20468093
A Multiplier Structure Based on a Novel Real-time CSD Recoding
Implementation of digital signal processing (DSP) algorithms in hardware, such as field programmable gate arrays (FPGAs), requires a large number of multiplications. In this paper, we introduce a novel multiplier structure that converts from 2's complement to canonical signed digit (CSD) representation in real time. The proposed algorithm increases the number of zero partial products (which can be simplified by shift operations) to approximately 66.7% compared with 50% for modified Booth's recoding. Also, the proposed hardware structure reduces the non-zero partial products to a minimum, and consequently the number of arithmetic operations in the carry-save structure is reduced. So, our proposed hardware decreases both the time required for multiplication and the power consumption of the multiplier. Furthermore, because the proposed structure uses real time CSD recoding, and does not require a fixed value for the multiplier input to be known a priori, the proposed multiplier can be used to implement digital filters with non-fixed filter coefficients, such as adaptive filters.
206963206
Efficient adaptive Volterra filters for active nonlinear noise control with a linear secondary-path
Using a nonlinear filter to control a linear device has been studied in Strauch and Mulgrew (1998), and been proved to be effective in active noise control (ANC) when: i) the secondary path has a linear and nonminimum phase transfer function, and the reference noise is a nonlinear, predictable noise or non-Gaussian noise; ii) the primary path has a nonlinear effect. Tan et al. (2001) reinforced these statements and successfully implemented this idea with an adaptive Volterra filter, and developed an algorithm called the Volterra filtered-x LMS (VFXLMS) algorithm. However this VFXLMS suffers from a heavy computational burden as well as stability problems. In this paper, we provide several alternatives to VFXLMS: the modified Volterra LMS algorithm that increases the convergence rate by slightly increasing the computational burden, the filtered-error Volterra LMS algorithms (including the adjoint Volterra LMS algorithm and the secondary-path equalization Volterra LMS algorithm) that greatly reduce the computational complexity and improves the convergence rate. Analysis and simulation results prove the effectiveness of our proposed adaptive algorithms.
8020389
Learning from Labeled and Unlabeled Data Using Random Walks
We consider the general problem of learning from labeled and unlabeled data. Given a set of points, some of them are labeled, and the remaining points are unlabeled. The goal is to predict the labels of the unlabeled points. Any supervised learning algorithm can be applied to this problem, for instance, Support Vector Machines (SVMs). The problem of our interest is if we can implement a classifier which uses the unlabeled data information in some way and has higher accuracy than the classifiers which use the labeled data only. Recently we proposed a simple algorithm, which can substantially benefit from large amounts of unlabeled data and demonstrates clear superiority to supervised learning methods. Here we further investigate the algorithm using random walks and spectral graph theory, which shed light on the key steps in this algorithm.
7316344
CLINCH: Clustering Incomplete High-Dimensional Data for Data Mining Application
Clustering is a common technique in data mining to discover hidden patterns from massive datasets. With the development of privacy-maintaining data mining application, clustering incomplete high-dimensional data has becoming more and more useful. Motivated by these limits, we develop a novel algorithm CLINCH, which could produce fine clusters on incomplete high-dimensional data space. To handle missing attributes, CLINCH employs a prediction method that can be more precise than traditional techniques. On the other hand, we also introduce an efficient way in which dimensions are processed one by one to attack the “curse of dimensionality”. Experiments show that our algorithm not only outperforms many existing high-dimensional clustering algorithms in scalability and efficiency, but also produces precise results.
16394993
Regularization on Discrete Spaces
We consider the classification problem on a finite set of objects. Some of them are labeled, and the task is to predict the labels of the remaining unlabeled ones. Such an estimation problem is generally referred to as transductive inference. It is well-known that many meaningful inductive or supervised methods can be derived from a regularization framework, which minimizes a loss function plus a regularization term. In the same spirit, we propose a general discrete regularization framework defined on finite object sets, which can be thought of as discrete analogue of classical regularization theory. A family of transductive inference schemes is then systemically derived from the framework, including our earlier algorithm for transductive inference, with which we obtained encouraging results on many practical classification problems. The discrete regularization framework is built on discrete analysis and geometry developed by ourselves, in which a number of discrete differential operators of various orders are constructed, which can be thought of as discrete analogues of their counterparts in the continuous case.
12261862
Capacity of reproducing kernel spaces in learning theory
The capacity of reproducing kernel Hilbert spaces (RKHS) plays an essential role in the analysis of learning theory. Covering numbers and packing numbers of balls of these reproducing kernel spaces are important measurements of this capacity. We first present lower bound estimates for the packing numbers by means of nodal functions. Then we show that if a Mercer kernel is C/sup s/ (for some s>0 being not an even integer), the RKHS associated with this kernel can be embedded into C/sup s/2/. This gives upper-bound estimates for the covering number concerning Sobolev smooth kernels.Examples and applications to V/sub /spl gamma// dimension and Tikhonov (1977) regularization are presented to illustrate the upper- and lower-bound estimates.
508435
Learning with Local and Global Consistency
We consider the general problem of learning from labeled and unlabeled data, which is often called semi-supervised learning or transductive inference. A principled approach to semi-supervised learning is to design a classifying function which is sufficiently smooth with respect to the intrinsic structure collectively revealed by known labeled and unlabeled points. We present a simple algorithm to obtain such a smooth solution. Our method yields encouraging experimental results on a number of classification problems and demonstrates effective use of unlabeled data.