Jianguo Liu

A Novel Geometric Approach to Binary Classification Based on Scaled Convex Hulls

Geometric methods are very intuitive and provide a theoretical foundation to many optimization problems in the fields of pattern recognition and machine learning. In this brief, the notion of scaled convex hull (SCH) is defined and a set of theoretical results are exploited to support it. These results allow the existing nearest point algorithms to be directly applied to solve both the separable and nonseparable classification problems successfully and efficiently. Then, the popular S-K algorithm has been presented to solve the nonseparable problems in the context of the SCH framework. The theoretical analysis and some experiments show that the proposed method may achieve better performance than the state-of-the-art methods in terms of the number of kernel evaluations and the execution time.

Entropy flow-aided navigation

Integrating the visual navigation mechanism of flying insects with a nonlinear Kalman filter, this paper proposes a novel navigation algorithm. New concepts of entropic map and entropy flow are presented, which can characterize topographic features and measure changes of the image respectively. Meanwhile, an auto-selecting algorithm of assessment threshold is proposed to improve computational accuracy and efficiency of global motion estimation. The simulation results suggest that the navigation algorithm can perform real-time rectification of the missiles trajectory well, and can reduce the cost of the missiles hardware.

Novel Convolutions Using First-Order Moments

This paper presents a novel fast algorithm for digital convolutions. It is able to compute arbitrary-length convolutions more efficiently via transforming the convolution into a first-order moment. Although many additions are required, the proposed algorithm has some advantages such as the avoidance of multiplications, simple computation structure, and only integer additions. These advantages contribute to this algorithm being so easy that it can compute convolutions rapidly. Based on the proposed algorithm a very simple and scalable systolic array without multipliers and ROM has been developed leading to more efficient VLSI implementation of convolutions.

An optical flow-based integrated navigation system inspired by insect vision

Some insects use optic flow (OF) to perform their navigational tasks perfectly. Learning from insects’ OF navigation strategies, this article proposes a bio-inspired integrated navigation system based on OF. The integrated navigation system is composed of an OF navigation system (OFNS) and an OF aided navigation system (OFAN). The OFNS uses a simple OF method to measure motion at each step along a path. The position information is then obtained by path integration. However, path integration leads to cumulative position errors which increase rapidly with time. To overcome this problem, the OFAN is employed to assist the OFNS in estimating and correcting these cumulative errors. The OFAN adopts an OF-based Kalman filter (KF) to continuously estimate the position errors. Moreover, based on the OF technique used in the OFNS, we develop a new OF method employed by the OFAN to generate the measurement input of the OF-based KF. As a result, both the OFNS and the OFAN in our integrated navigation system are derived from the same OF method so that they share input signals and some operations. The proposed integrated navigation system can provide accurate position information without interference from cumulative errors yet doing so with low computational effort. Simulations and comparisons have demonstrated its efficiency.

Exponential Stability of Jump-Diffusion Systems with Neutral Term and Impulses

We study jump-diffusion systems with neutral term and impulses. Under some conditions, we prove that the jump-diffusion systems with neutral term and impulses are mean square and almost surely exponentially stable. Finally, we give an example to describe the theoretical results.

Efficient systolic implementation of DFT using only the first-order moments

The Discrete Fourier transform (DFT) is an important tool in digital signal processing. In this paper, a novel approach to DFT is proposed. The computation of DFT is transformed to the computation of the first-order moments by the simple mathematical deductions. It is well known that the first-order moments can be computed efficiently using only additions. An efficient systolic array is designed to implement DFT. The comparison with the existing methods shows the advantages of our method. The approach is also applicable to DFT inverses.

An Arbitrary-length and Multiplierless DCT Algorithm and Systolic Implementation

Discrete Cosine transform (DCT) is an important tool in digital signal processing. In this paper, a novel algorithm to perform DCT multiplierlessly is proposed. First, by modular mapping and truncating Taylor series expansion, the DCT is expressed in the form of the product of the constants and discrete moments. Second, by performing appropriate bit operations and shift operations in binary system, the product can be transformed to some additions of integers. The proposed algorithm only involves integer additions and shifts because the discrete moments can be computed only by integer additions. An efficient and regular systolic array is designed to implement the proposed algorithm , and the complexity analysis is also given. Different to other fast Cosine transforms, our algorithm can deal with arbitrary length signals and get high precision. The approach is also applicable to multi-dimensional DCT and DCT inverses.

Moments based fast fourier transform without multiplications

Discrete Fourier transform (DFT) is an important tool in digital signal processing. We have proposed an approach to performing DFT via linear sums of discrete moments. In this paper, based on the previous work, we present a new method of performing fast Fourier transform without multiplications by performing appropriate bit operations and shift operations in binary system, which can be implemented by integer additions of fixed points. The systolic implementation is a demonstration of the locality of dataflow in the algorithms and hence it implies an easy and potential hardware/VLSI realization. The approach is also applicable to DFT inverses.

Hardware-efficient implementation of digital FIR filter using fast first-order moment algorithm

As the digital finite impulse response (FIR) filter can be transformed into the shift-add form of multiple small-sized firstorder moments, based on the existing fast first-order moment algorithm, this paper presents a novel multiplier-less structure to calculate any number of sequential filtering results in parallel. The theoretical analysis on its hardware and time-complexities reveals that by appropriately setting the degree of parallelism and the decomposition factor of a fixed word width, the proposed structure may achieve better area-time efficiency than the existing two-dimensional (2-D) memoryless-based filter. To evaluate the performance concretely, the proposed designs for different taps along with the existing 2-D memoryless-based filters, are synthesized by Synopsys Design Compiler with 0.18-μm SMIC library. The comparisons show that the proposed design has less area-time complexity and power consumption when the number of filter taps is larger than 48.

Stability analysis for a class of jump-diffusion systems with parameter

Stochastic jump systems have great potential in finance engineering and stochastic control. In this paper, we mainly consider stability of stochastic jump-diffusion systems with parameter. We establish the criteria of locally exponential stability of mild solutions of the systems by using stochastic integral inequalities technique. We extend some existing results to more general cases. Finally, we use an example to show our result.