LGFeb 15, 2023Code
Zero-Shot Anomaly Detection via Batch NormalizationAodong Li, Chen Qiu, Marius Kloft et al.
Anomaly detection (AD) plays a crucial role in many safety-critical application domains. The challenge of adapting an anomaly detector to drift in the normal data distribution, especially when no training data is available for the "new normal," has led to the development of zero-shot AD techniques. In this paper, we propose a simple yet effective method called Adaptive Centered Representations (ACR) for zero-shot batch-level AD. Our approach trains off-the-shelf deep anomaly detectors (such as deep SVDD) to adapt to a set of inter-related training data distributions in combination with batch normalization, enabling automatic zero-shot generalization for unseen AD tasks. This simple recipe, batch normalization plus meta-training, is a highly effective and versatile tool. Our theoretical results guarantee the zero-shot generalization for unseen AD tasks; our empirical results demonstrate the first zero-shot AD results for tabular data and outperform existing methods in zero-shot anomaly detection and segmentation on image data from specialized domains. Code is at https://github.com/aodongli/zero-shot-ad-via-batch-norm
LGMay 27, 2022
Raising the Bar in Graph-level Anomaly DetectionChen Qiu, Marius Kloft, Stephan Mandt et al.
Graph-level anomaly detection has become a critical topic in diverse areas, such as financial fraud detection and detecting anomalous activities in social networks. While most research has focused on anomaly detection for visual data such as images, where high detection accuracies have been obtained, existing deep learning approaches for graphs currently show considerably worse performance. This paper raises the bar on graph-level anomaly detection, i.e., the task of detecting abnormal graphs in a set of graphs. By drawing on ideas from self-supervised learning and transformation learning, we present a new deep learning approach that significantly improves existing deep one-class approaches by fixing some of their known problems, including hypersphere collapse and performance flip. Experiments on nine real-world data sets involving nine techniques reveal that our method achieves an average performance improvement of 11.8% AUC compared to the best existing approach.
LGFeb 15, 2023
Deep Anomaly Detection under Labeling Budget ConstraintsAodong Li, Chen Qiu, Marius Kloft et al.
Selecting informative data points for expert feedback can significantly improve the performance of anomaly detection (AD) in various contexts, such as medical diagnostics or fraud detection. In this paper, we determine a set of theoretical conditions under which anomaly scores generalize from labeled queries to unlabeled data. Motivated by these results, we propose a data labeling strategy with optimal data coverage under labeling budget constraints. In addition, we propose a new learning framework for semi-supervised AD. Extensive experiments on image, tabular, and video data sets show that our approach results in state-of-the-art semi-supervised AD performance under labeling budget constraints.
CLOct 24, 2022
Multilingual Multimodal Learning with Machine Translated TextChen Qiu, Dan Oneata, Emanuele Bugliarello et al.
Most vision-and-language pretraining research focuses on English tasks. However, the creation of multilingual multimodal evaluation datasets (e.g. Multi30K, xGQA, XVNLI, and MaRVL) poses a new challenge in finding high-quality training data that is both multilingual and multimodal. In this paper, we investigate whether machine translating English multimodal data can be an effective proxy for the lack of readily available multilingual data. We call this framework TD-MML: Translated Data for Multilingual Multimodal Learning, and it can be applied to any multimodal dataset and model. We apply it to both pretraining and fine-tuning data with a state-of-the-art model. In order to prevent models from learning from low-quality translated text, we propose two metrics for automatically removing such translations from the resulting datasets. In experiments on five tasks across 20 languages in the IGLUE benchmark, we show that translated data can provide a useful signal for multilingual multimodal learning, both at pretraining and fine-tuning.
AIJul 2, 2022
Enabling Harmonious Human-Machine Interaction with Visual-Context Augmented Dialogue System: A ReviewHao Wang, Bin Guo, Yating Zeng et al.
The intelligent dialogue system, aiming at communicating with humans harmoniously with natural language, is brilliant for promoting the advancement of human-machine interaction in the era of artificial intelligence. With the gradually complex human-computer interaction requirements (e.g., multimodal inputs, time sensitivity), it is difficult for traditional text-based dialogue system to meet the demands for more vivid and convenient interaction. Consequently, Visual Context Augmented Dialogue System (VAD), which has the potential to communicate with humans by perceiving and understanding multimodal information (i.e., visual context in images or videos, textual dialogue history), has become a predominant research paradigm. Benefiting from the consistency and complementarity between visual and textual context, VAD possesses the potential to generate engaging and context-aware responses. For depicting the development of VAD, we first characterize the concepts and unique features of VAD, and then present its generic system architecture to illustrate the system workflow. Subsequently, several research challenges and representative works are detailed investigated, followed by the summary of authoritative benchmarks. We conclude this paper by putting forward some open issues and promising research trends for VAD, e.g., the cognitive mechanisms of human-machine dialogue under cross-modal dialogue context, and knowledge-enhanced cross-modal semantic interaction.
CVOct 9, 2023
Text-driven Prompt Generation for Vision-Language Models in Federated LearningChen Qiu, Xingyu Li, Chaithanya Kumar Mummadi et al.
Prompt learning for vision-language models, e.g., CoOp, has shown great success in adapting CLIP to different downstream tasks, making it a promising solution for federated learning due to computational reasons. Existing prompt learning techniques replace hand-crafted text prompts with learned vectors that offer improvements on seen classes, but struggle to generalize to unseen classes. Our work addresses this challenge by proposing Federated Text-driven Prompt Generation (FedTPG), which learns a unified prompt generation network across multiple remote clients in a scalable manner. The prompt generation network is conditioned on task-related text input, thus is context-aware, making it suitable to generalize for both seen and unseen classes. Our comprehensive empirical evaluations on nine diverse image classification datasets show that our method is superior to existing federated prompt learning methods, that achieve overall better generalization on both seen and unseen classes and is also generalizable to unseen datasets.
LGOct 16, 2023
Model Selection of Anomaly Detectors in the Absence of Labeled Validation DataClement Fung, Chen Qiu, Aodong Li et al.
Anomaly detection is the task of identifying abnormal samples in large unlabeled datasets. While the advent of foundation models has produced powerful zero-shot anomaly detection methods, their deployment in practice is often hindered by the absence of labeled validation data -- without it, their detection performance cannot be evaluated reliably. In this work, we propose SWSA (Selection With Synthetic Anomalies): a general-purpose framework to select image-based anomaly detectors without labeled validation data. Instead of collecting labeled validation data, we generate synthetic anomalies without any training or fine-tuning, using only a small support set of normal images. Our synthetic anomalies are used to create detection tasks that compose a validation framework for model selection. In an empirical study, we evaluate SWSA with three types of synthetic anomalies and on two selection tasks: model selection of image-based anomaly detectors and prompt selection for CLIP-based anomaly detection. SWSA often selects models and prompts that match selections made with a ground-truth validation set, outperforming baseline selection strategies.
CLApr 15
ART: Attention Run-time Termination for Efficient Large Language Model DecodingChen Qiu, Guozhong Li, Panos Kalnis
Long-context decoding in Large Language Models (LLMs) is severely constrained by the memory bandwidth required to fetch the extensive Key-Value (KV) cache. Most existing KV management methods rely on key-only pruning before decoding, despite the evidence that attention outputs depend jointly on keys and values, as incorporating values in their methods incurs prohibitive additional overhead. In this paper, we propose Attention Run-time Termination (ART), a lightweight run-time mechanism that tracks accumulated attention outputs during kernel execution and terminates subsequent KV block accesses once further contributions become negligible. This design makes ART orthogonal to existing key-based KV cache management methods, enabling seamless integration with them. Experiments on LongBench benchmarks show that ART achieves 20% higher generation throughput in large batch size than state-of-the-art baseline while maintaining comparable accuracy.
ROApr 14
Learning Versatile Humanoid Manipulation with Touch DreamingYaru Niu, Zhenlong Fang, Binghong Chen et al.
Humanoid robots promise general-purpose assistance, yet real-world humanoid loco-manipulation remains challenging because it requires whole-body stability, dexterous hands, and contact-aware perception under frequent contact changes. In this work, we study dexterous, contact-rich humanoid loco-manipulation. We first develop an RL-based whole-body controller that provides stable lower-body and torso execution during complex manipulation. Built on this controller, we develop a whole-body humanoid data collection system that combines VR-based teleoperation with human-to-humanoid motion mapping, enabling efficient collection of real-world demonstrations. We then propose Humanoid Transformer with Touch Dreaming (HTD), a multimodal encoder--decoder Transformer that models touch as a core modality alongside multi-view vision and proprioception. HTD is trained in a single stage with behavioral cloning augmented by touch dreaming: in addition to predicting action chunks, the policy predicts future hand-joint forces and future tactile latents, encouraging the shared Transformer trunk to learn contact-aware representations for dexterous interaction. Across five contact-rich tasks, Insert-T, Book Organization, Towel Folding, Cat Litter Scooping, and Tea Serving, HTD achieves a 90.9% relative improvement in average success rate over the stronger baseline. Ablation results further show that latent-space tactile prediction is more effective than raw tactile prediction, yielding a 30% relative gain in success rate. These results demonstrate that combining robust whole-body execution, scalable humanoid data collection, and predictive touch-centered learning enables versatile, high-dexterity humanoid manipulation in the real world. Project webpage: humanoid-touch-dream.github.io.
ROApr 7Code
Delta6: A Low-Cost, 6-DOF Force-Sensing Flexible End-EffectorYue Feng, Weicheng Huang, Chen Qiu et al.
This paper presents Delta6, a low-cost, six-degree-of-freedom (6-DOF) force/torque end-effector that combines antagonistic springs with magnetic encoders to deliver accurate wrench sensing while remaining as simple to assemble as flat-pack furniture. A fully 3D-printed prototype, assembled entirely from off-the-shelf parts, withstands peak forces above +/-14.4 N and torques of +/-0.33 N.m per axis; these limits can be further extended by leveraging the proposed parametric analytical model. Without calibration, Delta6 attains a 99th-percentile error of 7% full scale (FS). With lightweight sequence models, the error is reduced to 3.8% FS by the best-performing network. Benchmarks on multiple computing platforms confirm that the device's bandwidth is adjustable, enabling balanced trade-offs among update rate, accuracy, and cost, while durability, thermal drift, and zero-calibration tests confirm its robustness. With Delta6 mounted on a robot arm governed by a force-impedance controller, the system successfully performs two contact-rich tasks: buffing curved surfaces and tight assemblies. Experiments validate the design, showing that Delta6 is a robust, low-cost alternative to existing 6-DOF force sensing solutions. Open-source site: https://wings-robotics.github.io/delta6 .
ITApr 7
Generative Channel Knowledge Base With Environmental Information for Joint Source-Channel Coding in Semantic CommunicationsXudong Long, Hao Chen, Dan Wang et al.
Semantic knowledge bases are regarded as a promising technology for upcoming 6G communications. However, existing studies mainly focus on source-side semantic modeling while overlooking the structural impact of propagation environments on semantic transmission performance. To address this issue, we propose a generative channel knowledge base (CKB) with environmental information to facilitate joint source-channel coding (JSCC) in semantic communications (SemCom) systems. First, to enable the construction of the CKB, an environment-aware dataset is established by collecting spatial position information, global image features, fine-grained semantic features, and the corresponding channel matrices. A region-of-interest (ROI)-based filtering algorithm is further designed to remove semantic components that are irrelevant to signal propagation. Second, a Transformer-based generative framework is developed to learn the mapping between multidimensional environmental information and channel matrices. A self-attention mechanism is introduced to adaptively fuse heterogeneous features, enabling the construction of a structured CKB. Third, a CKB-driven JSCC SemCom architecture is proposed, where the generated channel knowledge is injected into both of the encoder and decoder to jointly exploit source semantics and channel-environment priors in an end-to-end manner. Experimental results demonstrate that the proposed multidimensional feature fusion method achieves a channel matrix estimation error at the $10^{-3}$ level. Moreover, the CKB-driven JSCC SemCom framework integrated into SemCom systems significantly outperforms existing benchmark schemes in terms of transmission performance.
LGMay 22, 2024
Uncertainty-aware Evaluation of Auxiliary Anomalies with the Expected Anomaly PosteriorLorenzo Perini, Maja Rudolph, Sabrina Schmedding et al.
Anomaly detection is the task of identifying examples that do not behave as expected. Because anomalies are rare and unexpected events, collecting real anomalous examples is often challenging in several applications. In addition, learning an anomaly detector with limited (or no) anomalies often yields poor prediction performance. One option is to employ auxiliary synthetic anomalies to improve the model training. However, synthetic anomalies may be of poor quality: anomalies that are unrealistic or indistinguishable from normal samples may deteriorate the detector's performance. Unfortunately, no existing methods quantify the quality of auxiliary anomalies. We fill in this gap and propose the expected anomaly posterior (EAP), an uncertainty-based score function that measures the quality of auxiliary anomalies by quantifying the total uncertainty of an anomaly detector. Experimentally on 40 benchmark datasets of images and tabular data, we show that EAP outperforms 12 adapted data quality estimators in the majority of cases.
CVOct 1, 2025
Visual Self-Refinement for Autoregressive ModelsJiamian Wang, Ziqi Zhou, Chaithanya Kumar Mummadi et al.
Autoregressive models excel in sequential modeling and have proven to be effective for vision-language data. However, the spatial nature of visual signals conflicts with the sequential dependencies of next-token prediction, leading to suboptimal results. This work proposes a plug-and-play refinement module to enhance the complex spatial correspondence modeling within the generated visual sequence. This module operates as a post-pretraining step to jointly refine all generated tokens of autoregressive model, enhancing vision-language modeling under a shared sequential prediction framework. By leveraging global context and relationship across the tokens, our method mitigates the error accumulation issue within the sequential generation. Experiments demonstrate that the proposed method improves the generation quality, enhancing the model's ability to produce semantically consistent results.
LGJun 24, 2024
Anomaly Detection of Tabular Data Using LLMsAodong Li, Yunhan Zhao, Chen Qiu et al.
Large language models (LLMs) have shown their potential in long-context understanding and mathematical reasoning. In this paper, we study the problem of using LLMs to detect tabular anomalies and show that pre-trained LLMs are zero-shot batch-level anomaly detectors. That is, without extra distribution-specific model fitting, they can discover hidden outliers in a batch of data, demonstrating their ability to identify low-density data regions. For LLMs that are not well aligned with anomaly detection and frequently output factual errors, we apply simple yet effective data-generating processes to simulate synthetic batch-level anomaly detection datasets and propose an end-to-end fine-tuning strategy to bring out the potential of LLMs in detecting real anomalies. Experiments on a large anomaly detection benchmark (ODDS) showcase i) GPT-4 has on-par performance with the state-of-the-art transductive learning-based anomaly detection methods and ii) the efficacy of our synthetic dataset and fine-tuning strategy in aligning LLMs to this task.
CVMay 5, 2023
The Role of Data Curation in Image CaptioningWenyan Li, Jonas F. Lotz, Chen Qiu et al.
Image captioning models are typically trained by treating all samples equally, neglecting to account for mismatched or otherwise difficult data points. In contrast, recent work has shown the effectiveness of training models by scheduling the data using curriculum learning strategies. This paper contributes to this direction by actively curating difficult samples in datasets without increasing the total number of samples. We explore the effect of using three data curation methods within the training process: complete removal of an sample, caption replacement, or image replacement via a text-to-image generation model. Experiments on the Flickr30K and COCO datasets with the BLIP and BEiT-3 models demonstrate that these curation methods do indeed yield improved image captioning models, underscoring their efficacy.
LGFeb 16, 2022
Latent Outlier Exposure for Anomaly Detection with Contaminated DataChen Qiu, Aodong Li, Marius Kloft et al.
Anomaly detection aims at identifying data points that show systematic deviations from the majority of data in an unlabeled dataset. A common assumption is that clean training data (free of anomalies) is available, which is often violated in practice. We propose a strategy for training an anomaly detector in the presence of unlabeled anomalies that is compatible with a broad class of models. The idea is to jointly infer binary labels to each datum (normal vs. anomalous) while updating the model parameters. Inspired by outlier exposure (Hendrycks et al., 2018) that considers synthetically created, labeled anomalies, we thereby use a combination of two losses that share parameters: one for the normal and one for the anomalous data. We then iteratively proceed with block coordinate updates on the parameters and the most likely (latent) labels. Our experiments with several backbone models on three image datasets, 30 tabular data sets, and a video anomaly detection benchmark showed consistent and significant improvements over the baselines.
LGFeb 8, 2022
Detecting Anomalies within Time Series using Local Neural TransformationsTim Schneider, Chen Qiu, Marius Kloft et al.
We develop a new method to detect anomalies within time series, which is essential in many application domains, reaching from self-driving cars, finance, and marketing to medical diagnosis and epidemiology. The method is based on self-supervised deep learning that has played a key role in facilitating deep anomaly detection on images, where powerful image transformations are available. However, such transformations are widely unavailable for time series. Addressing this, we develop Local Neural Transformations(LNT), a method learning local transformations of time series from data. The method produces an anomaly score for each time step and thus can be used to detect anomalies within time series. We prove in a theoretical analysis that our novel training objective is more suitable for transformation learning than previous deep Anomaly detection(AD) methods. Our experiments demonstrate that LNT can find anomalies in speech segments from the LibriSpeech data set and better detect interruptions to cyber-physical systems than previous work. Visualization of the learned transformations gives insight into the type of transformations that LNT learns.
LGNov 16, 2021
Switching Recurrent Kalman NetworksGiao Nguyen-Quynh, Philipp Becker, Chen Qiu et al.
Forecasting driving behavior or other sensor measurements is an essential component of autonomous driving systems. Often real-world multivariate time series data is hard to model because the underlying dynamics are nonlinear and the observations are noisy. In addition, driving data can often be multimodal in distribution, meaning that there are distinct predictions that are likely, but averaging can hurt model performance. To address this, we propose the Switching Recurrent Kalman Network (SRKN) for efficient inference and prediction on nonlinear and multi-modal time-series data. The model switches among several Kalman filters that model different aspects of the dynamics in a factorized latent state. We empirically test the resulting scalable and interpretable deep state-space model on toy data sets and real driving data from taxis in Porto. In all cases, the model can capture the multimodal nature of the dynamics in the data.
RONov 7, 2021
GSG: A Granary Soft Gripper with Mechanical Force Sensing via 3-Dimensional Snap-Through StructureHuixu Dong, Chao-Yu Chen, Chen Qiu et al.
Grasping is an essential capability for most robots in practical applications. Soft robotic grippers are considered as a critical part of robotic grasping and have attracted considerable attention in terms of the advantages of the high compliance and robustness to variance in object geometry; however, they are still limited by the corresponding sensing capabilities and actuation mechanisms. We propose a novel soft gripper that looks like a granary with a compliant snap-through bistable mechanism fabricated by integrated mold technology, achieving sensing and actuation purely mechanically. In particular, the snap-through bistable structure in the proposed gripper allows us to reduce the complexity of the mechanism, control, sensing designs since the grasping and sensing behaviors are completely passive. The grasping behaviors are automatically motivated once the trigger position of the gripper touches an object and applies sufficient force. To grasp objects with various profiles, the proposed granary soft gripper (GSG) is designed to be capable of enveloping, pinching and caging grasps. The gripper consists of a chamber palm, a palm cap and three fingers. First, the design of the gripper is analyzed. Then, after the theoretical model is constructed, finite element (FE) simulations are conducted to verify the built model. Finally, a series of grasping experiments is carried out to assess the snap-through behavior of the proposed gripper on grasping and sensing. The experimental results illustrate that the proposed gripper can manipulate a variety of soft and rigid objects and remain stable even though it undertakes external disturbances.
CLSep 13, 2021
On Language Models for CreolesHeather Lent, Emanuele Bugliarello, Miryam de Lhoneux et al.
Creole languages such as Nigerian Pidgin English and Haitian Creole are under-resourced and largely ignored in the NLP literature. Creoles typically result from the fusion of a foreign language with multiple local languages, and what grammatical and lexical features are transferred to the creole is a complex process. While creoles are generally stable, the prominence of some features may be much stronger with certain demographics or in some linguistic situations. This paper makes several contributions: We collect existing corpora and release models for Haitian Creole, Nigerian Pidgin English, and Singaporean Colloquial English. We evaluate these models on intrinsic and extrinsic tasks. Motivated by the above literature, we compare standard language models with distributionally robust ones and find that, somewhat surprisingly, the standard language models are superior to the distributionally robust ones. We investigate whether this is an effect of over-parameterization or relative distributional stability, and find that the difference persists in the absence of over-parameterization, and that drift is limited, confirming the relative stability of creole languages.
LGMar 30, 2021
Neural Transformation Learning for Deep Anomaly Detection Beyond ImagesChen Qiu, Timo Pfrommer, Marius Kloft et al.
Data transformations (e.g. rotations, reflections, and cropping) play an important role in self-supervised learning. Typically, images are transformed into different views, and neural networks trained on tasks involving these views produce useful feature representations for downstream tasks, including anomaly detection. However, for anomaly detection beyond image data, it is often unclear which transformations to use. Here we present a simple end-to-end procedure for anomaly detection with learnable transformations. The key idea is to embed the transformed data into a semantic space such that the transformed data still resemble their untransformed form, while different transformations are easily distinguishable. Extensive experiments on time series demonstrate that our proposed method outperforms existing approaches in the one-vs.-rest setting and is competitive in the more challenging n-vs.-rest anomaly detection task. On tabular datasets from the medical and cyber-security domains, our method learns domain-specific transformations and detects anomalies more accurately than previous work.
LGOct 20, 2020
Variational Dynamic MixturesChen Qiu, Stephan Mandt, Maja Rudolph
Deep probabilistic time series forecasting models have become an integral part of machine learning. While several powerful generative models have been proposed, we provide evidence that their associated inference models are oftentimes too limited and cause the generative model to predict mode-averaged dynamics. Modeaveraging is problematic since many real-world sequences are highly multi-modal, and their averaged dynamics are unphysical (e.g., predicted taxi trajectories might run through buildings on the street map). To better capture multi-modality, we develop variational dynamic mixtures (VDM): a new variational family to infer sequential latent variables. The VDM approximate posterior at each time step is a mixture density network, whose parameters come from propagating multiple samples through a recurrent architecture. This results in an expressive multi-modal posterior approximation. In an empirical study, we show that VDM outperforms competing approaches on highly multi-modal datasets from different domains.
CVJan 10, 2020
Learning Topometric Semantic Maps from Occupancy GridsMarkus Hiller, Chen Qiu, Florian Particke et al.
Today's mobile robots are expected to operate in complex environments they share with humans. To allow intuitive human-robot collaboration, robots require a human-like understanding of their surroundings in terms of semantically classified instances. In this paper, we propose a new approach for deriving such instance-based semantic maps purely from occupancy grids. We employ a combination of deep learning techniques to detect, segment and extract door hypotheses from a random-sized map. The extraction is followed by a post-processing chain to further increase the accuracy of our approach, as well as place categorization for the three classes room, door and corridor. All detected and classified entities are described as instances specified in a common coordinate system, while a topological map is derived to capture their spatial links. To train our two neural networks used for detection and map segmentation, we contribute a simulator that automatically creates and annotates the required training data. We further provide insight into which features are learned to detect doorways, and how the simulated training data can be augmented to train networks for the direct application on real-world grid maps. We evaluate our approach on several publicly available real-world data sets. Even though the used networks are solely trained on simulated data, our approach demonstrates high robustness and effectiveness in various real-world indoor environments.
CLSep 5, 2019
Rewarding Coreference Resolvers for Being Consistent with World KnowledgeRahul Aralikatte, Heather Lent, Ana Valeria Gonzalez et al.
Unresolved coreference is a bottleneck for relation extraction, and high-quality coreference resolvers may produce an output that makes it a lot easier to extract knowledge triples. We show how to improve coreference resolvers by forwarding their input to a relation extraction system and reward the resolvers for producing triples that are found in knowledge bases. Since relation extraction systems can rely on different forms of supervision and be biased in different ways, we obtain the best performance, improving over the state of the art, using multi-task reinforcement learning.
ROOct 19, 2018
Enabling Grasp Action: Generalized Evaluation of Grasp Stability via Contact Stiffness from Contact Mechanics InsightHuixu Dong, Chen Qiu, Dilip K. Prasad et al.
Performing a grasp is a pivotal capability for a robotic gripper. We propose a new evaluation approach of grasping stability via constructing a model of grasping stiffness based on the theory of contact mechanics. First, the mathematical models are built to explore soft contact and the general grasp stiffness between a finger and an object. Next, the grasping stiffness matrix is constructed to reflect the normal, tangential and torsion stiffness coefficients. Finally, we design two grasping cases to verify the proposed measurement criterion of grasping stability by comparing different grasping configurations. Specifically, a standard grasping index is used and compared with the minimum eigenvalue index of the constructed grasping stiffness we built. The comparison result reveals a similar tendency between them for measuring the grasping stability and thus, validates the proposed approach.