Matching algorithms : fundamentals, applications and challenges
- Ren, Jing, Xia, Feng, Chen, Xiangtai, Liu, Jiaying, Sultanova, Nargiz
- Authors: Ren, Jing , Xia, Feng , Chen, Xiangtai , Liu, Jiaying , Sultanova, Nargiz
- Date: 2021
- Type: Text , Journal article , Review
- Relation: IEEE Transactions on Emerging Topics in Computational Intelligence Vol. 5, no. 3 (2021), p. 332-350
- Full Text:
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- Description: Matching plays a vital role in the rational allocation of resources in many areas, ranging from market operation to people's daily lives. In economics, the term matching theory is coined for pairing two agents in a specific market to reach a stable or optimal state. In computer science, all branches of matching problems have emerged, such as the question-answer matching in information retrieval, user-item matching in a recommender system, and entity-relation matching in the knowledge graph. A preference list is the core element during a matching process, which can either be obtained directly from the agents or generated indirectly by prediction. Based on the preference list access, matching problems are divided into two categories, i.e., explicit matching and implicit matching. In this paper, we first introduce the matching theory's basic models and algorithms in explicit matching. The existing methods for coping with various matching problems in implicit matching are reviewed, such as retrieval matching, user-item matching, entity-relation matching, and image matching. Furthermore, we look into representative applications in these areas, including marriage and labor markets in explicit matching and several similarity-based matching problems in implicit matching. Finally, this survey paper concludes with a discussion of open issues and promising future directions in the field of matching. © 2017 IEEE. **Please note that there are multiple authors for this article therefore only the name of the first 5 including Federation University Australia affiliate “Jing Ren, Xia Feng, Nargiz Sultanova" is provided in this record**
- Authors: Ren, Jing , Xia, Feng , Chen, Xiangtai , Liu, Jiaying , Sultanova, Nargiz
- Date: 2021
- Type: Text , Journal article , Review
- Relation: IEEE Transactions on Emerging Topics in Computational Intelligence Vol. 5, no. 3 (2021), p. 332-350
- Full Text:
- Reviewed:
- Description: Matching plays a vital role in the rational allocation of resources in many areas, ranging from market operation to people's daily lives. In economics, the term matching theory is coined for pairing two agents in a specific market to reach a stable or optimal state. In computer science, all branches of matching problems have emerged, such as the question-answer matching in information retrieval, user-item matching in a recommender system, and entity-relation matching in the knowledge graph. A preference list is the core element during a matching process, which can either be obtained directly from the agents or generated indirectly by prediction. Based on the preference list access, matching problems are divided into two categories, i.e., explicit matching and implicit matching. In this paper, we first introduce the matching theory's basic models and algorithms in explicit matching. The existing methods for coping with various matching problems in implicit matching are reviewed, such as retrieval matching, user-item matching, entity-relation matching, and image matching. Furthermore, we look into representative applications in these areas, including marriage and labor markets in explicit matching and several similarity-based matching problems in implicit matching. Finally, this survey paper concludes with a discussion of open issues and promising future directions in the field of matching. © 2017 IEEE. **Please note that there are multiple authors for this article therefore only the name of the first 5 including Federation University Australia affiliate “Jing Ren, Xia Feng, Nargiz Sultanova" is provided in this record**
Lost in optimisation of water distribution systems? A literature review of system operation
- Mala-Jetmarova, Helena, Sultanova, Nargiz, Savic, Dragan
- Authors: Mala-Jetmarova, Helena , Sultanova, Nargiz , Savic, Dragan
- Date: 2017
- Type: Text , Journal article , Review
- Relation: Environmental Modelling and Software Vol. 93, no. (2017), p. 209-254
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- Description: Optimisation of the operation of water distribution systems has been an active research field for almost half a century. It has focused mainly on optimal pump operation to minimise pumping costs and optimal water quality management to ensure that standards at customer nodes are met. This paper provides a systematic review by bringing together over two hundred publications from the past three decades, which are relevant to operational optimisation of water distribution systems, particularly optimal pump operation, valve control and system operation for water quality purposes of both urban drinking and regional multiquality water distribution systems. Uniquely, it also contains substantial and thorough information for over one hundred publications in a tabular form, which lists optimisation models inclusive of objectives, constraints, decision variables, solution methodologies used and other details. Research challenges in terms of simulation models, optimisation model formulation, selection of optimisation method and postprocessing needs have also been identified. © 2017
- Authors: Mala-Jetmarova, Helena , Sultanova, Nargiz , Savic, Dragan
- Date: 2017
- Type: Text , Journal article , Review
- Relation: Environmental Modelling and Software Vol. 93, no. (2017), p. 209-254
- Full Text:
- Reviewed:
- Description: Optimisation of the operation of water distribution systems has been an active research field for almost half a century. It has focused mainly on optimal pump operation to minimise pumping costs and optimal water quality management to ensure that standards at customer nodes are met. This paper provides a systematic review by bringing together over two hundred publications from the past three decades, which are relevant to operational optimisation of water distribution systems, particularly optimal pump operation, valve control and system operation for water quality purposes of both urban drinking and regional multiquality water distribution systems. Uniquely, it also contains substantial and thorough information for over one hundred publications in a tabular form, which lists optimisation models inclusive of objectives, constraints, decision variables, solution methodologies used and other details. Research challenges in terms of simulation models, optimisation model formulation, selection of optimisation method and postprocessing needs have also been identified. © 2017
Reconstruction of tropical cyclone and depression proxies for the South Pacific since the 1850s
- Yeasmin, Alea, Chand, Savin, Sultanova, Nargiz
- Authors: Yeasmin, Alea , Chand, Savin , Sultanova, Nargiz
- Date: 2023
- Type: Text , Journal article
- Relation: Weather and Climate Extremes Vol. 39, no. (2023), p.
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- Description: Southwest Pacific nations are highly vulnerable to extreme weather and climate events, particularly those associated with synoptic-scale systems such as tropical cyclones (TCs) and depressions (TDs). This study utilises the Okubo–Weiss–Zeta parameter (OWZP) method to reconstruct historical records of both TCs and TDs for the South Pacific basin using state-of-the-art NOAA-CIRES Twentieth Century Reanalysis (20CR) product. Extensive statistical assessments of these reconstructions are carried out using observational records for the satellite period (i.e., 1979–2014) as ‘ground-truths’. Results show that 20CR-derived TCs and TDs resemble several key characteristics of the observational records, including spatial distribution of genesis locations and track shapes. This gives us confidence that the 20CR-derived long-term records of TCs and TDs can serve as an effective tool for examining historical changes in various characteristics of TCs and TDs, particularly in the context of anthropogenic climate change. © 2022
- Authors: Yeasmin, Alea , Chand, Savin , Sultanova, Nargiz
- Date: 2023
- Type: Text , Journal article
- Relation: Weather and Climate Extremes Vol. 39, no. (2023), p.
- Full Text:
- Reviewed:
- Description: Southwest Pacific nations are highly vulnerable to extreme weather and climate events, particularly those associated with synoptic-scale systems such as tropical cyclones (TCs) and depressions (TDs). This study utilises the Okubo–Weiss–Zeta parameter (OWZP) method to reconstruct historical records of both TCs and TDs for the South Pacific basin using state-of-the-art NOAA-CIRES Twentieth Century Reanalysis (20CR) product. Extensive statistical assessments of these reconstructions are carried out using observational records for the satellite period (i.e., 1979–2014) as ‘ground-truths’. Results show that 20CR-derived TCs and TDs resemble several key characteristics of the observational records, including spatial distribution of genesis locations and track shapes. This gives us confidence that the 20CR-derived long-term records of TCs and TDs can serve as an effective tool for examining historical changes in various characteristics of TCs and TDs, particularly in the context of anthropogenic climate change. © 2022
Subseasonal prediction framework for tropical cyclone activity in the Solomon Islands region
- Haruhiru, Alick, Chand, Savin, Sultanova, Nargiz, Ramsay, Hamish, Sharma, Krishneel, Tahani, Lloyd
- Authors: Haruhiru, Alick , Chand, Savin , Sultanova, Nargiz , Ramsay, Hamish , Sharma, Krishneel , Tahani, Lloyd
- Date: 2023
- Type: Text , Journal article
- Relation: International Journal of Climatology Vol. 43, no. 12 (2023), p. 5763-5777
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- Reviewed:
- Description: Recently, we developed seasonal prediction schemes with improved skill to predict tropical cyclone (TC) activity up to 3 months in advance for the Solomon Islands (SI) region (5°–15°S, 155°–170°E) using sophisticated Bayesian regression techniques. However, TC prediction at subseasonal timescale (i.e., 1–4 weeks in advance) is not being researched for that region despite growing demands from decision makers at sectoral level. In this paper, we first assess the feasibility of developing subseasonal prediction frameworks for the SI region using a pool of predictors that are known to affect TC activity in the region. We then evaluate multiple predictor combinations to develop the most appropriate models using a statistical approach to forecast weekly TC activity up to 4 weeks in advance. Predictors used include indices of various natural climate variability modes, namely the Madden–Julian Oscillation (MJO), the El Niño–Southern Oscillation (ENSO), the Indian Ocean Dipole (IOD) and the Interdecadal Pacific Oscillation (IPO). These modes often have robust physical and statistical relationships with TC occurrences in the SI region and the broader southwest Pacific territory as shown by preceding studies. Additionally, we incorporate TC seasonality as a potential predictor given the persistence of TCs occurring more in certain months than others. Note that a model with seasonality predictor alone (hereafter called the “climatology” model) forms a baseline for comparisons. The hindcast verifications of the forecasts using leave-one-out cross-validation procedure over the study period 1975–2019 indicate considerable improvements in prediction skill of our logistic regression models over climatology, even up to 4 weeks in advance. This study sets the foundation for introducing subseasonal prediction services, which is a national priority for improved decision making in sectors like agriculture and food security, water, health and disaster risk mitigation in the Solomon Islands. © 2023 The Authors. International Journal of Climatology published by John Wiley & Sons Ltd on behalf of Royal Meteorological Society.
- Authors: Haruhiru, Alick , Chand, Savin , Sultanova, Nargiz , Ramsay, Hamish , Sharma, Krishneel , Tahani, Lloyd
- Date: 2023
- Type: Text , Journal article
- Relation: International Journal of Climatology Vol. 43, no. 12 (2023), p. 5763-5777
- Full Text:
- Reviewed:
- Description: Recently, we developed seasonal prediction schemes with improved skill to predict tropical cyclone (TC) activity up to 3 months in advance for the Solomon Islands (SI) region (5°–15°S, 155°–170°E) using sophisticated Bayesian regression techniques. However, TC prediction at subseasonal timescale (i.e., 1–4 weeks in advance) is not being researched for that region despite growing demands from decision makers at sectoral level. In this paper, we first assess the feasibility of developing subseasonal prediction frameworks for the SI region using a pool of predictors that are known to affect TC activity in the region. We then evaluate multiple predictor combinations to develop the most appropriate models using a statistical approach to forecast weekly TC activity up to 4 weeks in advance. Predictors used include indices of various natural climate variability modes, namely the Madden–Julian Oscillation (MJO), the El Niño–Southern Oscillation (ENSO), the Indian Ocean Dipole (IOD) and the Interdecadal Pacific Oscillation (IPO). These modes often have robust physical and statistical relationships with TC occurrences in the SI region and the broader southwest Pacific territory as shown by preceding studies. Additionally, we incorporate TC seasonality as a potential predictor given the persistence of TCs occurring more in certain months than others. Note that a model with seasonality predictor alone (hereafter called the “climatology” model) forms a baseline for comparisons. The hindcast verifications of the forecasts using leave-one-out cross-validation procedure over the study period 1975–2019 indicate considerable improvements in prediction skill of our logistic regression models over climatology, even up to 4 weeks in advance. This study sets the foundation for introducing subseasonal prediction services, which is a national priority for improved decision making in sectors like agriculture and food security, water, health and disaster risk mitigation in the Solomon Islands. © 2023 The Authors. International Journal of Climatology published by John Wiley & Sons Ltd on behalf of Royal Meteorological Society.
Tropical cyclones and depressions over the South Pacific Ocean since the late 19th century : assessing synergistic relationship between the El Niño Southern Oscillation and Interdecadal Pacific Oscillation
- Yeasmin, Alea, Chand, Savin, Sultanova, Nargiz
- Authors: Yeasmin, Alea , Chand, Savin , Sultanova, Nargiz
- Date: 2023
- Type: Text , Journal article
- Relation: International Journal of Climatology Vol. 43, no. 12 (2023), p. 5422-5443
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- Description: Tropical cyclones (TCs) and tropical depressions (TDs), hereafter collectively referred to as tropical storms, often exhibit large year-to-year variability in the South Pacific Ocean basin. Many past studies have examined this variability in relation to the El Niño Southern Oscillation (ENSO) phenomenon, particularly using observational data from the post-satellite era (i.e., after the 1970s when TC observations became more consistent). However, less emphasis is placed on how tropical storms are modulated at interdecadal and decadal time scales such as due to Interdecadal Pacific Oscillation (IPO). This is because post-satellite data are available for relatively short time period (i.e., post-1970s), limiting our understanding of the IPO–TC relationship in the South Pacific. Here, using NOAA-CIRES 20th Century Reanalysis (20CR) dataset, we reconstruct historical records (1871–2014) of TC and depression proxies for the South Pacific Ocean basin, and then utilize these reconstructed proxies to first understand the connections between TC–ENSO and TC–IPO over the 20th century, and then investigate the combined effects of ENSO–IPO effects on TCs and depressions. Results show that La Niña (El Niño) is more dominant on TC activity than El Niño (La Niña) over the western subregion 140–170° E (eastern sub-region, 170–220° E) as expected. We also show that TC numbers are strongly modulated by the IPO phenomenon with, on average, more TCs occurring during the positive phase than during the negative phase of the IPO in both western and eastern sub-regions. We show for the first time (using a long-term reconstructed TC dataset) that the combined phases of El Niño and + IPO account for increased TC activity, as opposed to the combined phase of La Niña and
- Authors: Yeasmin, Alea , Chand, Savin , Sultanova, Nargiz
- Date: 2023
- Type: Text , Journal article
- Relation: International Journal of Climatology Vol. 43, no. 12 (2023), p. 5422-5443
- Full Text:
- Reviewed:
- Description: Tropical cyclones (TCs) and tropical depressions (TDs), hereafter collectively referred to as tropical storms, often exhibit large year-to-year variability in the South Pacific Ocean basin. Many past studies have examined this variability in relation to the El Niño Southern Oscillation (ENSO) phenomenon, particularly using observational data from the post-satellite era (i.e., after the 1970s when TC observations became more consistent). However, less emphasis is placed on how tropical storms are modulated at interdecadal and decadal time scales such as due to Interdecadal Pacific Oscillation (IPO). This is because post-satellite data are available for relatively short time period (i.e., post-1970s), limiting our understanding of the IPO–TC relationship in the South Pacific. Here, using NOAA-CIRES 20th Century Reanalysis (20CR) dataset, we reconstruct historical records (1871–2014) of TC and depression proxies for the South Pacific Ocean basin, and then utilize these reconstructed proxies to first understand the connections between TC–ENSO and TC–IPO over the 20th century, and then investigate the combined effects of ENSO–IPO effects on TCs and depressions. Results show that La Niña (El Niño) is more dominant on TC activity than El Niño (La Niña) over the western subregion 140–170° E (eastern sub-region, 170–220° E) as expected. We also show that TC numbers are strongly modulated by the IPO phenomenon with, on average, more TCs occurring during the positive phase than during the negative phase of the IPO in both western and eastern sub-regions. We show for the first time (using a long-term reconstructed TC dataset) that the combined phases of El Niño and + IPO account for increased TC activity, as opposed to the combined phase of La Niña and
Methods and applications of clusterwise linear regression : a survey and comparison
- Long, Qiang, Bagirov, Adil, Taheri, Sona, Sultanova, Nargiz, Wu, Xue
- Authors: Long, Qiang , Bagirov, Adil , Taheri, Sona , Sultanova, Nargiz , Wu, Xue
- Date: 2023
- Type: Text , Journal article
- Relation: ACM Transactions on Knowledge Discovery from Data Vol. 17, no. 3 (2023), p.
- Relation: https://purl.org/au-research/grants/arc/DP190100580
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- Description: Clusterwise linear regression (CLR) is a well-known technique for approximating a data using more than one linear function. It is based on the combination of clustering and multiple linear regression methods. This article provides a comprehensive survey and comparative assessments of CLR including model formulations, description of algorithms, and their performance on small to large-scale synthetic and real-world datasets. Some applications of the CLR algorithms and possible future research directions are also discussed. © 2023 Association for Computing Machinery.
- Authors: Long, Qiang , Bagirov, Adil , Taheri, Sona , Sultanova, Nargiz , Wu, Xue
- Date: 2023
- Type: Text , Journal article
- Relation: ACM Transactions on Knowledge Discovery from Data Vol. 17, no. 3 (2023), p.
- Relation: https://purl.org/au-research/grants/arc/DP190100580
- Full Text:
- Reviewed:
- Description: Clusterwise linear regression (CLR) is a well-known technique for approximating a data using more than one linear function. It is based on the combination of clustering and multiple linear regression methods. This article provides a comprehensive survey and comparative assessments of CLR including model formulations, description of algorithms, and their performance on small to large-scale synthetic and real-world datasets. Some applications of the CLR algorithms and possible future research directions are also discussed. © 2023 Association for Computing Machinery.
A class of Increasing Positively Homogeneous functions for which global optimization problem is NP-hard
- Authors: Sultanova, Nargiz
- Date: 2009
- Type: Text , Thesis , Masters
- Full Text:
- Description: It is well known that global optimization problems are, generally speaking, computationally infeasible, that is solving them would require an unreasonably large amount of time and/or space. In certain cases, for example, when objective functions and constraints are convex, it is possible to construct a feasible algorithm for solving global optimization problem successfully. Convexity, however, is not a phenomenon to be often expected in the applications. Nonconvex problems frequently arise in many industrial and scienti¯c areas. Therefore, it is only natural to try to replace convexity with some other structure at least for some classes of nonconvex optimization problems to render the global optimization problem feasible. A theory of abstract convexity has been developed as a result of the above considerations. Monotonic analysis, a branch of abstract convex analysis, is analogous in many ways to convex analysis, and sometimes is even simpler. It turned out that many problems of nonconvex optimization encountered in applications can be described in terms of monotonic functions. The analogies with convex analysis were considered to aid in solving some classes of nonconvex optimization problems. In this thesis we will focus on one of the elements of monotonic analysis - Increasing Positively Homogeneous functions of degree one or in short IPH functions. The aim of present research is to show that finding the solution and ²-approximation to the solution of the global optimization problem for IPH functions restricted to a unit simplex is an NP-hard problem. These results can be further extended to positively homogeneous functions of degree ´, ´ > 0.
- Description: Master of Mathematical Sciences (Research)
- Authors: Sultanova, Nargiz
- Date: 2009
- Type: Text , Thesis , Masters
- Full Text:
- Description: It is well known that global optimization problems are, generally speaking, computationally infeasible, that is solving them would require an unreasonably large amount of time and/or space. In certain cases, for example, when objective functions and constraints are convex, it is possible to construct a feasible algorithm for solving global optimization problem successfully. Convexity, however, is not a phenomenon to be often expected in the applications. Nonconvex problems frequently arise in many industrial and scienti¯c areas. Therefore, it is only natural to try to replace convexity with some other structure at least for some classes of nonconvex optimization problems to render the global optimization problem feasible. A theory of abstract convexity has been developed as a result of the above considerations. Monotonic analysis, a branch of abstract convex analysis, is analogous in many ways to convex analysis, and sometimes is even simpler. It turned out that many problems of nonconvex optimization encountered in applications can be described in terms of monotonic functions. The analogies with convex analysis were considered to aid in solving some classes of nonconvex optimization problems. In this thesis we will focus on one of the elements of monotonic analysis - Increasing Positively Homogeneous functions of degree one or in short IPH functions. The aim of present research is to show that finding the solution and ²-approximation to the solution of the global optimization problem for IPH functions restricted to a unit simplex is an NP-hard problem. These results can be further extended to positively homogeneous functions of degree ´, ´ > 0.
- Description: Master of Mathematical Sciences (Research)
How are we progressing with academic numeracy at regional universities? Perspectives from first-year undergraduate studies
- Woolcott, Geoff, Galligan, Linda, Whannell, Robert, Marshman, Margaret, Sultanova, Nargiz
- Authors: Woolcott, Geoff , Galligan, Linda , Whannell, Robert , Marshman, Margaret , Sultanova, Nargiz
- Date: 2021
- Type: Text , Journal article
- Relation: Mathematics Education Research Journal Vol. 33, no. 3 (2021), p. 451-468
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- Description: This study provides an overview of the support provided for academic numeracy for first-year students across six Australian regional universities. Survey analysis of university academics provided an overview of the approaches used in academic numeracy in diverse cohorts. Further investigations via semi-structured interviews and secondary data were performed, providing details of the level of academic numeracy required in the subjects offered, identification of at-risk students and strategies for student support, and student responses to service provision. A case study at one university provided a more detailed view of the factors influencing attrition in first-year academic numeracy subjects. This case study highlighted issues related to a one-size-fits-all approach and findings argue for a more nuanced cohort-based approach that combines conventional statistical analysis with analysis that provides a more detailed view of complex scenarios. The study suggests that while support services are not responding well to the issue of attrition, better targeting individual student support may lead to improvements. © 2020, Mathematics Education Research Group of Australasia, Inc. **Please note that there are multiple authors for this article therefore only the name of the first 5 including Federation University Australia affiliate “Nargiz Sultanova ” is provided in this record** Sultanova, Nargiz
- Authors: Woolcott, Geoff , Galligan, Linda , Whannell, Robert , Marshman, Margaret , Sultanova, Nargiz
- Date: 2021
- Type: Text , Journal article
- Relation: Mathematics Education Research Journal Vol. 33, no. 3 (2021), p. 451-468
- Full Text:
- Reviewed:
- Description: This study provides an overview of the support provided for academic numeracy for first-year students across six Australian regional universities. Survey analysis of university academics provided an overview of the approaches used in academic numeracy in diverse cohorts. Further investigations via semi-structured interviews and secondary data were performed, providing details of the level of academic numeracy required in the subjects offered, identification of at-risk students and strategies for student support, and student responses to service provision. A case study at one university provided a more detailed view of the factors influencing attrition in first-year academic numeracy subjects. This case study highlighted issues related to a one-size-fits-all approach and findings argue for a more nuanced cohort-based approach that combines conventional statistical analysis with analysis that provides a more detailed view of complex scenarios. The study suggests that while support services are not responding well to the issue of attrition, better targeting individual student support may lead to improvements. © 2020, Mathematics Education Research Group of Australasia, Inc. **Please note that there are multiple authors for this article therefore only the name of the first 5 including Federation University Australia affiliate “Nargiz Sultanova ” is provided in this record** Sultanova, Nargiz
Bregman proximal linearized ADMM for minimizing separable sums coupled by a difference of functions
- Pham, Tan, Dao, Minh, Eberhard, Andrew, Sultanova, Nargiz
- Authors: Pham, Tan , Dao, Minh , Eberhard, Andrew , Sultanova, Nargiz
- Date: 2024
- Type: Text , Journal article
- Relation: Journal of Optimization Theory and Applications Vol. 203, no. 2 (2024), p. 1622-1658
- Full Text:
- Reviewed:
- Description: In this paper, we develop a splitting algorithm incorporating Bregman distances to solve a broad class of linearly constrained composite optimization problems, whose objective function is the separable sum of possibly nonconvex nonsmooth functions and a smooth function, coupled by a difference of functions. This structure encapsulates numerous significant nonconvex and nonsmooth optimization problems in the current literature including the linearly constrained difference-of-convex problems. Relying on the successive linearization and alternating direction method of multipliers (ADMM), the proposed algorithm exhibits the global subsequential convergence to a stationary point of the underlying problem. We also establish the convergence of the full sequence generated by our algorithm under the Kurdyka–
- Authors: Pham, Tan , Dao, Minh , Eberhard, Andrew , Sultanova, Nargiz
- Date: 2024
- Type: Text , Journal article
- Relation: Journal of Optimization Theory and Applications Vol. 203, no. 2 (2024), p. 1622-1658
- Full Text:
- Reviewed:
- Description: In this paper, we develop a splitting algorithm incorporating Bregman distances to solve a broad class of linearly constrained composite optimization problems, whose objective function is the separable sum of possibly nonconvex nonsmooth functions and a smooth function, coupled by a difference of functions. This structure encapsulates numerous significant nonconvex and nonsmooth optimization problems in the current literature including the linearly constrained difference-of-convex problems. Relying on the successive linearization and alternating direction method of multipliers (ADMM), the proposed algorithm exhibits the global subsequential convergence to a stationary point of the underlying problem. We also establish the convergence of the full sequence generated by our algorithm under the Kurdyka–
Robust clustering algorithm : the use of soft trimming approach
- Taheri, Sona, Bagirov, Adil, Sultanova, Nargiz, Ordin, Burak
- Authors: Taheri, Sona , Bagirov, Adil , Sultanova, Nargiz , Ordin, Burak
- Date: 2024
- Type: Text , Journal article
- Relation: Pattern Recognition Letters Vol. 185, no. (2024), p. 15-22
- Relation: https://purl.org/au-research/grants/arc/DP190100580
- Full Text:
- Reviewed:
- Description: The presence of noise or outliers in data sets may heavily affect the performance of clustering algorithms and lead to unsatisfactory results. The majority of conventional clustering algorithms are sensitive to noise and outliers. Robust clustering algorithms often overcome difficulties associated with noise and outliers and find true cluster structures. We introduce a soft trimming approach for the hard clustering problem where its objective is modeled as a sum of the cluster function and a function represented as a composition of the algebraic and distance functions. We utilize the composite function to estimate the degree of the significance of each data point in clustering. A robust clustering algorithm based on the new model and a procedure for generating starting cluster centers is developed. We demonstrate the performance of the proposed algorithm using some synthetic and real-world data sets containing noise and outliers. We also compare its performance with that of some well-known clustering techniques. Results show that the new algorithm is robust to noise and outliers and finds true cluster structures. © 2024
- Authors: Taheri, Sona , Bagirov, Adil , Sultanova, Nargiz , Ordin, Burak
- Date: 2024
- Type: Text , Journal article
- Relation: Pattern Recognition Letters Vol. 185, no. (2024), p. 15-22
- Relation: https://purl.org/au-research/grants/arc/DP190100580
- Full Text:
- Reviewed:
- Description: The presence of noise or outliers in data sets may heavily affect the performance of clustering algorithms and lead to unsatisfactory results. The majority of conventional clustering algorithms are sensitive to noise and outliers. Robust clustering algorithms often overcome difficulties associated with noise and outliers and find true cluster structures. We introduce a soft trimming approach for the hard clustering problem where its objective is modeled as a sum of the cluster function and a function represented as a composition of the algebraic and distance functions. We utilize the composite function to estimate the degree of the significance of each data point in clustering. A robust clustering algorithm based on the new model and a procedure for generating starting cluster centers is developed. We demonstrate the performance of the proposed algorithm using some synthetic and real-world data sets containing noise and outliers. We also compare its performance with that of some well-known clustering techniques. Results show that the new algorithm is robust to noise and outliers and finds true cluster structures. © 2024
A proximal subgradient algorithm with extrapolation for structured nonconvex nonsmooth problems
- Pham, Tan, Dao, Minh, Shah, Rakibuzzaman, Sultanova, Nargiz, Li, Guoyin, Islam, Syed
- Authors: Pham, Tan , Dao, Minh , Shah, Rakibuzzaman , Sultanova, Nargiz , Li, Guoyin , Islam, Syed
- Date: 2023
- Type: Text , Journal article
- Relation: Numerical Algorithms Vol. 94, no. 4 (2023), p. 1763-1795
- Full Text:
- Reviewed:
- Description: In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by the sum of a possibly nonsmooth nonconvex function and a differentiable function with Lipschitz continuous gradient, subtracted by a weakly convex function. This general framework allows us to tackle problems involving nonconvex loss functions and problems with specific nonconvex constraints, and it has many applications such as signal recovery, compressed sensing, and optimal power flow distribution. We develop a proximal subgradient algorithm with extrapolation for solving these problems with guaranteed subsequential convergence to a stationary point. The convergence of the whole sequence generated by our algorithm is also established under the widely used Kurdyka–Łojasiewicz property. To illustrate the promising numerical performance of the proposed algorithm, we conduct numerical experiments on two important nonconvex models. These include a compressed sensing problem with a nonconvex regularization and an optimal power flow problem with distributed energy resources. © 2023, The Author(s).
- Authors: Pham, Tan , Dao, Minh , Shah, Rakibuzzaman , Sultanova, Nargiz , Li, Guoyin , Islam, Syed
- Date: 2023
- Type: Text , Journal article
- Relation: Numerical Algorithms Vol. 94, no. 4 (2023), p. 1763-1795
- Full Text:
- Reviewed:
- Description: In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by the sum of a possibly nonsmooth nonconvex function and a differentiable function with Lipschitz continuous gradient, subtracted by a weakly convex function. This general framework allows us to tackle problems involving nonconvex loss functions and problems with specific nonconvex constraints, and it has many applications such as signal recovery, compressed sensing, and optimal power flow distribution. We develop a proximal subgradient algorithm with extrapolation for solving these problems with guaranteed subsequential convergence to a stationary point. The convergence of the whole sequence generated by our algorithm is also established under the widely used Kurdyka–Łojasiewicz property. To illustrate the promising numerical performance of the proposed algorithm, we conduct numerical experiments on two important nonconvex models. These include a compressed sensing problem with a nonconvex regularization and an optimal power flow problem with distributed energy resources. © 2023, The Author(s).
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