Instance Reduction Research Articles

Improving the sustainability of WiFi-enabled indoor localization systems through meta-heuristic based instance selection approach

Due to rapid urban development, many indoor and semi-indoor structures, such as underground malls, metro stations, and bus-stops, have emerged. Traditional GNSS outdoor navigation fails in these locations. To meet urban citizens’ needs, we require sustainable ubiquitous localization solutions, leveraging existing WiFi infrastructure. In such applications, processing data at the edge within constrained environments is imperative. Many prior studies neglect the practical challenge of implementing machine learning-based edge device localization, as they assume reliance on cloud servers. Selecting well-distributed data instances that preserve location class boundaries is essential for effective training in such conditions. In this work, we propose an instance selection approach that is modeled by applying a modified Binary Particle Swarm Optimization (BPSO) technique. The k-differentiating neighbor-based measure is incorporated to determine instance hardness while exploring the solution space through BPSO. The work is implemented on three publicly available benchmark datasets that are collected from two university campuses and one shopping mall. The proposed work is found to have achieved an instance reduction of 35% with only 1%–2% decrease in the accuracy measurement and an appreciable error deviation metric of 2.78 m.

Instance reduction algorithm based on elitist min-max ant colony optimization technique

Although the advancement of technology has made data processing quite easier, it is still an enormous task, especially if the volume is large and can affect the learning capability of the classifier. Instance Reduction techniques can be employed on data to attain best results while making a substantial difference in terms of data storage needs, and processing speed. The proposed novel algorithm – Elitist Min-Max Ant Colony based Instance Reduction (ÆIR), can be attributed to the hybridization of bio-inspired optimization algorithms and Machine Learning algorithms for instance reduction. The primary features of ÆIR are the introduction of new hyperparameters such as the elitist ants, the min-max bounding of pheromones, and the incorporation of the length of the reduced set, all which aid in electing better instances for the reduced set. To evaluate the performance of the proposed ÆIR algorithm, 18 benchmark datasets of various dimensions were used alongside 4 different classifiers: Random Forest, Decision Tree, K-Nearest Neighbor and Naïve Bayes. The experiments demonstrated the effectiveness of ÆIR in reducing the size of the instances. On an average, approximately 50 % reduction in the number instances was observed. This can result in an equivalent decline in terms of the storage requirements, while contemporaneously improving the prediction accuracy.

Correction to: A heuristic hybrid instance reduction approach based on adaptive relative distance and k-means clustering

Correction to: A heuristic hybrid instance reduction approach based on adaptive relative distance and k-means clustering

Extension of CMSA with a Learning Mechanism: Application to the Far from Most String Problem

One of the problems with exact techniques for solving combinatorial optimization problems is that they tend to run into problems with growing problem instance size. Nevertheless, they might still be very usefully employed, even in the context of large problem instances, as a sub-ordinate method within so-called hybrid metaheuristics. “Construct, Merge, Solve and Adapt” (Cmsa) is a hybrid metaheuristic technique that allows the application of exact methods to large-scale problem instances through intelligent instance reduction. However, Cmsa does not make use of an explicit learning mechanism. In this work, an algorithm called LEARN_CMSA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsc {Learn}\\_\ extsc {Cmsa}$$\\end{document} is presented for the application to the far from most string problem (FFMSP), which is an NP-hard combinatorial optimization problem from the field of string consensus problems. LEARN_CMSA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsc {Learn}\\_\ extsc {Cmsa}$$\\end{document} results from hybridization between Cmsa and a population-based algorithm. By means of this hybridization, explicit learning is introduced to Cmsa. Even though the FFMSP is a well-studied problem, LEARN_CMSA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsc {Learn}\\_\ extsc {Cmsa}$$\\end{document} achieves superior performance when compared to current state-of-the-art solvers.

A selective LVQ algorithm for improving instance reduction techniques and its application for text classification

Instance-Based Learning, such as the k Nearest Neighbor (kNN), offers a straightforward and effective solution for text classification. However, as a lazy learner, kNN’s performance heavily relies on the quality and quantity of training instances, often leading to time and space inefficiencies. This challenge has spurred the development of instance-reduction techniques aimed at retaining essential instances and discarding redundant ones. While such trimming optimizes computational demands, it might adversely affect classification accuracy. This study introduces the novel Selective Learning Vector Quantization (SLVQ) algorithm, specifically designed to enhance the performance of datasets reduced through such techniques. Unlike traditional LVQ algorithms that employ random vector weights (codebook vectors), SLVQ utilizes instances selected by the reduction algorithm as the initial weight vectors. Importantly, as these instances often contain nominal values, SLVQ modifies the distances between these nominal values, rather than modifying the values themselves, aiming to improve their representation of the training set. This approach is crucial because nominal attributes are common in real-world datasets and require effective distance measures, such as the Value Difference Measure (VDM), to handle them properly. Therefore, SLVQ adjusts the VDM distances between nominal values, instead of altering the attribute values of the codebook vectors. Hence, the innovation of the SLVQ approach lies in its integration of instance reduction techniques for selecting initial codebook vectors and its effective handling of nominal attributes. Our experiments, conducted on 17 text classification datasets with four different instance reduction algorithms, confirm SLVQ’s effectiveness. It significantly enhances the kNN’s classification accuracy of reduced datasets. In our empirical study, the SLVQ method improved the performance of these datasets, achieving average classification accuracies of 82.55%, 84.07%, 78.54%, and 83.18%, compared to the average accuracies of 76.25%, 79.62%, 66.54%, and 78.19% achieved by non-fine-tuned datasets, respectively.

Privacy-Preserving Deep Learning Framework Based on Restricted Boltzmann Machines and Instance Reduction Algorithms

The combination of collaborative deep learning and Cyber-Physical Systems (CPSs) has the potential to improve decision-making, adaptability, and efficiency in dynamic and distributed environments. However, it brings privacy, communication, and resource restrictions concerns that must be properly addressed for successful implementation in real-world CPS systems. Various privacy-preserving techniques have been proposed, but they often add complexity and decrease accuracy and utility. In this paper, we propose a privacy-preserving deep learning framework that combines Instance Reduction Techniques (IR) and the Restricted Boltzmann Machine (RBM) to preserve privacy while overcoming the limitations of other frameworks. The RBM encodes training data to retain relevant features, and IR selects the relevant encoded instances to send to the server for training. Privacy is preserved because only a small subset of the training data is sent to the server. Moreover, it is sent after encoding it using RBM. Experiments show that our framework preserves privacy with little loss of accuracy and a substantial reduction in training time. For example, using our framework, a CNN model for the MNIST dataset achieves 96% accuracy compared to 99% in a standard collaborative framework (with no privacy measures taken), with training time reduced from 133.259 s to 99.391 s. Our MLP model for MNIST achieves 97% accuracy compared to 98% in the standard collaborative framework, with training time reduced from 118.146 s to 87.873 s. Compared to other studies, our method is a simple approach that protects privacy, maintains the utility of deep learning models, and reduces training time and communication costs.

Botnet attacks detection in IoT environment using machine learning techniques

IoT devices with weak security designs are a serious threat to organizations. They are the building blocks of Botnets, the platforms that launch organized attacks that are capable of shutting down an entire infrastructure. Researchers have been developing IDS solutions that can counter such threats, often by employing innovation from other disciplines like artificial intelligence and machine learning. One of the issues that may be encountered when machine learning is used is dataset purity. Since they are not captured from perfect environments, datasets may contain data that could affect the machine learning process, negatively. Algorithms already exist for such problems. Repeated Edited Nearest Neighbor (RENN), Encoding Length (Explore), and Decremental Reduction Optimization Procedure 5 (DROP5) algorithm can filter noises out of datasets. They also provide other benefits such as instance reduction which could help reduce larger Botnet datasets, without sacrificing their quality. Three datasets were chosen in this study to construct an IDS: IoTID20, N-BaIoT and MedBIoT. The filtering algorithms, RENN, Explore, and DROP5 were used on them to filter noise and reduce instances. Noise was also injected and filtered again to assess the resilience of these filters. Then feature optimizations were used to shrink the dataset features. Finally, machine learning was applied on the processed dataset and the resulting IDS was evaluated with the standard supervised learning metrics: Accuracy, Precision, Recall, Specificity, F-Score and G-Mean. Results showed that RENN and DROP5 filtering delivered excellent results. DROP5, in particular, managed to reduce the dataset substantially without sacrificing accuracy. However, when noise got injected, the DROP5 accuracy went down and could not keep up. Of the three dataset, N-BaIoT delivers the best accuracy overall across the learning techniques.

Fuzzy prototype selection-based classifiers for imbalanced data. Case study

• Two classification methods based on prototype selection are presented. • These methods are based on fuzzy similarity relations as a more flexible alternative. • Proposed methods demonstrate good performance on imbalanced datasets. • These methods allow instance reduction in the learning process. • Prototypes help explain and interpret events. Imbalanced data are popular in the machine learning community due to their likelihood of appearing in real-world application areas and the problems they present for classical classifiers. The goal of this work is to extend the capabilities of prototype-based classifiers using fuzzy similarity relations and to make them sensitive to class-imbalanced data classification. This paper proposes two new fuzzy logic-based prototype selection classifiers for imbalanced datasets, Imb-SPBASIR-Fuzzy_V1 (FPS-v1) and Imb-SPBASIR-Fuzzy_V2 (FPS-v1), and shows a comparative study of them with state-of-the-art methods on public datasets from the UCI machine learning repository. The results on the selected datasets suggest that fuzzy logic-based prototype selection classifiers perform well and efficiently, indicating that it is a viable alternative. The fuzzy relationships provided by this approach allow better results than the state-of-the-art models. Further analysis showed that the proposed fuzzy-based prototypes methods permit obtaining more accurate to deal with the correct prophylaxis, timely diagnosis and treatment of postoperative mediastinitis.

Optimal instance subset selection from big data using genetic algorithm and open source framework

Data is accumulating at an incredible rate, and the era of big data has arrived. Big data brings great challenges to traditional machine learning algorithms, it is difficult for learning tasks in big data scenario to be completed on stand-alone. Data reduction is an effective way to solve this problem. Data reduction includes attribute reduction and instance reduction. In this study, we focus on instance reduction also called instance selection, and view the instance selection as an optimal instance subset selection problem. Inspired by the ideas of cross validation and divide and conquer, we defined a novel criterion called combined information entropy with respect to a set of classifiers to measure the importance of an instance subset, the criterion uses multiple independent classifiers trained on different subsets to measure the optimality of an instance subset. Based on the criterion, we proposed an approach which uses genetic algorithm and open source framework to select optimal instance subset from big data. The proposed algorithm is implemented on two open source big data platforms Hadoop and Spark, the conducted experiments on four artificial data sets demonstrate the feasibility of the proposed algorithm and visualize the distribution of selected instances, and the conducted experiments on four real data sets compared with three closely related methods on test accuracy and compression ratio demonstrate the effectiveness of the proposed algorithm. Furthermore, the two implementations on Hadoop and Spark are also experimentally compared. The experimental results show that the proposed algorithm provides excellent performance and outperforms the three methods.

A fast instance reduction algorithm for intrusion detection scenarios

We live in a world that is being driven by data. This leads to challenges of extracting and analyzing knowledge from large volumes of data. An example of such a challenge is intrusion detection. Intrusion detection data sets are characterized by huge volumes, which affects the learning of the classifier. So there is a need to reduce the size of the training sets. Fortunately, inspection and analysis of available intrusion detection data sets showed that many instances are very similar and do not provide relevant information to the classification process. This prompted to look for possibilities to use a fast algorithm that, as much as possible, removes similar instances in intrusion detection data sets while enforcing the detection rate. In this work, a new fast instance reduction algorithm is presented. The proposed algorithm provides greater efficiency during the training stage, without significantly affecting the efficacy during the intrusion detection task.

SPMS-ALS: A Single-Point Memetic structure with accelerated local search for instance reduction

• SPMS-ALS is a single-point memetic structure for instance reduction. • SPMS-ALS proposes a domain specific accelerated local search based on Pattern Search. • SPMS-ALS is a memetic approach designed according to a bottom-up strategy. • SPMS-ALS can save up to 85% of the runtime and yet achieves an excellent performance. Real-world optimisation problems pose domain specific challenges that often require an ad-hoc algorithmic design to be efficiently addressed. The present paper investigates the optimisation of a key stage in data mining, known as instance reduction, which aims to shrink the input data prior to applying a learning algorithm. Performing a smart selection or creation of a reduced number of samples that represent the original data may become a complex large-scale optimisation problem, characterised by a computationally expensive objective function, which has been often tackled by sophisticated population-based metaheuristics that suffer from a high runtime. Instead, by following the Ockham’s Razor in Memetic Computing, we propose a Memetic Computing approach that we refer to as fast Single-Point Memetic Structure with Accelerated Local Search (SPMS-ALS). Using the k-nearest neighbours algorithm as base classifier, we first employ a simple local search for large-scale problems that exploits the search logic of Pattern Search, perturbing an n -dimensional vector along the directions identified by its design variables one by one. This point-by-point perturbation mechanism allows us to design a strategy to re-use most of the calculations previously made to compute the objective function of a candidate solution. The proposed Accelerated Local Search is integrated within a single-point memetic framework and coupled with a resampling mechanism and a crossover. A thorough experimental analysis shows that SPMS-ALS, despite its simplicity, displays an excellent performance which is as good as that of the state-of-the-art while reducing up to approximately 85% of the runtime with respect to any other algorithm that performs the same number of function calls.

A Modified Ant Lion Optimization Method and Its Application for Instance Reduction Problem in Balanced and Imbalanced Data

Instance reduction is a pre-processing step devised to improve the task of classification. Instance reduction algorithms search for a reduced set of instances to mitigate the low computational efficiency and high storage requirements. Hence, finding the optimal subset of instances is of utmost importance. Metaheuristic techniques are used to search for the optimal subset of instances as a potential application. Antlion optimization (ALO) is a recent metaheuristic algorithm that simulates antlion’s foraging performance in finding and attacking ants. However, the ALO algorithm suffers from local optima stagnation and slow convergence speed for some optimization problems. In this study, a new modified antlion optimization (MALO) algorithm is recommended to improve the primary ALO performance by adding a new parameter that depends on the step length of each ant while revising the antlion position. Furthermore, the suggested MALO algorithm is adapted to the challenge of instance reduction to obtain better results in terms of many metrics. The results based on twenty-three benchmark functions at 500 iterations and thirteen benchmark functions at 1000 iterations demonstrate that the proposed MALO algorithm escapes the local optima and provides a better convergence rate as compared to the basic ALO algorithm and some well-known and recent optimization algorithms. In addition, the results based on 15 balanced and imbalanced datasets and 18 oversampled imbalanced datasets show that the instance reduction proposed method can statistically outperform the basic ALO algorithm and has strong competitiveness against other comparative algorithms in terms of four performance measures: Accuracy, Balanced Accuracy (BACC), Geometric mean (G-mean), and Area Under the Curve (AUC) in addition to the run time. MALO algorithm results show increment in Accuracy, BACC, G-mean, and AUC rates up to 7%, 3%, 15%, and 9%, respectively, for some datasets over the basic ALO algorithm while keeping less computational time.

Improving Association Rules Accuracy in Noisy Domains Using Instance Reduction Techniques

Association rules’ learning is a machine learning method used in finding underlying associations in large datasets. Whether intentionally or unintentionally present, noise in training instances causes overfitting while building the classifier and negatively impacts classification accuracy. This paper uses instance reduction techniques for the datasets before mining the association rules and building the classifier. Instance reduction techniques were originally developed to reduce memory requirements in instance-based learning. This paper utilizes them to remove noise from the dataset before training the association rules classifier. Extensive experiments were conducted to assess the accuracy of association rules with different instance reduction techniques, namely: Decremental Reduction Optimization Procedure (DROP) 3, DROP5, ALL K-Nearest Neighbors (ALLKNN), Edited Nearest Neighbor (ENN), and Repeated Edited Nearest Neighbor (RENN) in different noise ratios. Experiments show that instance reduction techniques substantially improved the average classification accuracy on three different noise levels: 0%, 5%, and 10%. The RENN algorithm achieved the highest levels of accuracy with a significant improvement on seven out of eight used datasets from the University of California Irvine (UCI) machine learning repository. The improvements were more apparent in the 5% and the 10% noise cases. When RENN was applied, the average classification accuracy for the eight datasets in the zero-noise test enhanced from 70.47% to 76.65% compared to the original test. The average accuracy was improved from 66.08% to 77.47% for the 5%-noise case and from 59.89% to 77.59% in the 10%-noise case. Higher confidence was also reported in building the association rules when RENN was used. The above results indicate that RENN is a good solution in removing noise and avoiding overfitting during the construction of the association rules classifier, especially in noisy domains.

VVC Subpicture-Based Frame Packing for MPEG Immersive Video

The moving picture experts group (MPEG) video coding group started an immersive video coding standard project to accomplish acceptable bandwidth and decoding resources for multiple immersive videos with texture (color) and geometry (depth) information. The MPEG immersive video (MIV) coding standard provides functionality to remove inter-view redundancy and merge the residuals into videos defined as atlases. Although MIV reduces the number of videos to decode, an efficient decoder instance reduction method has not been investigated. This study proposes a frame packing implementation in MIV software. The proposed method conducts frame packing for geometry atlases to align with texture atlases, encodes them as subpicture bitstreams, and merges one texture / geometry atlas into a single bitstream with a bitstream merger. Furthermore, the proposed method provides control over the number of decoder instances without significantly increasing the computational complexity compared to existing frame packing methods. Therefore, the proposed method was accepted in MIV and will be implemented on the recent version of the reference software of MIV.

Obstructive sleep apnoea/hypopnoea syndrome: relationship with obesity and management in obese patients.

SUMMARYObstructive sleep apnoea/hypopnoea syndrome (OSAHS) is a disease characterised by upper airway obstruction during sleep, quite frequent in the general population, even if underestimated. Snoring, sleep apnoea and diurnal hypersomnia are common in these patients. Central obesity plays a key role: it reduces the size and changes the conformation of the upper airways, besides preventing lung expansion, with consequent reduction of lung volumes. Furthermore, obese people are also resistant to leptin, which physiologically stimulates ventilation; as a result, this causes scarce awakening during apnoea. OSAHS diagnosis is based on the combination of clinical parameters, such as apnoea/hypopnoea index (AHI), medical history, physical examination and Mallampati score. The first objective reference method to identify OSAHS is polysomnography followed by sleep endoscopy. Therapy provides in the first instance reduction of body weight, followed by continuous positive airway pressure (CPAP), which still remains the treatment of choice in most patients, mandibular advancement devices (MAD) and finally otolaryngology or maxillofacial surgery. Among surgical techniques, central is barbed reposition pharyngoplasty (BRP), used in the field of multilevel surgery.

Instance Reduction for Avoiding Overfitting in Decision Trees

Abstract Decision trees learning is one of the most practical classification methods in machine learning, which is used for approximating discrete-valued target functions. However, they may overfit the training data, which limits their ability to generalize to unseen instances. In this study, we investigated the use of instance reduction techniques to smooth the decision boundaries before training the decision trees. Noise filters such as ENN, RENN, and ALLKNN remove noisy instances while DROP3 and DROP5 may remove genuine instances. Extensive empirical experiments were conducted on 13 benchmark datasets from UCI machine learning repository with and without intentionally introduced noise. Empirical results show that eliminating border instances improves the classification accuracy of decision trees and reduces the tree size, which reduces the training and classification times. In datasets without intentionally added noise, applying noise filters without the use of the built-in Reduced Error Pruning gave the best classification accuracy. ENN, RENN, and ALLKNN outperformed decision trees learning without pruning in 9, 9, and 8 out of 13 datasets, respectively. The datasets reduced using ENN and RENN without built-in pruning were more effective when noise was intentionally introduced in different ratios.

Interpretation of the 1/C2 Curvature and Discontinuity in Electrochemical Capacitance Voltage Profiling of Heavily Ga Implanted SiGe Followed by Melt Laser Annealing

Electrochemical Capacitance Voltage Profiling (ECVP) is one of the most widely used characterization methods in semiconductor industry to measure the activation of dopants in doped semiconductor materials owing to its low-cost and easy-to-use features. Today, there are some specific industrial needs, for instance reduction of the contact resistance in advanced transistors, for which heavily-doped semiconductor materials must be implemented. A clear challenge addressed to ECVP here is that the interpretation of measured data becomes much more complex in such materials because of the appearance of curvatures and discontinuity on the curve given by the inverse of the square of the capacitance within the space charge zone as a function of the applied polarisation voltage. In this paper, we present a case of silicon-germanium doped by heavy gallium ion-implantation and annealed by melt laser annealing, where a metastable dopant activation can be expected. We develop a fitting model with different deep levels, highlighting their possibly different time constants to provide a more reliable interpretation on the measurements.

A semi-online algorithm and its competitive analysis for parallel-machine scheduling problem with rejection

In this paper, we focus on a semi-online scheduling problem with rejection on identical parallel machines, where “semi-online” means that the ratio of the longest processing time among all jobs to the shortest one is no more than γ with γ ≥ 1. In particular, in this setting, there are a coupling of independent jobs arriving online over time with the flexibility of rejection, which implies that each job will be either accepted and scheduled on one of identical machines or rejected at the cost of penalty cost. Our objective is minimizing the total completion time of the accepted jobs plus the total penalty cost of the rejected jobs. For this problem, we design a deterministic polynomial time semi-online algorithm entitled as α Delayed Shortest Processing Time with Rejection (ADSPTR). In competitive analysis, by adopting the approach “Improved Instance Reduction”, we obtain the competitive ratio of ADSPTR is at most 1+1+γ(γ−1)−1γ.

Theoretical Description, Synthesis, and Structural Characterization of β-Na0.33V2O5 and Its Fluorinated Derivative β-Na0.33V2O4.67F0.33: Influence of Oxygen Substitution by Fluorine on the Electrochemical Properties.

The structure of β-Na0.33V2O4.67F0.33 has been investigated by both theoretical and experimental methods. It exhibits the same structure as that of the parent bronze β-Na0.33V2O5. The partial substitution of oxygen by fluorine has little effect on the average structure and cell parameters, but the sodium environment changes significantly. Using DFT calculations, we determined the most stable positions of fluorine atoms in the unit cell. It was found that the partial replacement of oxide by fluoride takes mainly place in the coordination sphere of Na producing a shortening of the Na-anion bond lengths. We also analyzed the electronic properties based on density of states and Bader charge distribution. The crystallochemical situation of sodium ions in β-Na0.33V2O4.67F0.33 oxyfluoride, detected by both experimental and computational methods, affects its mobility with respect to the parent oxide. The higher ionicity in the Na coordination sphere of β-Na0.33V2O4.67F0.33 is related to a sodium ion diffusion coefficient, DNa+, that is 1 order of magnitude lower (1.24 × 10-13 cm2 s-1) than in the case of β-Na0.33V2O5 (1.13 × 10-12 cm2 s-1). Electrochemical sodium insertion/deinsertion properties of the oxyfluoride have been also investigated and are compared to the oxide. Insertion/deinsertion equilibrium potential for the same formal oxidation state of vanadium increases due to fluorination (for instance reduction of V+4.3 occurs at 1.5 V in the oxide and at 1.75 V in the oxyfluoride). However, the capacity of Na0.33V2O4.67F0.33 at constant current is lower than in the case of β-Na0.33V2O5 due to a less adequate morphology, a lower DNa+, and a lower oxidation state of vanadium owing to the aliovalent O/F substitution.

A Competitive Online Algorithm for Minimizing Total Weighted Completion Time on Uniform Machines

We consider the classic online scheduling problem on m uniform machines in the online setting where jobs arrive over time. Preemption is not allowed. The objective is to minimize total weighted completion time. An online algorithm based on the directly waiting strategy is proposed. Its competitive performance is proved to be max2smax1−1/2∑si,2smax/1+smax2.5−1/2m by the idea of instance reduction, where sm is the fastest machine speed after being normalized by the slowest machine speed.