Please ensure that your password is at least 8 characters and contains each of the following:
- a special character: @$#!%*?&
- Solve equations and inequalities
- Simplify expressions
- Factor polynomials
- Graph equations and inequalities
- Advanced solvers
- All solvers
- Arithmetics
- Determinant
- Percentages
- Scientific Notation
- Inequalities
- Math Articles
Graphing functions
In this tutorial you will learn about graphing basic parent functions and derived functions
In this article we are going to learn about equations of circle and parabolas with some graphical examples.
This tutorial will introduce you to functions with one or more variable.
In this article we are going the learn about coordinates in the plane and graphing equation in two variables with some examples.
Math Topics
More solvers.
- Add Fractions
- Simplify Fractions
Graphing Calculator
What do you want to calculate.
- Solve for Variable
- Practice Mode
- Step-By-Step
Example (Click to try)
How to graph your problem.
- Type in your equation like y=2x+1 (If you have a second equation use a semicolon like y=2x+1 ; y=x+3)
- Press Calculate it to graph!
Graphing Equations Video Lessons
- Khan Academy Video: Graphing Lines
- Khan Academy Video: Graphing a Quadratic Function
Need more problem types? Try MathPapa Algebra Calculator
Clear Graphing Calculator »
Math Solver
Geogebra math solver.
Get accurate solutions and step-by-step explanations for algebra and other math problems, while enhancing your problem-solving skills!
Graph of a function
- 1 Graphing Points
- 2.1 Problem
- 2.2 Solution
- 3.1 Problem
- 3.2 Solution
- 3.3 Problem
- 3.4 Solution
Graphing Points
Graphing Lines
Given two distinct points on a line, one can construct the whole line. So one way to graph a line given its equation is to just find two points on it and to draw a straight line through them.
Now plot these in the coordinate plane and draw a line through them:
The arrowheads on the ends of the line segment indicate that the line goes on infinitely in both directions.
Graphing Polynomials
Something appears to not have loaded correctly.
Click to refresh .
Function Grapher and Calculator
Description :: All Functions
Description
Function Grapher is a full featured Graphing Utility that supports graphing up to 5 functions together.
You can also save your work as a URL (website link).
To plot a function just type it into the function box.
Use "x" as the variable like this:
- (x−3)(x+3)
Zooming and Re-centering
To zoom, use the zoom slider. To the left zooms in, to the right zooms out. When you let go of the slider it goes back to the middle so you can zoom more.
You can click-and-drag to move the graph around.
If you just click-and-release (without moving), then the spot you clicked on will be the new center
To reset the zoom to the original click on the Reset button.
Using "a" Values
There is a slider with "a =" on it. You can use "a" in your formula and then use the slider to change the value of "a" to see how it affects the graph.
- 2x−3a
All Functions
| + | Addition operator | |
|---|---|---|
| - | Subtraction operator | |
| * | Multiplication operator | |
| / | Division operator | |
| ^ | (Power) operator |
| Square Root of a value or expression. | ||
| sine of a value or expression | ||
| cosine of a value or expression | ||
| tangent of a value or expression | ||
| inverse sine (arcsine) of a value or expression | ||
| inverse cosine (arccos) of a value or expression | ||
| inverse tangent (arctangent) of a value or expression | ||
| sine (sinh) of a value or expression | ||
| Hyperbolic cosine (cosh) of a value or expression | ||
| Hyperbolic tangent (tanh) of a value or expression | ||
| e ( ) raised to the power of a value or expression | ||
| The natural logarithm of a value or expression | ||
| The base−10 logarithm of a value or expression | ||
| floor | Returns the largest (closest to positive infinity) value that is not greater than the argument and is equal to a mathematical integer. | |
| ceil | Returns the smallest (closest to negative infinity) value that is not less than the argument and is equal to a mathematical integer. | |
| round | Round to the nearest integer. Examples: round(−2.5) = −2, round(-0.1) = 0, round(0.1) = 0, round(2.5) = 3 | |
| abs | Absolute value (distance from zero) of a value or expression | |
| sign | Sign (+1 or −1) of a value or expression |
| pi | The number (3.14159265...) | |
|---|---|---|
| e | (2.71828...), the base for the natural logarithm |
Game Central
Similar problems from web search.
- {{subColumn.name}}
AIMS Mathematics
- {{newsColumn.name}}
- Share facebook twitter google linkedin
Generalized variational inclusion: graph convergence and dynamical system approach
- Doaa Filali 1 ,
- Mohammad Dilshad 2 ,
- Mohammad Akram 3 , ,
- 1. Department of Mathematical Science, College of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
- 2. Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia
- 3. Department of Mathematics, Islamic University of Madinah, Madinah 42351, Saudi Arabia
- Received: 29 May 2024 Revised: 13 July 2024 Accepted: 25 July 2024 Published: 21 August 2024
MSC : 47H05, 47H09, 47H10, 47H22, 47H25, 49J40
- Full Text(HTML)
- Download PDF
This work focused on the investigation of a generalized variation inclusion problem. The resolvent operator for generalized $ \eta $-co-monotone mapping was structured, the Lipschitz constant was estimated and its relationship with the graph convergence was accomplished. An Ishikawa type iterative algorithm was designed by incorporating the resolvent operator and total asymptotically non-expansive mapping. By employing the novel implication of graph convergence and analyzing the convergence of the considered iterative method, the common solution of the generalized variational inclusion and the set of fixed points of a total asymptotically non-expansive mapping was obtained. Moreover, a generalized resolvent dynamical system was investigated. Some of its attributes were discussed and implemented to examine the considered generalized variation inclusion problem.
- $ \eta $-co-monotone mapping ,
- graph convergence ,
- total asymptotically non-expansive mapping ,
- resolvent dynamical system ,
- generalized variational inclusion
Citation: Doaa Filali, Mohammad Dilshad, Mohammad Akram. Generalized variational inclusion: graph convergence and dynamical system approach[J]. AIMS Mathematics, 2024, 9(9): 24525-24545. doi: 10.3934/math.20241194
Related Papers:
| [1] | , (2023), 109–127. https://doi.org/10.33993/jnaat522-1351 --> H. A. Abass, K. O. Aremu, O. K. Oyewole, A. A. Mebawondu, O. K. Narain, Forward-backward splitting algorithm with self-adaptive method for finite family of split minimization and fixed point problems in Hilbert spaces, , (2023), 109–127. https://doi.org/10.33993/jnaat522-1351 doi: |
| [2] | , (2015), 1481–1506. https://doi.org/10.1007/s40840-014-0103-z --> R. Ahmad, M. Akram, M. Dilshad, Graph convergence for the $H(\cdot, \cdot)$-co-accretive mapping with an application, , (2015), 1481–1506. https://doi.org/10.1007/s40840-014-0103-z doi: |
| [3] | , (2011), 261534. https://doi.org/10.1155/2011/261534 --> R. Ahmad, M. Dilshad, M. M. Wong, J. C. Yao, $H(\cdot, \cdot)$-co-coercive operators and an application for solving generalized variational inclusions, , (2011), 261534. https://doi.org/10.1155/2011/261534 doi: |
| [4] | , (2013), 324–346. https://doi.org/10.1007/s10957-012-0182-7 --> R. Ahmad, M. Akram, J. C. Yao, Generalized monotone mapping with an application for solving variational inclusion problem, , (2013), 324–346. https://doi.org/10.1007/s10957-012-0182-7 doi: |
| [5] | , (2013), 411–427. --> R. Ahmad, B. S. Lee, M. Akram, $H(\cdot, \cdot)$-co-accretive mapping with an application for solving a system of variational inclusions, , (2013), 411–427. |
| [6] | , (2017), 155–163. https://doi.org/10.1007/s40096-017-0221-5 --> R. Ahmad, M. Ishtyak, M. Rahaman, I. Ahmad, Graph convergence and generalized Yosida approximation operator with an application, , (2017), 155–163. https://doi.org/10.1007/s40096-017-0221-5 doi: |
| [7] | , (2019), 153–167. --> M. Akram, M. Dilshad, Graph convergence for $\eta$-subdifferential mapping with application, , (2019), 153–167. |
| [8] | , (2006), 1–20. --> Y. I. Alber, C. E. Chidume, H. Zegeye, Approximating fixed points of total asymptotically nonexpansive mappings, , (2006), 1–20. |
| [9] | , (2023), 9557–9575. https://doi.org/10.3934/math.2023482 --> A. Arunchai, T. Seangwattana, K. Sitthithakerngkiet, K. Sombut, Image restoration by using a modified proximal point algorithm, , (2023), 9557–9575. https://doi.org/10.3934/math.2023482 doi: |
| [10] | , (2022), 112. https://doi.org/10.1186/s13660-022-02848-3 --> J. Balooee, J. C. Yao, Graph convergence with an application for system of variational inclusions and fixed-point problems, , (2022), 112. https://doi.org/10.1186/s13660-022-02848-3 doi: |
| [11] | , (2023), 1681–1701. https://doi.org/10.1080/02331934.2023.2173525 --> S. Dey, S. Reich, A dynamical system for solving inverse quasi-variational inequalities, , (2023), 1681–1701. https://doi.org/10.1080/02331934.2023.2173525 doi: |
| [12] | , (2015), 311–325. https://doi.org/10.1007/s10851-014-0523-2 --> A. L. Dirk, T. Pock, An inertial forward–backward algorithm for monotone inclusions, , (2015), 311–325. https://doi.org/10.1007/s10851-014-0523-2 doi: |
| [13] | , (1996), 35–44. https://doi.org/10.1016/0895-7177(96)00088-X --> J. Dong, D. Zhang, A. Nagurney, A projected dynamical systems model of general financial equilibrium with stability analysis, , (1996), 35–44. https://doi.org/10.1016/0895-7177(96)00088-X doi: |
| [14] | , (1993), 7–42. https://doi.org/10.1007/BF02073589 --> P. Dupuis, A. Nagurney, Dynamical systems and variational inequalities, advances in equilibrium modeling, analysis and computation, , (1993), 7–42. https://doi.org/10.1007/BF02073589 doi: |
| [15] | , (2003), 795–803. https://doi.org/10.1016/S0096-3003(03)00275-3 --> Y. P. Fang, N. J. Huang, $H$-monotone operator and resolvent operator technique for variational inclusions, , (2003), 795–803. https://doi.org/10.1016/S0096-3003(03)00275-3 doi: |
| [16] | , (2004), 647–653. https://doi.org/10.1016/S0893-9659(04)90099-7 --> Y. P. Fang, N. J. Huang, $H$-accretive operators and resolvent operator technique for solving variational inclusions in Banach spaces, , (2004), 647–653. https://doi.org/10.1016/S0893-9659(04)90099-7 doi: |
| [17] | , (2023), 12922–12942. https://doi.org/10.3934/math.2023651 --> M. Dilshad, M. Akram, M. Nasiruzzaman, D. Filali, A. A. Khidir, Adaptive inertial Yosida approximation iterative algorithms for split variational inclusion and fixed point problems, , (2023), 12922–12942. https://doi.org/10.3934/math.2023651 doi: |
| [18] | , (1994), 1120–1136. https://doi.org/10.1287/opre.42.6.1120 --> T. L. Friesz, D. Bernstein, N. J. Mehta, R. L. Tobin, S. Ganjalizadeh, Day-to-day dynamic network disequilibria and idealized traveler information systems, , (1994), 1120–1136. https://doi.org/10.1287/opre.42.6.1120 doi: |
| [19] | , (1972), 171–174. --> K. Goebel, W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, , (1972), 171–174. |
| [20] | , (2001), 591–592. --> N. J. Huang, Y. P. Fang, Generalized $m$-accretive mappings in Banach spaces, , (2001), 591–592. |
| [21] | , (2023), 118–145. https://doi.org/10.3846/mma.2023.14858 --> A. Khan, M. Akram, M. Dilshad, Approximation of iterative methods for altering points problem with applications, , (2023), 118–145. https://doi.org/10.3846/mma.2023.14858 doi: |
| [22] | , (2011), 9053–9061. https://doi.org/10.1016/j.amc.2011.03.119 --> X. Li, N. J. Huang, Graph convergence for the $H(\cdot, \cdot)$-accretive operator in Banach spaces with an application, , (2011), 9053–9061. https://doi.org/10.1016/j.amc.2011.03.119 doi: |
| [23] | , (2024), 363. https://doi.org/10.3390/sym16030363 --> R. Maluleka, G. C. Ugwunnadi, M. Aphane, H. A. Abass, A. R. Khan, Modified Tseng method for solving pseudomonotone variational inequality problem in Banach spaces, , (2024), 363. https://doi.org/10.3390/sym16030363 doi: |
| [24] | , (2002), 173–182. --> M. A. Noor, A Wiener-Hopf dynamical system for variational inequalities, , (2002), 173–182. |
| [25] | , (2002), 216–226. https://doi.org/10.1016/S0022-247X(02)00014-8 --> M. A. Noor, Implicit resolvent dynamical systems for quasi variational inclusions, , (2002), 216–226. https://doi.org/10.1016/S0022-247X(02)00014-8 doi: |
| [26] | , (2003), 69–81. https://doi.org/10.1016/S0096-3003(01)00269-7 --> M. A. Noor, Implicit dynamical systems and quasi variational inequalities, , (2003), 69–81. https://doi.org/10.1016/S0096-3003(01)00269-7 doi: |
| [27] | , (2020), 675–693. https://doi.org/10.1007/s12215-019-00427-y --> C. C. Okeke, C. Izuchukwu, O. T. Mewomo, Strong convergence results for convex minimization and monotone variational inclusion problems in Hilbert space, , (2020), 675–693. https://doi.org/10.1007/s12215-019-00427-y doi: |
| [28] | , (2021), 1–14. https://doi.org/10.1002/cmm4.1088 --> A. Padcharoen, D. Kitkuan, W. Kumam, P. Kumam, Tseng methods with inertial for solving inclusion problems and application to image deblurring and image recovery problems, , (2021), 1–14. https://doi.org/10.1002/cmm4.1088 doi: |
| [29] | , (2022), 112048. https://doi.org/10.1016/j.chaos.2022.112048 --> P. Peeyada, R. Suparatulatorn, W. Cholamjiak, An inertial mann forward–backward splitting algorithm of variational inclusion problems and its applications, , (2022), 112048. https://doi.org/10.1016/j.chaos.2022.112048 doi: |
| [30] | , (2005), 653–666. --> D. R. Sahu, Fixed points of demicontinuous nearly Lipschitzian mappings in Banach spaces, , (2005), 653–666. |
| [31] | , (1964), 4413–4416. --> G. Stampacchia, Formes bilineaires coercivites sur les ensembles convexes, , (1964), 4413–4416. |
| [32] | , (2012), 196–214. https://doi.org/10.1007/s10957-012-0030-9 --> R. U. Verma, General class of implicit variational inclusions and graph convergence on A-maximal relaxed monotonicity, , (2012), 196–214. https://doi.org/10.1007/s10957-012-0030-9 doi: |
| [33] | , (2022), 1612. https://doi.org/10.3390/math10091612 --> Y. Wang, T. Xu, J. C. Yao, B. Jiang, Self-adaptive method and inertial modification for solving the split feasibility problem and fixed point problem of quasi-nonexpansive mapping, , (2022), 1612. https://doi.org/10.3390/math10091612 doi: |
| [34] | , (1991), 727–732. --> X. Weng, Fixed point iteration for local strictly pseudo-contractive mapping, , (1991), 727–732. |
| [35] | , (204) (2008), 809–816. https://doi.org/10.1016/j.amc.2008.07.024 --> Y. Z. Zou, N. J. Huang, $H(\cdot, \cdot)$-accretive operator with an application for solving variational inclusions in Banach spaces, , (204) (2008), 809–816. https://doi.org/10.1016/j.amc.2008.07.024 doi: |
- This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/4.0/ -->
Supplements
Access History
- Corresponding author: Email: [email protected]
Reader Comments
- © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License ( http://creativecommons.org/licenses/by/4.0 )
通讯作者: 陈斌, [email protected]
沈阳化工大学材料科学与工程学院 沈阳 110142
Article views( 79 ) PDF downloads( 25 ) Cited by( 0 )
Figures and Tables
Figures( 1 )
Associated material
Other articles by authors.
- Doaa Filali
- Mohammad Dilshad
- Mohammad Akram
Related pages
- on Google Scholar
- Email to a friend
- Order reprints
Export File
- Figure 1. Convergence behavior of $ \{\theta_{n}\} $ for Example 3.1 and Example 3.2 with initial values $ \theta_{0} = -10.5, \theta_{0} = 1.5 $, and $ \theta_{0} = -6, \theta_{0} = 1 $, respectively
Semi-supervised regression with label-guided adaptive graph optimization
- Published: 24 August 2024
Cite this article
- Xiaohan Zheng 1 ,
- Li Zhang ORCID: orcid.org/0000-0001-7914-0679 1 ,
- Leilei Yan 1 &
- Lei Zhao 1
For the semi-supervised regression task, both the similarity of paired samples and the limited label information serve as core indicators. Nevertheless, most traditional semi-supervised regression methods cannot make full use of both simultaneously. To alleviate the above deficiency, this paper proposes a novel semi-supervised regression with label-guided adaptive graph optimization (LGAGO-SSR). Basically, LGAGO-SSR involves two phases: graph representation and label-guided adaptive graph construction. The first phase seeks two low-dimensional manifold spaces based on two similarity matrices. The second phase aims at adaptively learning these similarity matrices by integrating the data structure information in both the low-dimensional manifold spaces and the label spaces. Each phase has its optimization problems, and the final solution is obtained by iteratively solving problems in two phases. Additionally, the idea of decomposition optimization in twin support vector regression (TSVR) is used to accelerate the training of our LGAGO-SSR. Regression results on 12 benchmark datasets with different unlabeled rates demonstrate the effectiveness of LGAGO-SSR in semi-supervised regression tasks.
Graphical abstract
This is a preview of subscription content, log in via an institution to check access.
Access this article
Subscribe and save.
- Get 10 units per month
- Download Article/Chapter or eBook
- 1 Unit = 1 Article or 1 Chapter
- Cancel anytime
Price includes VAT (Russian Federation)
Instant access to the full article PDF.
Rent this article via DeepDyve
Institutional subscriptions
Explore related subjects
- Artificial Intelligence
Data availability and access
After obtaining a license to use the data, the data can be accessed by visiting the following websites: https://archive.ics.uci.edu/ml/index.php , https://hastie.su.domains/ElemStatLearn/data.html and https://tianchi.aliyun.com/dataset/159885 . Users can use the data for study and research purposes, but not for commercial purposes.
https://tianchi.aliyun.com/dataset/159885
Smola AJ, Schölkopf B (2004) A tutorial on support vector regression. Statistics and Computing 14:199–222
Article MathSciNet Google Scholar
Myles AJ, Feudale RN, Liu Y, Woody NA, Brown SD (2004) An introduction to decision tree modeling. Journal of Chemometrics: J Chemometr Soc 18(6):275–285
Article Google Scholar
Tibshirani R (1996) Regression shrinkage and selection via the lasso. J R Stat Soc Ser B Stat Methodol 58(1):267–288
Czajkowski M, Jurczuk K, Kretowski M (20230) Steering the interpretability of decision trees using lasso regression - an evolutionary perspective. Inform Sci 638118944
Jain N, Jana PK (2023) LRF: A logically randomized forest algorithm for classification and regression problems. Expert Syst Appl 213.(Part C) 119225
Chen H, Wu L, Chen J, Lu W, Ding J (2022) A comparative study of automated legal text classification using random forests and deep learning. Inf Process Manag 59(2):102798
Zhou Z, Li M (2005) Semi-supervised regression with co-training. In: Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence, pp 908–913. Morgan Kaufmann, San Francisco, USA
Zhou Z, Li M (2007) Semisupervised regression with cotraining-style algorithms. IEEE Trans Knowl Data Eng 19(11):1479–1493
Wang X, Ma L, Wang X (2010) Apply semi-supervised support vector regression for remote sensing water quality retrieving. IEEE Int Geosci Remote Sens Symp. IEEE, Piscataway, USA, pp 2757–2760
Google Scholar
Emadi M, Tanha J, Shiri ME, Aghdam MH (2021) A selection metric for semi-supervised learning based on neighborhood construction. Inf Process Manag 58(2):102444
Lin K, Pai P, Lu Y, Chang P (2013) Revenue forecasting using a least-squares support vector regression model in a fuzzy environment. Inf Sci 220196–209
Yue Y, Wang G, Hu J, Li Y (2023) An improved label propagation algorithm based on community core node and label importance for community detection in sparse network. Appl Intell 5317935–17951
Hua Z, Yang Y (2022) Robust and sparse label propagation for graph-based semi-supervised classification. Appl Intell 523337–3351
Hua Z, Yang Y, Qiu H (2021) Node influence-based label propagation algorithm for semi-supervised learning. Neural Comput & Applic 332753–2768
Wang B, Tsotsos J (2016) Dynamic label propagation for semi-supervised multi-class multi-label classification. Pattern Recogn 5275–84
Yoo J, Kim HJ (2014) Semisupervised location awareness in wireless sensor networks using Laplacian support vector regression. Int J Distrib Sensor Netw 10265801
Belkin M, Niyogi P, Sindhwani V (2006) Manifold regularization: A geometric framework for learning from labeled and unlabeled examples. J Mach Learn Res 72399–2434
Yu J, Son Y (2021) Weighted co-association rate-based Laplacian regularized label description for semi-supervised regression. Inf Sci 545688–712
Yu Z, Ye F, Yang K, Cao W, Chen CLP, Cheng L, You J, Wong H (2022) Semisupervised classification with novel graph construction for high-dimensional data. IEEE Trans Neural Netw Learn Syst 33(1):75–88
Zhou B, Liu W, Zhang W, Lu Z, Tan Q (2022) Multi-kernel graph fusion for spectral clustering. Inf Process Manag 59(5):103003
Nie F, Dong X, Li X (2021) Unsupervised and semisupervised projection with graph optimization. IEEE Trans Neural Netw Learn Syst 32(4):1547–1559
Wang S, Chen Y, Yi S, Chao G (2022) Frobenius norm-regularized robust graph learning for multi-view subspace clustering. Appl Intell 52(13):14935–14948
Zhang R, Nie F, Li X (2019) Semisupervised learning with parameter-free similarity of label and side information. IEEE Trans Neural Netw Learn Syst 30(2):405–414
Zhang L, Liu Z, Pu J, Song B (2020) Adaptive graph regularized nonnegative matrix factorization for data representation. Appl Intell 50438–447
Li D, Madden AD (2019) Cascade embedding model for knowledge graph inference and retrieval. Inf Process Manag 56(6):102093
Chen L, Zhong Z (2022) Adaptive and structured graph learning for semi-supervised clustering. Inf Process Manag 59(4):102949
Liu J, Lin M, Zhao M, Zhan C, Li B, Chui JKT (2023) Person re-identification via semi-supervised adaptive graph embedding. Appl Intell 53(3):2656–2672
Zhang L, Zhou W, Chang P, Liu J, Yan Z, Wang T, Li FZ (2012) Kernel sparse representation-based classifier. IEEE Trans Signal Process 60(4):1684–1695
Nie F, Wang X, Huang H (2014) Clustering and projected clustering with adaptive neighbors. International Conference on Knowledge Discovery and Data Mining. ACM, New York, USA, pp 977–986
Peng X (2010) TSVR: A n efficient twin support vector machine for regression. Neural Netw 23(3):365–372
Zhuang L, Zhou Z, Gao S, Yin J, Lin Z, Ma Y (2017) Label information guided graph construction for semi-supervised learning. IEEE Trans Image Process 26(9):4182–4192
Peng X, Chen D, Xu D (2019) Hyperplane-based nonnegative matrix factorization with label information. Inf Sc 4931–19
Liu Z, Wang T, Zhu F, Chen X, Pelusi D, Vasilakos AV (2024) Domain adaptive learning based on equilibrium distribution and dynamic subspace approximation. Expert Syst Appl 249123673
Kiyadeh APH, Zamiri A, Yazdi HS, Ghaemi H (2015) Discernible visualization of high dimensional data using label information. Appl Soft Comput 27474–486
Zhu X, Ghahramani Z (2002)Learning from labeled and unlabeled data with label propagation. Technical Report, Technical Report CMU-CALD-02–107, Carnegie Mellon University
Quinlan JR (1993) Combining instance-based and model-based learning. In: Machine Learning, Proceedings of the Tenth International Conference, University of Massachusetts, pp 236–243. Morgan Kaufmann, San Francisco, USA
Breiman L, Friedman JH (1985) Estimating optimal transformations for multiple regression and correlation. J Am Stat Assoc 80(391):580–598
Zhou F, Q C, King RD (2014) Predicting the geographical origin of music. 2014 IEEE Int Conf Data Min. IEEE Computer Society, Los Alamitos, USA, pp 1115–1120
Yeh IC, Hsu TK (2018) Building real estate valuation models with comparative approach through case-based reasoning. Appl Soft Comput 65260–271
Yeh IC (1998) Modeling of strength of high-performance concrete using artificial neural networks. Cem Concr Res 28(12):1797–1808
Yeh IC (2007) Modeling slump flow of concrete using second-order regressions and artificial neural networks. Cem Concr Res 29(6):474–480
Grisoni F, Consonni V, Vighi M, Villa S, Todeschini R (2016) Investigating the mechanisms of bioconcentration through QSAR classification trees. Environ Int 88198–205
Akbilgic O, Bozdogan H, Balaban ME (2014) A novel hybrid RBF neural networks model as a forecaster. Stat Comput 24(3):365–375
Owen AB (1999) Tubular neighbors for regression and classification. Citeseer
Nash W, Sellers T, Talbot S, Cawthorn A, Ford W (1995) Abalone. UCI Machine Learning Repository. https://doi.org/10.24432/C55C7W
Cortez P, Cerdeira A, Almeida F, Matos T, Reis J (2009) Modeling wine preferences by data mining from physicochemical properties. Decision support systems 47(4):547–553
Timilsina M, Figueroa A, d’Aquin M, Yang H (2021) Semi-supervised regression using diffusion on graphs. Appl Soft Comput 104107188
Liu L, Huang P, Yu H, Min F (2023) Safe co-training for semi-supervised regression. Intelligent Data Analysis 27:959–975
Demsar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res Learning Research 7(1):1–30
MathSciNet Google Scholar
Dunn OJ (1961) Multiple comparisons among means. J Am Stat Assoc 56(293):52–64
Download references
Acknowledgements
We would like to thank five anonymous reviewers and Editor for their valuable comments and suggestions, which have significantly improved this paper. This work was supported in part by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under Grant No. 19KJA550002, by the Six Talent Peak Project of Jiangsu Province of China under Grant No. XYDXX-054, by the Priority Academic Program Development of Jiangsu Higher Education Institutions, and by the Collaborative Innovation Center of Novel Software Technology and Industrialization.
Author information
Authors and affiliations.
School of Computer Science and Technology, Soochow University, 215006, Suzhou, Jiangsu, China
Xiaohan Zheng, Li Zhang, Leilei Yan & Lei Zhao
You can also search for this author in PubMed Google Scholar
Contributions
Xiaohan Zheng : Methodology, Software, Validation, Writing - original draft, Writing - review & editing. Li Zhang : Conceptualization, Methodology, Software, Writing - review & editing, Validation, Project administration, Funding acquisition. Leilei Yan : Investigation, Software, Visualization. Lei Zhao : Investigation, Software, Visualization.
Corresponding author
Correspondence to Li Zhang .
Ethics declarations
Competing interests.
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Ethical and informed consent for data used
This article does not contain any studies with human participants or animals performed by any of the authors
Additional information
Publisher's note.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
1.1 Appendix A: Derivation from ( 13 ) to ( 17 )
Let \(v^{low}_{ij}={\Vert \varvec{w}_1^T \varvec{x}_i-\varvec{w}_1^T \varvec{x}_j\Vert }_2^2+\Vert y^{low}_i-y^{low}_j\Vert _2^2\) , then the objective function in ( 13 ) can be rewritten as
where \(\varvec{v}^{low}_i=[v^{low}_{i1},v^{low}_{i2},\cdots ,v^{low}_{in}]^T\) .
Because \(\lambda ^{low}_i\) and \(\varvec{v}^{low}_{i}\) are unrelated to \(\varvec{s}_i^{low}\) , the last term in ( 57 ) is a constant. Therefore, the objective function in ( 13 ) is equivalent to
In a summary, we have completed the derivation from ( 13 ) to ( 17 ).
1.2 Appendix B: Proof of Theorem 1
The sequences \(\left\{ \left( \varvec{w}_1^{(p)},b_1^{(p)},\varvec{\xi }_1^{(p)},{\varvec{S}^{low}}^{(p)},{\varvec{y}^{low}}^{(p)}\right) \right\} \) and \(\left\{ \!(\varvec{w}_2^{(p)},b_2^{(p)},{\varvec{\xi }_2}^{(p)},{\varvec{S}^{up}}^{(p)},{\varvec{y}^{up}}^{(p)})\!\right\} \) generated by Algorithm 1 can guarantee that \(\left\{ G_1(\varvec{w}_1^{(p)},b_1^{(p)},\varvec{\xi }_1^{(p)},{\varvec{S}^{low}}^{(p)},{\varvec{y}^{low}}^{(p)})\right\} \) and \(\left\{ G_2(\varvec{w}_2^{(p)},b_2^{(p)},{\varvec{\xi }_2}^{(p)},{\varvec{S}^{up}}^{(p)},{\varvec{y}^{up}}^{(p)})\right\} \) are monotonic decreasing and bounded, respectively, where p refers to the current number of iterations.
Assume that p is the current iteration. First, we prove that the sequence \(\left\{ G_1\left( \varvec{w}_1^{(p)},b_1^{(p)},\varvec{\xi }_1^{(p)},{\varvec{S}^{low}}^{(p)},{\varvec{y}^{low}}^{(p)}\right) \right\} \) decreases monotonically. Given \(\left( \varvec{w}_1^{(p)},b_1^{(p)},\varvec{\xi }_1^{(p)}\right) \) , we optimize ( 13 ) to obtain \(\left( {\varvec{S}^{low}}^{(p+1)},{\varvec{y}^{low}}^{(p+1)}\right) \) , thus we have
Given \(\left( {\varvec{S}^{low}}^{(p+1)},{\varvec{y}^{low}}^{(p+1)}\right) \) , we optimize ( 9 ) to obtain \(\left( \varvec{w}_1^{(p+1)},b_1^{(p+1)},\varvec{\xi }_1^{(p+1)}\right) \) , thus we have
By combining ( 59 ) and ( 60 ), we have
which indicates that the sequence \(\Big \{G_1\Big (\varvec{w}_1^{(p)},b_1^{(p)},\varvec{\xi }_1^{(p)},\) \({\varvec{S}^{low}}^{(p)},{\varvec{y}^{low}}^{(p)}\Big )\Big \}\) for \(p=1, 2, \cdots \) is monotonic decreasing. In the same way, we can prove that the sequence \(\left\{ G_2\left( \varvec{w}_2^{(p)},b_2^{(p)},{\varvec{\xi }_2}^{(p)},{\varvec{S}^{up}}^{(p)},{\varvec{y}^{up}}^{(p)}\right) \right\} \) is monotonic dec-reasing when \(p=1,2,\cdots \) .
Next, we prove that both the sequences \(\Big \{G_1\Big (\varvec{w}_1^{(p)},b_1^{(p)},\) \(\varvec{\xi }_1^{(p)},{\varvec{S}^{low}}^{(p)},{\varvec{y}^{low}}^{(p)}\Big )\Big \}\) and \(\Big \{G_2\Big (\varvec{w}_2^{(p)},b_2^{(p)},{\varvec{\xi }_2}^{(p)},{\varvec{S}^{up}}^{(p)},\) \({\varvec{y}^{up}}^{(p)}\Big )\Big \}\) have the infimum. In ( 15 ) and ( 16 ), we know that \(s^{low}_{ij}\) , \(s^{up}_{ij}\) , \(\lambda ^{low}_i\) , \(\lambda ^{up}_i\) , and \(C_i~(i=1,2,3,4)\) are all great than zero. Thus, it is easy to infer that
In the other word, \(\left\{ G_1\!\left( \varvec{w}_1^{(p)},b_1^{(p)},\varvec{\xi }_1^{(p)},\!{\varvec{S}^{low}}^{(p)},{\varvec{y}^{low}}^{(p)}\right) \!\right\} \) and \(\left\{ G_2\left( \varvec{w}_2^{(p)},b_2^{(p)},{\varvec{\xi }_2}^{(p)},{\varvec{S}^{up}}^{(p)},{\varvec{y}^{up}}^{(p)}\right) \right\} \) have the infimum that equals 0.
This completes the proof of Theorem 1 .
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
Reprints and permissions
About this article
Zheng, X., Zhang, L., Yan, L. et al. Semi-supervised regression with label-guided adaptive graph optimization. Appl Intell (2024). https://doi.org/10.1007/s10489-024-05766-7
Download citation
Accepted : 11 August 2024
Published : 24 August 2024
DOI : https://doi.org/10.1007/s10489-024-05766-7
Share this article
Anyone you share the following link with will be able to read this content:
Sorry, a shareable link is not currently available for this article.
Provided by the Springer Nature SharedIt content-sharing initiative
- Semi-supervised regression
- Adaptive graph construction
- Graph representation
- Manifold space
- Label space
- Find a journal
- Publish with us
- Track your research
- AI Math Solver Graphing Calculator Popular Problems Worksheets Study Guides Cheat Sheets Calculators Verify Solution
- Solutions Integral Calculator Derivative Calculator Algebra Calculator Matrix Calculator More...
- Graphing Line Graph Exponential Graph Quadratic Graph Sine Graph More...
- Calculators BMI Calculator Compound Interest Calculator Percentage Calculator Acceleration Calculator More...
- Geometry Pythagorean Theorem Calculator Circle Area Calculator Isosceles Triangle Calculator Triangles Calculator More...
- Tools Notebook Groups Cheat Sheets Worksheets Study Guides Practice Verify Solution
| x^{\msquare} | \log_{\msquare} | \sqrt{\square} | \nthroot[\msquare]{\square} | \le | \ge | \frac{\msquare}{\msquare} | \cdot | \div | x^{\circ} | \pi | |||||||||||
| \left(\square\right)^{'} | \frac{d}{dx} | \frac{\partial}{\partial x} | \int | \int_{\msquare}^{\msquare} | \lim | \sum | \infty | \theta | (f\:\circ\:g) | f(x) | |||||||||||
| ▭\:\longdivision{▭} | \times \twostack{▭}{▭} | + \twostack{▭}{▭} | - \twostack{▭}{▭} | \left( | \right) | \times | \square\frac{\square}{\square} |
- Pre Algebra Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Number Line Expanded Form Mean, Median & Mode
- Algebra Equations Inequalities System of Equations System of Inequalities Basic Operations Algebraic Properties Partial Fractions Polynomials Rational Expressions Sequences Power Sums Interval Notation Pi (Product) Notation Induction Prove That Logical Sets Word Problems
- Pre Calculus Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Coterminal Angle Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections Trigonometry
- Calculus Derivatives Derivative Applications Limits Integrals Integral Applications Integral Approximation Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin Series Fourier Series Fourier Transform
- Functions Line Equations Functions Arithmetic & Comp. Conic Sections Transformation
- Linear Algebra Matrices Vectors
- Trigonometry Identities Proving Identities Trig Equations Trig Inequalities Evaluate Functions Simplify
- Statistics Mean Geometric Mean Quadratic Mean Average Median Mode Order Minimum Maximum Probability Mid-Range Range Standard Deviation Variance Lower Quartile Upper Quartile Interquartile Range Midhinge Standard Normal Distribution
- Physics Mechanics
- Chemistry Chemical Reactions Chemical Properties
- Finance Simple Interest Compound Interest Present Value Future Value
- Economics Point of Diminishing Return
- Conversions Roman Numerals Radical to Exponent Exponent to Radical To Fraction To Decimal To Mixed Number To Improper Fraction Radians to Degrees Degrees to Radians Hexadecimal Scientific Notation Distance Weight Time Volume
- Pre Algebra
- Pre Calculus
- Given Points
- Given Slope & Point
- Slope Intercept Form
- Start Point
- Parallel Lines
- Perpendicular
- Perpendicular Lines
- Perpendicular Slope
- Is a Function
- Domain & Range
- Slope & Intercepts
- Periodicity
- Domain of Inverse
- Critical Points
- Inflection Points
- Monotone Intervals
- Extreme Points
- Global Extreme Points
- Absolute Extreme
- Turning Points
- End Behavior
- Average Rate of Change
- Piecewise Functions
- Discontinuity
- Values Table
- Compositions
- Arithmetics
- Circumference
- Eccentricity
- Conic Inequalities
- Transformation
- Linear Algebra
- Trigonometry
- Conversions
| x^{\msquare} | \log_{\msquare} | \sqrt{\square} | \nthroot[\msquare]{\square} | \le | \ge | \frac{\msquare}{\msquare} | \cdot | \div | x^{\circ} | \pi | |||||||||||
| \left(\square\right)^{'} | \frac{d}{dx} | \frac{\partial}{\partial x} | \int | \int_{\msquare}^{\msquare} | \lim | \sum | \infty | \theta | (f\:\circ\:g) | f(x) | |||||||||||
| - \twostack{▭}{▭} | \lt | 7 | 8 | 9 | \div | AC |
| + \twostack{▭}{▭} | \gt | 4 | 5 | 6 | \times | \square\frac{\square}{\square} |
| \times \twostack{▭}{▭} | \left( | 1 | 2 | 3 | - | x |
| ▭\:\longdivision{▭} | \right) | . | 0 | = | + | y |
Number Line
- y=\frac{x^2+x+1}{x}
- f(x)=\ln (x-5)
- f(x)=\frac{1}{x^2}
- y=\frac{x}{x^2-6x+8}
- f(x)=\sqrt{x+3}
- f(x)=\cos(2x+5)
- f(x)=\sin(3x)
| 🌐 Languages | EN, ES, PT & more |
|---|---|
| 🏆 Practice | Improve your math skills |
| 😍 Step by step | In depth solution steps |
| ⭐️ Rating | based on 20924 reviews |
functions-calculator
- Functions A function basically relates an input to an output, there’s an input, a relationship and an output. For every input...
We want your feedback
Please add a message.
Message received. Thanks for the feedback.
IMAGES
COMMENTS
Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.
Free online graphing calculator - graph functions, conics, and inequalities interactively.
Free graphing calculator instantly graphs your math problems.
Learn how to solve equations by graphing them on a coordinate plane. Watch a video with examples and practice problems. Khan Academy offers free, world-class education for anyone, anywhere.
Use QuickMath to graph quadratic, system, or linear equations with a free step-by-step math calculator.
Graphing basic functions and their variations. In this tutorial you will learn about graphing basic parent functions and derived functions.
Interactive, free online graphing calculator from GeoGebra: graph functions, plot data, drag sliders, and much more!
Example 2 Sketch the graph of the following piecewise function. g(x) ={−x2 +4 if x <1 2x−1 if x ≥ 1 g ( x) = { − x 2 + 4 if x < 1 2 x − 1 if x ≥ 1. Show Solution. Okay, now when we are graphing piecewise functions we are really graphing several functions at once, except we are only going to graph them on very specific intervals.
Graph your equations with MathPapa! This graphing calculator will show you how to graph your problems.
Get accurate solutions and step-by-step explanations for algebra and other math problems with the free GeoGebra Math Solver. Enhance your problem-solving skills while learning how to solve equations on your own. Try it now!
Symbolab: equation search and math solver - solves algebra, trigonometry and calculus problems step by step
Solution. To graph a line, it is necesasry to find two points that satisfy . Letting gives . So is one point on the graph. Find another point by letting . Plugging this in and solving gives . So is our other point. Now plot these in the coordinate plane and draw a line through them: The arrowheads on the ends of the line segment indicate that ...
Symbolab is the best step by step calculator for a wide range of math problems, from basic arithmetic to advanced calculus and linear algebra. It shows you the solution, graph, detailed steps and explanations for each problem.
Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.
Explore and plot functions with this interactive tool. Math is Fun offers you a function grapher and calculator for free.
Inverse Hyperbolic Functions. From the graphs of the hyperbolic functions, we see that all of them are one-to-one except \(\cosh x\) and \(\operatorname{sech}x\). If we restrict the domains of these two functions to the interval \([0,∞),\) then all the hyperbolic functions are one-to-one, and we can define the inverse hyperbolic functions ...
Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more.
Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more.
Gromov-Hausdorff distances measure shape difference between the objects representable as compact metric spaces, e.g. point clouds, manifolds, or graphs. Computing any Gromov-Hausdorff distance is equivalent to solving an NP-hard optimization problem, deeming the notion impractical for applications. In this paper we propose a polynomial algorithm for estimating the so-called modified Gromov ...
Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.
Free functions and line calculator - analyze and graph line equations and functions step-by-step.
This work focused on the investigation of a generalized variation inclusion problem. The resolvent operator for generalized $ \eta $-co-monotone mapping was structured, the Lipschitz constant was estimated and its relationship with the graph convergence was accomplished. An Ishikawa type iterative algorithm was designed by incorporating the resolvent operator and total asymptotically non ...
Abstract For the semi-supervised regression task, both the similarity of paired samples and the limited label information serve as core indicators. Nevertheless, most traditional semi-supervised regression methods cannot make full use of both simultaneously. To alleviate the above deficiency, this paper proposes a novel semi-supervised regression with label-guided adaptive graph optimization ...
Free functions calculator - explore function domain, range, intercepts, extreme points and asymptotes step-by-step.