scholarly journals Online Semi-supervised Multi-label Classification with Label Compression and Local Smooth Regression

2020 ◽  
Author(s):  
Peiyan Li ◽  
Honglian Wang ◽  
Christian Böhm ◽  
Junming Shao
Keyword(s):  
Learning Algorithm ◽  
Dimensional Space ◽  
Closed Form Solution ◽  
Regression Function ◽  
Form Solution ◽  
Target Space ◽  
Stream Classification ◽  
Low Dimensional ◽  
Adaptive Decoding ◽  
Smooth Regression

Online semi-supervised multi-label classification serves a practical yet challenging task since only a small number of labeled instances are available in real streaming environments. However, the mainstream of existing online classification techniques are focused on the single-label case, while only a few multi-label stream classification algorithms exist, and they are mainly trained on labeled instances. In this paper, we present a novel Online Semi-supervised Multi-Label learning algorithm (OnSeML) based on label compression and local smooth regression, which allows real-time multi-label predictions in a semi-supervised setting and is robust to evolving label distributions. Specifically, to capture the high-order label relationship and to build a compact target space for regression, OnSeML compresses the label set into a low-dimensional space by a fixed orthogonal label encoder. Then a locally defined regression function for each incoming instance is obtained with a closed-form solution. Targeting the evolving label distribution problem, we propose an adaptive decoding scheme to adequately integrate newly arriving labeled data. Extensive experiments provide empirical evidence for the effectiveness of our approach.

Induction Proof for a General Exponential Integral Formula

1995 ◽  
Vol 80 (2) ◽  
pp. 424-426
Author(s):  
Frank O'Brien ◽  
Sherry E. Hammel ◽  
Chung T. Nguyen
Keyword(s):  
Closed Form ◽  
Integral Formula ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Probability Method ◽  
Exponential Integral ◽  
Need To Evaluate ◽  
Three Dimensional Space

The authors' Poisson probability method for detecting stochastic randomness in three-dimensional space involved the need to evaluate an integral for which no appropriate closed-form solution could be located in standard handbooks. This resulted in a formula specifically calculated to solve this integral in closed form. In this paper the calculation is verified by the method of mathematical induction.

scholarly journals Revisiting Online Quantum State Learning

2020 ◽  
Vol 34 (04) ◽  
pp. 6607-6614
Author(s):  
Feidiao Yang ◽  
Jiaqing Jiang ◽  
Jialin Zhang ◽  
Xiaoming Sun
Keyword(s):  
Theoretical Analysis ◽  
Quantum State ◽  
Learning Algorithm ◽  
Closed Form Solution ◽  
Form Solution ◽  
Quantum States ◽  
Frobenius Norm ◽  
Deterministic Learning ◽  
State Learning ◽  
Almost All

In this paper, we study the online quantum state learning problem which is recently proposed by Aaronson et al. (2018). In this problem, the learning algorithm sequentially predicts quantum states based on observed measurements and losses and the goal is to minimize the regret. In the previous work, the existing algorithms may output mixed quantum states. However, in many scenarios, the prediction of a pure quantum state is required. In this paper, we first propose a Follow-the-Perturbed-Leader (FTPL) algorithm that can guarantee to predict pure quantum states. Theoretical analysis shows that our algorithm can achieve an O(√T) expected regret under some reasonable settings. In the case that the pure state prediction is not mandatory, we propose another deterministic learning algorithm which is simpler and more efficient. The algorithm is based on the online gradient descent (OGD) method and can also achieve an O(√T) regret bound. The main technical contribution of this result is an algorithm of projecting an arbitrary Hermitian matrix onto the set of density matrices with respect to the Frobenius norm. We think this subroutine is of independent interest and can be widely used in many other problems in the quantum computing area. In addition to the theoretical analysis, we evaluate the algorithms with a series of simulation experiments. The experimental results show that our FTPL method and OGD method outperform the existing RFTL approach proposed by Aaronson et al. (2018) in almost all settings. In the implementation of the RFTL approach, we give a closed-form solution to the algorithm. This provides an efficient, accurate, and completely executable solution to the RFTL method.

UWB Positioning Performance Tests Based on Chan Algorithm in IEEE 802.15.4a Channel Model

2012 ◽  
Vol 433-440 ◽  
pp. 2663-2669 ◽  
Author(s):  
Xiao Long Mu ◽  
Xue Rong Cui ◽  
Hao Zhang ◽  
T. Aaron Gulliver
Keyword(s):  
Channel Model ◽  
Dimensional Space ◽  
Moving Average ◽  
Weighted Least Squares ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Ultra Wideband ◽  
Time Of Arrival ◽  
High Degree

Chan algorithm is a closed form solution to the non-recursive equation set. This algorithm needs only a small amount of calculations but has a high degree of precision on positioning. It is valuable for academic reference. Firstly, it obtains the preliminary solution by using WLS (Weighted Least Squares) twice. Then, it uses the preliminary solution to linearise the nonlinear equation and finally makes the estimation of the position. The channel model can provide the model of indoor office environment ranging from 2 GHz to 10 GHz. Through the UWB (Ultra WideBand) positioning system of the channel model, the LOS(line-of-sight) environment can be simulated and TOA(Time-Of-Arrival) data measured by distance can also be obtained by sampling. However, small LOS errors included in the TOA data may lead to big ones in the positioning of 3D(three-dimensional) space and the precision of positioning may be undermined, when the data are directly applied to the Chan algorithm which is based on the TOA. In order to solve this issue, the TOA data obtained can be processed with MA(Moving Average) algorithm and the precision can be improved.

scholarly journals The Longitudinal Deformation Profile of a Rock Tunnel: An Elastic Analysis

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Yonghong Wang ◽  
Wen Du ◽  
Guohui Zhang ◽  
Yang Song
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Elastic Model ◽  
Longitudinal Deformation ◽  
Tunnel Face ◽  
Wall Displacement ◽  
In Situ Experiments ◽  
Rock Tunnel

The longitudinal deformation profile (LDP) is the profile of wall displacement versus the distance from the tunnel face. To develop LDP equations, numerical methods and in situ experiments have been used to obtain the deformation of a tunnel in three-dimensional space. However, extant approaches are inadequate in terms of explaining the mechanical relation between the wall displacement and the conditions of a tunnel (e.g., properties of rock). In this paper, an analytical approach is proposed to develop a new LDP equation. First, on the basis of the axisymmetric elastic model of a tunnel, a closed-form solution of wall displacement is derived. Then, a new LDP equation is presented according to the solution developed above; the coefficient β, defined as the ratio of the effective range of the “face effect” to the radius of the tunnel, is proposed for the first time. Finally, a case study is proposed to validate the practicability of this equation.

scholarly journals Similarity Measure Learning in Closed-Form Solution for Image Classification

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Jing Chen ◽  
Yuan Yan Tang ◽  
C. L. Philip Chen ◽  
Bin Fang ◽  
Zhaowei Shang ◽  
...  
Keyword(s):  
Closed Form ◽  
Similarity Measure ◽  
Dimensional Space ◽  
Closed Form Solution ◽  
Optimal Solution ◽  
Research Problem ◽  
Form Solution ◽  
Similarity Learning ◽  
Learning Tasks ◽  
Active Research

Adopting a measure is essential in many multimedia applications. Recently, distance learning is becoming an active research problem. In fact, the distance is the natural measure for dissimilarity. Generally, a pairwise relationship between two objects in learning tasks includes two aspects: similarity and dissimilarity. The similarity measure provides different information for pairwise relationships. However, similarity learning has been paid less attention in learning problems. In this work, firstly, we propose a general framework for similarity measure learning (SML). Additionally, we define a generalized type of correlation as a similarity measure. By a set of parameters, generalized correlation provides flexibility for learning tasks. Based on this similarity measure, we present a specific algorithm under the SML framework, called correlation similarity measure learning (CSML), to learn a parameterized similarity measure over input space. A nonlinear extension version of CSML, kernel CSML, is also proposed. Particularly, we give a closed-form solution avoiding iterative search for a local optimal solution in the high-dimensional space as the previous work did. Finally, classification experiments have been performed on face databases and a handwritten digits database to demonstrate the efficiency and reliability of CSML and KCSML.

scholarly journals White whole (WW) grades cashew kernel’s classification using artificial neural network (ANN)

2020 ◽  
Vol 9 (1) ◽  
pp. 187
Author(s):  
Narendra VG ◽  
Dasharathraj K Shetty
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Learning Algorithm ◽  
Back Propagation ◽  
Closed Form Solution ◽  
Form Solution ◽  
Least Square ◽  
Least Square Approach ◽  
Artificial Neural ◽  
Artificial Neural Network Ann

In this paper, we introduce an algorithm for the fitting of bounding rectangle to a closed region of cashew kernel in a given image. We propose an algorithm to automatically compute the coordinates of the vertices closed form solution. Which is based on coordinate geometry and uses the boundary points of regions. The algorithm also computes directions of major and minor axis using least-square approach to compute the orientation of the given cashew kernel. More promising results were obtained by extracting shape features of a cashew kernel, it is proved that these features may predominantly use to make the better distinction of cashew kernels of different grades. The intelligent model was designed using Artificial Neural Network (ANN). The model was trained and tested using Back-Propagation learning algorithm and obtained classification accuracy of 89.74%. 

scholarly journals A Novel THz Differential Spectral Clustering Recognition Method Based on t-SNE

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Tie-Jun Li ◽  
Chih-Cheng Chen ◽  
Jian-jun Liu ◽  
Gui-fang Shao ◽  
Christopher Chun Ki Chan
Keyword(s):  
Learning Algorithm ◽  
Dimensional Space ◽  
Ceramic Matrix Composite ◽  
Data Sets ◽  
Conditional Probability Distribution ◽  
Computation Efficiency ◽  
Defect Recognition ◽  
Low Dimensional ◽  
T Distribution ◽  
Spectrum Data

We apply time-domain spectroscopy (THz) imaging technology to perform nondestructive detection on three industrial ceramic matrix composite (CMC) samples and one silicon slice with defects. In terms of spectrum recognition, a low-resolution THz spectrum image results in an ineffective recognition on sample defect features. Therefore, in this article, we propose a spectrum clustering recognition model based on t-distribution stochastic neighborhood embedding (t-SNE) to address this ineffective sample defect recognition. Firstly, we propose a model to recognize a reduced dimensional clustering of different spectrums drawn from the imaging spectrum data sets, in order to judge whether a sample includes a feature indicating a defect or not in a low-dimensional space. Second, we improve computation efficiency by mapping spectrum data samples from high-dimensional space to low-dimensional space by the use of a manifold learning algorithm (t-SNE). Finally, to achieve a visible observation of sample features in low-dimensional space, we use a conditional probability distribution to measure the distance invariant similarity. Comparative experiments indicate that our model can judge the existence of sample defect features or not through spectrum clustering, as a predetection process for image analysis.

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