Lempel-Ziv Complexity Research Articles

Unequal-step multiscale integrated mapping dispersion Lempel-Ziv complexity: A novel complexity metric for signal analysis

Dispersion Lempel-Ziv complexity (DLZC), as a more effective complexity metric proposed in recent years, can effectively quantify the dynamic change of signal. However, DLZC still has shortcomings of insufficient applicability and lack of scale information. To surmount these drawbacks, we fully utilize the advantages of multiple mapping methods and integrate these mapping methods into DLZC, thus the integrated mapping DLZC (IMDLZC) is proposed, which has higher separability and applicability. Moreover, we developed a coarse-grained method called unequal step multi scale analysis, which solves the problem that the defects of subsequences decrease sharply with the increase of scale in existing coarse-grained methods. Then a new complexity metric for signal analysis called unequal-step multiscale IMDLZC (UM-IMDLZC) is proposed by coupling unequal-step multiscale analysis and IMDLZC. The experimental results of three kinds of synthetic signals show that UM-IMDLZC is more sensitive to the dynamic changes of signals and has the more excellent robustness; moreover, compared with other four complexity metrics, the proposed UM-IMDLZC has the best classification effect for different types of realistic signals.

Dual feature extraction system for ship-radiated noise and its application extension

The complexity of maritime noise and the time-variability of hydroacoustic channels make it more and more difficult to extract feature from ship-radiated noise effectively. To accurately recognize ship-radiated noise, a dual feature extraction and recognition system based on pre-processing-dual feature extraction-recognition is proposed. Pre-processing: The primary decomposition and secondary decomposition are performed for the first time using variational mode decomposition optimized by giant trevally optimizer, in which the threshold is adaptively determined. Dual feature extraction: Grey relational analysis is calculated for the intrinsic mode function component after primary decomposition and the high-intrinsic mode function component after secondary decomposition, and two eigenvectors are selected separately. Then entropy of the combination of weighted fluctuation-based dispersion entropy and Lempel-Ziv complexity is proposed to calculate the eigenvalues for classification. Recognition: The feature values are recognized using random forest recognizer optimized by tuna swarm optimization to obtain the final recognition rate. The experimental results show that the proposed entropy has an overwhelming advantage over the others, such as permutation entropy, and dispersion entropy. It is proved that the proposed system for ship-radiated noise has good classification performance and the recognition rate is up to 97.5%. In addition, it is successfully applied to simulated chaotic signals as well as measured aquatic life signals.

Altered brain dynamics index levels of arousal in complete locked-in syndrome

Complete locked-in syndrome (CLIS) resulting from late-stage amyotrophic lateral sclerosis (ALS) is characterised by loss of motor function and eye movements. The absence of behavioural indicators of consciousness makes the search for neuronal correlates as possible biomarkers clinically and ethically urgent. EEG-based measures of brain dynamics such as power-law exponent (PLE) and Lempel-Ziv complexity (LZC) have been shown to have explanatory power for consciousness and may provide such neuronal indices for patients with CLIS. Here, we validated PLE and LZC (calculated in a dynamic way) as benchmarks of a wide range of arousal states across different reference states of consciousness (e.g., awake, sleep stages, ketamine, sevoflurane). We show a tendency toward high PLE and low LZC, with high intra-subject fluctuations and inter-subject variability in a cohort of CLIS patients with values graded along different arousal states as in our reference data sets. In conclusion, changes in brain dynamics indicate altered arousal in CLIS. Specifically, PLE and LZC are potentially relevant biomarkers to identify or diagnose the arousal level in CLIS and to determine the optimal time point for treatment, including communication attempts.

A novel feature extraction method for ship-radiated noise based on hierarchical refined composite multi-scale dispersion entropy-based Lempel-Ziv complexity

Accurate recognition of ship-radiated noise (SRN) is particularly important for coastal defense, where feature extraction is the key technology. As a recently proposed nonlinear dynamics index, dispersion entropy-based Lempel-Ziv complexity (DELZC) can effectively quantify the information contained in SRN. However, DELZC characterizes inadequately the complexity feature of SRN with the ignorance of the information under different scales and information hidden in high frequency. To correct these drawbacks, the refined composite coarse-graining operation is integrated into DELZC, and the refined composite multi-scale DELZC (RCMDELZC) is put forward and adequately reflects the scale information, subsequently the technology of hierarchical decomposition is introduced and proposed the hierarchical RCMDELZC (HRCMDELZC), which takes into account the abundant feature information of the signal contained in the time scale and different frequency bands. Then, on the basis of HRCMDELZC, a feature extraction method for SRN by combining with maximum relevance minimum redundancy (mRMR) is proposed. The simulation results show that HRCMDELZC can effectively classify different noise and chaotic signals; the realistic experimental results deliver that the HRCMDELZC features of SRNs have more excellent separability compared with the other seven categories of complexity features, and the proposed feature extraction method has the highest classification accuracy for various SRNs.

The Dopaminergic System Modulates the Electrophysiological Activity of the Suprachiasmatic Nucleus Dependent on the Circadian Cycle.

The suprachiasmatic nucleus of the hypothalamus (SCN) controls mammalian circadian rhythms. Circadian rhythms influence the dopaminergic system, and dopaminergic tone impresses the physiology and behavior of the circadian clock. However, little is known about the effect of dopamine and dopamine receptors, especially D1-like dopamine receptors (D1Rs), in regulating the circadian rhythm and the SCN neuron's activity. Therefore, the present study aimed to investigate the role of the D1Rs in SCN neural oscillations during the 24-h light-dark cycle using local field potential (LFP) recording. To this end, two groups of rats were given the SKF-38393 (1mg/kg; i.p.) as a D1-like receptor agonist in the morning or night. LFP recording was performed for ten minutes before and two hours after the SKF-38393 injection. The obtained results showed that diurnal changes affect LFP oscillations so that delta relative power declined substantially, whereas upper-frequency bands and Lempel-Ziv complexity (LZC) index increased at night, which is consistent with rodents' activity cycles. The D1Rs agonist administration in the morning dramatically altered these intrinsic oscillations, decreasing delta and theta relative power, and most of the higher frequency bands and LZC index were promoted. Some of these effects were reversed at the night after the SKF-38393 injection. In conclusion, findings showed that the SCN's neuronal activities are regulated based on the light-dark cycle in terms of population neural oscillatory activity which could be affected by dopaminergic stimulation in a time-dependent way.

Depression Detection Based on Analysis of EEG Signals in Multi Brain Regions.

As an objective method to detect the neural electrical activity of the brain, electroencephalography (EEG) has been successfully applied to detect major depressive disorder (MDD). However, the performance of the detection algorithm is directly affected by the selection of EEG channels and brain regions. To solve the aforementioned problems, nonlinear feature Lempel-Ziv complexity (LZC) and frequency domain feature power spectral density (PSD) were extracted to analyze the EEG signals. Additionally, effects of different brain regions and region combinations on detecting MDD were studied with eyes closed and opened in a resting state. The mean LZC of patients with MDD was higher than that of the control group, and the mean PSD of patients with MDD was generally lower than that of the control group. The temporal region is the best brain region for MDD detection with a detection accuracy of 87.4%. The best multi brain regions combination had a detection accuracy of 92.4% and was made up of the frontal, temporal, and central brain regions. This paper validates the effectiveness of multiple brain regions in detecting MDD. It provides new ideas for exploring the pathology of MDD and innovative methods of diagnosis and treatment.

Intraoperative cortical localization of music and language reveals signatures of structural complexity in posterior temporal cortex

Language and music involve the productive combination of basic units into structures. It remains unclear whether brain regions sensitive to linguistic and musical structure are co-localized. We report an intraoperative awake craniotomy in which a left-hemispheric language-dominant professional musician underwent cortical stimulation mapping (CSM) and electrocorticography of music and language perception and production during repetition tasks. Musical sequences were melodic or amelodic, and differed in algorithmic compressibility (Lempel-Ziv complexity). Auditory recordings of sentences differed in syntactic complexity (single vs. multiple phrasal embeddings). CSM of posterior superior temporal gyrus (pSTG) disrupted music perception and production, along with speech production. pSTG and posterior middle temporal gyrus (pMTG) activated for language and music (broadband gamma; 70-150Hz). pMTG activity was modulated by musical complexity, while pSTG activity was modulated by syntactic complexity. This points to shared resources for music and language comprehension, but distinct neural signatures for the processing of domain-specific structural features.

Linear mixed-effect models for correlated response to process electroencephalogram recordings.

A data set of clinical studies of electroencephalogram recordings (EEG) following data acquisition protocols in control individuals (Eyes Closed Wakefulness - Eyes Open Wakefulness, Hyperventilation, and Optostimulation) are quantified with information theory metrics, namely permutation Shanon entropy and permutation Lempel Ziv complexity, to identify functional changes. This work implement Linear mixed-effects models (LMEMs) for confirmatory hypothesis testing. The results show that EEGs have high variability for both metrics and there is a positive correlation between them. The mean of permutation Lempel-Ziv complexity and permutation Shanon entropy used simultaneously for each of the four states are distinguishable from each other. However, used separately, the differences between permutation Lempel-Ziv complexity or permutation Shanon entropy of some states were not statistically significant. This shows that the joint use of both metrics provides more information than the separate use of each of them. Despite their wide use in medicine, LMEMs have not been commonly applied to simultaneously model metrics that quantify EEG signals. Modeling EEGs using a model that characterizes more than one response variable and their possible correlations represents a new way of analyzing EEG data in neuroscience.

Complex Dynamics in Digital Nonlinear Oscillators: Experimental Analysis and Verification

A specific topology of Digital Nonlinear Oscillators (DNOs) has been implemented by using commercial off-the-shelf digital components to experimentally verify and demonstrate the capability of these circuits to support complex dynamics, independently from their implementation technology. In detail, a direct experimental evidence of the DNO dynamical behavior is presented at the analog level with a bifurcation diagram analysis, investigation of periodic and chaotic attractors, and dynamical stability. The autonomous circuit has been investigated as a source of entropy, adopting different figures of merit, including the Lempel–Ziv Complexity, to evaluate the dynamics measured under different operating conditions.

Comparative Study on Feature Extraction of Marine Background Noise Based on Nonlinear Dynamic Features.

Marine background noise (MBN) is the background noise of the marine environment, which can be used to invert the parameters of the marine environment. However, due to the complexity of the marine environment, it is difficult to extract the features of the MBN. In this paper, we study the feature extraction method of MBN based on nonlinear dynamics features, where the nonlinear dynamical features include two main categories: entropy and Lempel-Ziv complexity (LZC). We have performed single feature and multiple feature comparative experiments on feature extraction based on entropy and LZC, respectively: for entropy-based feature extraction experiments, we compared feature extraction methods based on dispersion entropy (DE), permutation entropy (PE), fuzzy entropy (FE), and sample entropy (SE); for LZC-based feature extraction experiments, we compared feature extraction methods based on LZC, dispersion LZC (DLZC) and permutation LZC (PLZC), and dispersion entropy-based LZC (DELZC). The simulation experiments prove that all kinds of nonlinear dynamics features can effectively detect the change of time series complexity, and the actual experimental results show that regardless of the entropy-based feature extraction method or LZC-based feature extraction method, they both present better feature extraction performance for MBN.

Diagnosis of neurodegenerative diseases with a refined Lempel-Ziv complexity.

The investigation into the distinctive difference of gait is of significance for the clinical diagnosis of neurodegenerative diseases. However, human gait is affected by many factors like behavior, occupation and so on, and they may confuse the gait differences among Parkinson's disease, amyotrophic lateral sclerosis, and Huntington's disease. For the purpose of examining distinctive gait differences of neurodegenerative diseases, this study extracts various features from both vertical ground reaction force and time intervals. Moreover, refined Lempel-Ziv complexity is proposed considering the detailed distribution of signals based on the median and quartiles. Basic features (mean, coefficient of variance, and the asymmetry index), nonlinear dynamic features (Hurst exponent, correlation dimension, largest Lyapunov exponent), and refined Lempel-Ziv complexity of different neurodegenerative diseases are compared statistically by violin plot and Kruskal-Wallis test to reveal distinction and regularities. The comparative analysis results illustrate the gait differences across these neurodegenerative diseases by basic features and nonlinear dynamic features. Classification results by random forest indicate that the refined Lempel-Ziv complexity can robustly enhance the diagnosis accuracy when combined with basic features.

The potential of the Lempel-Ziv complexity of the EEG in diagnosing cognitive impairment in patients with temporal lobe epilepsy.

To analyze whether the Lempel-Ziv Complexity (LZC) in quantitative electroencephalogram differs between the temporal lobe epilepsy (TLE) patients with or without cognitive impairment (CI) and explore the diagnostic value of LZC for identifying CI in TLE patients. Twenty-two clinical features and 20-min EEG recordings were collected from 48 TLE patients with CI and 27 cognitively normal (CON) TLE patients. Seventy-six LZC features were calculated for 19 leads in four frequency bands (alpha, beta, delta, and theta). The clinical and LZC features were compared between the two groups. A support vector machine (SVM) was subsequently constructed using the leave-one-out method of cross-validation for LZC features with statistical differences. Regarding the clinical features, the level of education (p < .001), hippocampal atrophy and sclerosis (p = .029), and depression (p = .037) were statistically different between the two groups. For the LZC features, there were statistically significant differences in the alpha (Fp1, Fz, Cz, Pz, C3, C4, T3, T4, T5, T6, F3, F4, F7, F8, O1, and O2), beta (Fp2), and theta (F7) oscillations. The mean LZC in the alpha band was higher in the TLE-CI group than that in the CON group, and there were no differences in the remaining bands. The SVM model showed 74.51% accuracy, 79.63% sensitivity, 84.30% F1 score, 68.75% specificity, and .85 area under the curve scores. The LZC in the alpha band might have the potential to be used as a biomarker for the diagnosis of TLE combined with CI. The TLE-CI group, on the other hand, exhibited a higher degree of complexity in alpha oscillations, which were widespread and occurred in all brain regions.

Sleep and cognition in aging dogs. A polysomnographic study.

Sleep is fundamental for cognitive homeostasis, especially in senior populations since clearance of amyloid beta (key in the pathophysiology of Alzheimer's disease) occurs during sleep. Some electroencephalographic characteristics of sleep and wakefulness have been considered a hallmark of dementia. Owners of dogs with canine cognitive dysfunction syndrome (a canine analog to Alzheimer's disease) report that their dogs suffer from difficulty sleeping. The aim of this study was to quantify age-related changes in the sleep-wakefulness cycle macrostructure and electroencephalographic features in senior dogs and to correlate them with their cognitive performance. We performed polysomnographic recordings in 28 senior dogs during a 2 h afternoon nap. Percentage of time spent in wakefulness, drowsiness, NREM, and REM sleep, as well as latency to the three sleep states were calculated. Spectral power, coherence, and Lempel Ziv Complexity of the brain oscillations were estimated. Finally, cognitive performance was evaluated by means of the Canine Dementia Scale Questionnaire and a battery of cognitive tests. Correlations between age, cognitive performance and sleep-wakefulness cycle macrostructure and electroencephalographic features were calculated. Dogs with higher dementia scores and with worse performance in a problem-solving task spent less time in NREM and REM sleep. Additionally, quantitative electroencephalographic analyses showed differences in dogs associated with age or cognitive performance, some of them reflecting shallower sleep in more affected dogs. Polysomnographic recordings in dogs can detect sleep-wakefulness cycle changes associated with dementia. Further studies should evaluate polysomnography's potential clinical use to monitor the progression of canine cognitive dysfunction syndrome.

Evolution over Time of Urban Thermal Conditions of a City Immersed in a Basin Geography and Mitigation

This work analyzes the evolution of an urban thermal environment using measurements, in the form of time series, of atmospheric pollutants (PM10, PM2.5, CO) and meteorological variables (temperature (T), relative humidity (RH) and magnitude of wind speed (WS)) of three periods, each of 3.25 years: 2010–2013, 2017–2020 and 2019–2022. The study region is the capital of Chile, Santiago de Chile, located in a rugged basin geography. Of the total communes that make up the capital, six communes that are at different heights from sea level were selected for this study, providing 3,074,004 data records. These communes have been subject to an intensive urban densification process. The time series are analyzed through the chaos theory, demonstrating that they are chaotic through the calculation of the parameters: Lyapunov exponent (λ &gt; 0), correlation dimension (DC &lt; 5), Kolmogorov entropy (SK &gt; 0), Hurst exponent (0.5 &lt; H &lt; 1), Lempel–Ziv complexity (LZ &gt; 0). Based on these parameters, the following is constructed for each commune: the CK ratio, which results from the ratio between the entropies of the meteorological variables and the entropies of the pollutants; the loss of information (&lt;ΔI&gt; &lt; 0) using the Lyapunov exponent; the fractal dimension (D) using the Hurst exponent. It is verified, when comparing the three periods for the six communes, that: CK evolves declining with height, with a greater influence of pollutants; the loss of information is faster in urban meteorology; an increase in fractality. The estimation of the entropic flows, based on the Clausius equation, confirm the trend. The descriptive framework shows the weakness of the mitigation measures.

Neural complexity EEG biomarkers of rapid and post-rapid ketamine effects in late-life treatment-resistant depression: a randomized control trial

Ketamine is an effective intervention for treatment-resistant depression (TRD), including late-in-life (LL-TRD). The proposed mechanism of antidepressant effects of ketamine is a glutamatergic surge, which can be measured by electroencephalogram (EEG) gamma oscillations. Yet, non-linear EEG biomarkers of ketamine effects such as neural complexity are needed to capture broader systemic effects, represent the level of organization of synaptic communication, and elucidate mechanisms of action for treatment responders. In a secondary analysis of a randomized control trial, we investigated two EEG neural complexity markers (Lempel-Ziv complexity [LZC] and multiscale entropy [MSE]) of rapid (baseline to 240 min) and post-rapid ketamine (24 h and 7 days) effects after one 40-min infusion of IV ketamine or midazolam (active control) in 33 military veterans with LL-TRD. We also studied the relationship between complexity and Montgomery-Åsberg Depression Rating Scale score change at 7 days post-infusion. We found that LZC and MSE both increased 30 min post-infusion, with effects not localized to a single timescale for MSE. Post-rapid effects of reduced complexity with ketamine were observed for MSE. No relationship was observed between complexity and reduction in depressive symptoms. Our findings support the hypothesis that a single sub-anesthetic ketamine infusion has time-varying effects on system-wide contributions to the evoked glutamatergic surge in LL-TRD. Further, changes to complexity were observable outside the time-window previously shown for effects on gamma oscillations. These preliminary results have clinical implications in providing a functional marker of ketamine that is non-linear, amplitude-independent, and represents larger dynamic properties, providing strong advantages over linear measures in highlighting ketamine’s effects.

Approach to the Quantitative Diagnosis of Rolling Bearings Based on Optimized VMD and Lempel-Ziv Complexity under Varying Conditions.

The quantitative diagnosis of rolling bearings is essential to automating maintenance decisions. Over recent years, Lempel-Ziv complexity (LZC) has been widely used for the quantitative assessment of mechanical failures as one of the most valuable indicators for detecting dynamic changes in nonlinear signals. However, LZC focuses on the binary conversion of 0-1 code, which can easily lose some effective information about the time series and cannot fully mine the fault characteristics. Additionally, the immunity of LZC to noise cannot be insured, and it is difficult to quantitatively characterize the fault signal under strong background noise. To overcome these limitations, a quantitative bearing fault diagnosis method based on the optimized Variational Modal Decomposition Lempel-Ziv complexity (VMD-LZC) was developed to fully extract the vibration characteristics and to quantitatively characterize the bearing faults under variable operating conditions. First, to compensate for the deficiency that the main parameters of the variational modal decomposition (VMD) have to be selected by human experience, a genetic algorithm (GA) is used to optimize the parameters of the VMD and adaptively determine the optimal parameters [k, α] of the bearing fault signal. Furthermore, the IMF components that contain the maximum fault information are selected for signal reconstruction based on the Kurtosis theory. The Lempel-Ziv index of the reconstructed signal is calculated and then weighted and summed to obtain the Lempel-Ziv composite index. The experimental results show that the proposed method is of high application value for the quantitative assessment and classification of bearing faults in turbine rolling bearings under various operating conditions such as mild and severe crack faults and variable loads.

Two-channel EEG based diagnosis of panic disorder and major depressive disorder using machine learning and non-linear dynamical methods

The current study aimed to investigate the possibility of rapid and accurate diagnoses of Panic disorder (PD) and Major depressive disorder (MDD) using machine learning. The support vector machine method was applied to 2-channel EEG signals from the frontal lobes (Fp1 and Fp2) of 149 participants to classify PD and MDD patients from healthy individuals using non-linear measures as features. We found significantly lower correlation dimension and Lempel-Ziv complexity in PD patients and MDD patients in the left hemisphere compared to healthy subjects at rest. Most importantly, we obtained a 90% accuracy in classifying MDD patients vs. healthy individuals, a 68% accuracy in classifying PD patients vs. controls, and a 59% classification accuracy between PD and MDD patients. In addition to demonstrating classification performance in a simplified setting, the observed differences in EEG complexity between subject groups suggest altered cortical processing present in the frontal lobes of PD patients that can be captured through non-linear measures. Overall, this study suggests that machine learning and non-linear measures using only 2-channel frontal EEGs are useful for aiding the rapid diagnosis of panic disorder and major depressive disorder.

Possible Neuropathological Mechanisms Underlying the Increased Complexity of Brain Electrical Activity in Schizophrenia: A Computational Study.

Objective: Schizophrenia is a complex neurodevelopmental illness that is associated with different deficits in the cerebral cortex and neural networks, resulting in irregularity of brain waves. Various neuropathological hypotheses have been proposed for this irregularity that we intend to examine in this computational study. Method : We used a mathematical model of a neuronal population based on cellular automata to examine two hypotheses about the neuropathology of schizophrenia: first, reducing neuronal stimulation thresholds to increase neuronal excitability; and second, increasing the percentage of excitatory neurons and decreasing the percentage of inhibitory neurons to increase the excitation to inhibition ratio in the neuronal population. Then, we compare the complexity of the output signals produced by the model in both cases with real healthy resting-state electroencephalogram (EEG) signals using the Lempel-Ziv complexity measure and see if these changes alter (increase or decrease) the complexity of the neuronal population dynamics. Results: By lowering the neuronal stimulation threshold (i.e., the first hypothesis), no significant change in the pattern and amplitude of the network complexity was observed, and the model complexity was very similar to the complexity of real EEG signals (P > 0.05). However, increasing the excitation to inhibition ratio (i.e., the second hypothesis) led to significant changes in the complexity pattern of the designed network (P < 0.05). More interestingly, in this case, the complexity of the output signals of the model increased significantly compared to real healthy EEGs (P = 0.002) and the model output of the unchanged condition (P = 0.028) and the first hypothesis (P = 0.001). Conclusion: Our computational model suggests that imbalances in the excitation to inhibition ratio in the neural network are probably the source of abnormal neuronal firing patterns and thus the cause of increased complexity of brain electrical activity in schizophrenia.

EEG complexity correlates with residual consciousness level of disorders of consciousness

Background and objectiveElectroencephalography (EEG) and neuroimaging measurements have been highly encouraged to be applied in clinics of disorders of consciousness (DOC) to improve consciousness detection. We tested the relationships between neural complexity measured on EEG and residual consciousness levels in DOC patients.MethodsResting-state EEG was recorded from twenty-five patients with DOC. Lempel–Ziv complexity (LZC) and permutation Lempel–Ziv complexity (PLZC) were measured on the EEG, and their relationships were analyzed with the consciousness levels of the patients.ResultsPLZC and LZC values significantly distinguished patients with a minimally conscious state (MCS), vegetative state/unresponsive wakefulness syndrome (VS/UWS), and healthy controls. PLZC was significantly correlated with the Coma Recovery Scale-Revised (CRS-R) scores of DOC patients in the global brain, particularly in electrodes locating in the anterior and posterior brain regions. Patients with higher CRS-R scores showed higher PLZC values. The significant difference in PLZC values between MCS and VS/UWS was mainly located in the bilateral frontal and right hemisphere regions.ConclusionNeural complexity measured on EEG correlates with residual consciousness levels of DOC patients. PLZC showed higher sensitivity than LZC in the classification of consciousness levels.

An unsupervised method to exploit low-resolution water meter data for detecting end-users with abnormal consumption: Employing the DBSCAN and time series complexity

The expansion of cities puts a high demand on water utilities to provide fresh water amidst global water stress. One of the most challenging issues that continuously menaces water sector sustainability is dealing with anomalous consumption as commercial water losses. To this end, this paper proposes a novel and elaborate unsupervised machine learning method with an effortless computation to detect end-user anomalies in water distribution systems. The method relies on density-based spatial clustering of applications with noise (DBSCAN) as the core and Lempel-Ziv Complexity as the key features to overcome the curse of dimensionality and low data resolution, while only users' billing records are needed. Building upon the method's outputs, six latent abnormal patterns were perceived in a large unlabeled real-life dataset after validation by a smaller but labeled (fraudulent or normal consumption) real-life dataset. The results exposed that the method meets reliable and efficacious outputs for anomaly detection, as the derived clustering could capture high accuracy of 98% and a hit rate of 92%. Also, this study provides valuable information that can be used for action planning like on-site inspections and improving water loss management practices, exceptionally when water utilities/authorities' budgets are constrained, and revenue declines occur.