforces this learning for future classifications. If the classifier fails to accept relevant documents or reject irrelevant documents on certain categories, then PLD will assign those documents as new positive/negative training instances. The classifier can then strengthen its weakness by learning from these new training instances. Our experiments’ results have demonstrated that the proposed algorithm can learn from user-identified misclassified documents, and then distil the rest successfully.

Interactive email filtering: Learning from misclassified examples

Learning from mistakes has proven to be an effective way of learning in the interactive document classifications. In this paper we propose an approach to effectively learning from mistakes in the email filtering process. Our system has employed both SVM and Winnow machine learning algorithms to learn from misclassified email documents and refine the email filtering process accordingly. Our experiments have shown that the training of an email filter becomes much effective and faster

Collaborative filtering on data streams

Collaborate Filtering is one of the most popular recommendation algorithms. Most Collaborative Filtering algorithms work with a static set of data. This paper introduces a novel approach to providing recommendations using Collaborative Filtering when user rating is received over an incoming data stream. In an incoming stream there are massive amounts of data arriving rapidly making it impossible to save all the records for later analysis. By dynamically building a decision tree for every item as data arrive, the incoming data stream is used effectively although an inevitable trade off between accuracy and amount of memory used is introduced. By adding a simple personalization step using a hierarchy of the items, it is possible to improve the predicted ratings made by each decision tree and generate recommendations in real-time. Empirical studies with the dynamically built decision trees show that the personalization step improves the overall predicted accuracy.

Time weight collaborative filtering

Collaborative filtering is regarded as one of the most promising recommendation algorithms. The item-based approaches for collaborative filtering identify the similarity between two items by comparing users' ratings on them. In these approaches, ratings produced at different times are weighted equally. That is to say, changes in user purchase interest are not taken into consideration. For example, an item that was rated recently by a user should have a bigger impact on the prediction of future user behaviour than an item that was rated a long time ago. In this paper, we present a novel algorithm to compute the time weights for different items in a manner that will assign a decreasing weight to old data. More specifically, the users' purchase habits vary. Even the same user has quite different attitudes towards different items. Our proposed algorithm uses clustering to discriminate between different kinds of items. To each item cluster, we trace each user's purchase interest change and introduce a personalized decay factor according to the user own purchase behaviour. Empirical studies have shown that our new algorithm substantially improves the precision of item-based collaborative filtering without introducing higher order computational complexity.

Filtering duplicate items over distributed data streams

In recent years many real time applications need to handle data streams. We consider the distributed environments in which remote data sources keep on collecting data from real world or from other data sources, and continuously push the data to a central stream processor. In these kinds of environments, significant communication is induced by the transmitting of rapid, high-volume and time-varying data streams. At the same time, the computing overhead at the central processor is also incurred. In this paper, we develop a novel filter approach, called DTFilter approach, for evaluating the windowed distinct queries in such a distributed system. DTFilter approach is based on the searching algorithm using a data structure of two height-balanced trees, and it avoids transmitting duplicate items in data streams, thus lots of network resources are saved. In addition, theoretical analysis of the time spent in performing the search, and of the amount of memory needed is provided. Extensive experiments also show that DTFilter approach owns high performance.