International Journal of Wavelets, Multiresolution and Information Processing

The problem of ranking/ordering instances, instead of simply classifying them, has recently gained much attention in machine learning. Ranking from binary comparisons is a ubiquitous problem in modern machine learning applications. In this paper, we consider ℓ¹-norm SVM for ranking. As well known, learning with ℓ¹-norm restrictions usually leads to sparsity. Moreover, instead of independently draw sample sequence, we are given sample of exponentially strongly mixing sequence. Under some mild conditions, a learning rate is established.

The aim of this paper is to extend (ψ, β)-derivatives to -derivatives for locally integrable functions on the real line and then investigate problems of approximation of the classes of functions determined by these derivatives with the use of entire functions of exponential type.

This paper surveys some of the scientific work on positive polynomial sums, Fourier analysis and spherical approximation on the sphere that Kunyang Wang did in the past 20 years.

Optimal estimates of Kolmogorov's n-widths, linear n-widths and Gelfand's n-widths of the weighted Sobolev classes on the unit sphere 𝕊^d are established. Similar results are also established on the unit ball B^d and on the simplex T^d.

In this paper, we discuss the average errors of function approximation by linear combinations of Bernstein–Kantorovich operators. The strongly asymptotic orders for the average errors of these operators sequence are determined on the Wiener space.

We consider the estimate of the best L₁-approximation of convolution classes , defined by a self-adjoint polynomial differential operator P_r(D), in the term of some kinds of generalized splines and get some exact constants.

Denote by J_ν the Bessel function of the first kind of order ν and μ_ν,k is its kth positive zero. For ν > ½, a theorem of Lorch, Muldoon and Szegö states that the sequence is decreasing, another theorem of theirs states that the sequence has higher monotonicity properties. In the present paper, we proved that when ν > ½ the sequence has higher monotonicity properties and the properties imply those of the sequence of the local maxima of the function x^-ν+1|J_ν-1(x)|, x ∈ (0, ∞), i.e. the sequence has higher monotonicity properties.

In this paper, we will give a survey on adaptive Fourier decompositions (AFDs) in one- and multi-dimensions. Theoretical formulations of three different types of AFDs in one-dimension, viz., Core AFD, Cyclic AFD in conjunction with best rational approximation and Unwending AFD are provided.

This paper proposes a new software system which provides algorithms for three variations of adaptive Fourier decomposition (AFD), including Core AFD, Cyclic AFD and Unwending AFD. The related time frequency distributions (TFDs) are also provided. Remarks are made for the algorithms design and development. The software system can be used to analyze any signal with finite energy.

In recent years, China's demand for satellite remote sensing images increased. Thus, the country launched a series of satellites equipped with high-resolution sensors. The resolutions of these satellites range from 30 m to a few meters, and the spectral range covers the visible to the near-infrared band. These satellite images are mainly used for environmental monitoring, mapping, land surface classification and other fields. However, haze is an important factor that often affects image quality. Thus, dehazing technology is becoming a critical step in high-resolution remote sensing image processing. This paper presents a rapid algorithm for dehazing based on a semi-physical haze model. Large-scale median filtering technique is used to extract large areas of bright, low-frequency information from images to estimate the distribution and thickness of the haze. Four images from different satellites are used for experiment. Results show that the algorithm is valid, fast, and suitable for the rapid dehazing of numerous large-sized high-resolution remote sensing images in engineering applications.

For MODIS NDVI time series with cloud noise and time distortion, we propose an effective time series clustering framework including similarity measure, prototype calculation, clustering algorithm and cloud noise handling. The core of this framework is dynamic time warping (DTW) distance and its corresponding averaging method, DTW barycenter averaging (DBA). We used 12 years of MODIS NDVI time series to perform annual land-cover clustering in Poyang Lake Wetlands. The experimental result shows that our method performs better than classic clustering based on ordinary Euclidean methods.

In this paper, we discuss the best approximation of functions on the sphere by spherical polynomials and the approximation by the Fourier partial summation operators and the Vallée-Poussin operators, on a Sobolev space with a Gaussian measure in the probabilistic case setting, and get the probabilistic error estimation. We show that in the probabilistic case setting, the Fourier partial summation operators and the Vallée-Poussin operators are the order optimal linear operators in the L_q space for 1 ≤ q ≤ ∞, but the spherical polynomial spaces are not order optimal in the L_q space for 2 < q ≤ ∞. This is completely different from the situation in the average case setting, which the spherical polynomial spaces are order optimal in the L_q space for 1 ≤ q < ∞. Also, in the L_q space for 1 ≤ q ≤ ∞, worst-case order optimal subspaces are also order optimal in the probabilistic case setting.

For weighted approximation in L_p-norm, we determine strongly asymptotic orders for simultaneous approximation average errors of sequence of Kantorovitch operators on r-fold integrated Wiener space. These results show the saturation properties of the Kantorovitch operators in the average case setting.

In this paper, we study the elliptic splines which include the well-known polyharmonic B-splines. We analyze their Fourier transforms, decay behaviors and polynomial reproducing properties. We also study the order of approximation in Sobolev spaces and consider their characterizations of Besov spaces by the scale projection operators, quasi-interpolation operators and wavelet operators.

In this paper, we analyze and explore the layout of reference tags and interpolation method in the reference tag based RFID scene analysis of indoor localization method, and propose triangular layout mode, as well as adopt Newtons interpolation polynomial to calculate virtual reference tags RSSI values instead of linear interpolation. Simulation experiment result shows that when given a error value, distribution probability accumulated by the triangular layout mode is larger than rectangular layout mode, with triangular accounting for a larger proportion and having better localization accuracy. Using of Newtons interpolation polynomial makes an improvement in localization accuracy over linear interpolation, but in terms of computational complexity, Newtons interpolation polynomial pay the price.