Mutual Information Function Research Articles

Calculation of Average Mutual Information (AMI) and False-Nearest Neighbors (FNN) for the Estimation of Embedding Parameters of Multidimensional Time Series in Matlab.

Using the method or time-delayed embedding, a signal can be embedded into higher-dimensional space in order to study its dynamics. This requires knowledge of two parameters: The delay parameter τ, and the embedding dimension parameter D. Two standard methods to estimate these parameters in one-dimensional time series involve the inspection of the Average Mutual Information (AMI) function and the False Nearest Neighbor (FNN) function. In some contexts, however, such as phase-space reconstruction for Multidimensional Recurrence Quantification Analysis (MdRQA), the empirical time series that need to be embedded already possess a dimensionality higher than one. In the current article, we present extensions of the AMI and FNN functions for higher dimensional time series and their application to data from the Lorenz system coded in Matlab.

Collective Secrecy Over the <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math> </inline-formula>-Transmitter Multiple Access Channel

This paper studies the problem of secure communication over a $K$ -transmitter multiple access channel (MAC) in the presence of an external eavesdropper, subject to a collective secrecy constraint (i.e., information leakage rate to an eavesdropper on a collection of messages that are from a pre-specified subset of the $K$ transmitters, say $\mathcal {S}\subseteq \mathcal {K}=\{1,2,\ldots, K\}$ , is made vanishing). Since secrecy is of concern only to transmitters $\{i|i\in \mathcal {S}\}$ but not to transmitters $\{i|i\in \mathcal {S}^{c}\}$ , where $\mathcal {S}^{c}=\mathcal {K}\backslash \mathcal {S}$ , different transmission strategies could be employed at transmitters $\{i|i\in \mathcal {S}^{c}\}$ . Consider the following two scenarios: 1) transmitters $\{i|i\in \mathcal {S}^{c}\}$ use deterministic encoders (which are conventionally used for MAC without secrecy), competing for the channel resource (i.e., being competitive) and 2) transmitters $\{i|i\in \mathcal {S}^{c}\}$ use stochastic encoders, helping to hide other transmitters’ messages from the eavesdropper (i.e., being cooperative). As a result, we establish the respective $\mathcal {S}$ -collective secrecy achievable rate regions and demonstrate the advantage of being cooperative theoretically and numerically. To this end, in addition to the standard techniques, our results build upon two techniques. The first is a generalization of Chia-El Gamal’s lemma on entropy bound for a set of codewords given partial information. The second is to utilize a compact representation of a list of sets that, together with submodular properties of mutual information functions involved, leads to an efficient Fourier-Motzkin elimination. These two approaches allow us to derive achievable regions in this work, and could also be of independent interest in other context.

Damage Detection Using Dissimilarity in Phase Space Topology of Dynamic Response of Structure Subjected to Shock Wave Loading

Shockwave is a high pressure and short duration pulse that induce damage and lead to progressive collapse of the structure. The shock load excites high-frequency vibrational modes and causes failure due to large deformation in the structure. Shockwave experiments were conducted by imparting repetitive localized shock loads to create progressive damage states in the structure. Two-phase novel damage detection algorithm is proposed, that quantify and segregate perturbative damage from microscale damage. The first phase performs dimension reduction and damage state segregation using principal component analysis (PCA). In the second phase, the embedding dimension was reduced through empirical mode decomposition (EMD). The embedding parameters were derived using singular system analysis (SSA) and average mutual information function (AMIF). Based, on Takens theorem and embedding parameters, the response was represented in a multidimensional phase space trajectory (PST). The dissimilarity in the multidimensional PST was used to derive the damage sensitive features (DSFs). The DSFs namely: (i) change in phase space topology (CPST) and (ii) Mahalanobis distance between phase space topology (MDPST) are evaluated to quantify progressive damage states. The DSFs are able to quantify the occurrence, magnitude, and localization of progressive damage state in the structure. The proposed algorithm is robust and efficient to detect and quantify the evolution of damage state for extreme loading scenarios.

Information-Theoretical Analysis of EEG Microstate Sequences in Python.

We present an open-source Python package to compute information-theoretical quantities for electroencephalographic data. Electroencephalography (EEG) measures the electrical potential generated by the cerebral cortex and the set of spatial patterns projected by the brain's electrical potential on the scalp surface can be clustered into a set of representative maps called EEG microstates. Microstate time series are obtained by competitively fitting the microstate maps back into the EEG data set, i.e., by substituting the EEG data at a given time with the label of the microstate that has the highest similarity with the actual EEG topography. As microstate sequences consist of non-metric random variables, e.g., the letters A–D, we recently introduced information-theoretical measures to quantify these time series. In wakeful resting state EEG recordings, we found new characteristics of microstate sequences such as periodicities related to EEG frequency bands. The algorithms used are here provided as an open-source package and their use is explained in a tutorial style. The package is self-contained and the programming style is procedural, focusing on code intelligibility and easy portability. Using a sample EEG file, we demonstrate how to perform EEG microstate segmentation using the modified K-means approach, and how to compute and visualize the recently introduced information-theoretical tests and quantities. The time-lagged mutual information function is derived as a discrete symbolic alternative to the autocorrelation function for metric time series and confidence intervals are computed from Markov chain surrogate data. The software package provides an open-source extension to the existing implementations of the microstate transform and is specifically designed to analyze resting state EEG recordings.

Mutual information identifies spurious Hurst phenomena in resting state EEG and fMRI data.

Long-range memory in time series is often quantified by the Hurst exponent H, a measure of the signal's variance across several time scales. We analyze neurophysiological time series from electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) resting state experiments with two standard Hurst exponent estimators and with the time-lagged mutual information function applied to discretized versions of the signals. A confidence interval for the mutual information function is obtained from surrogate Markov processes with equilibrium distribution and transition matrix identical to the underlying signal. For EEG signals, we construct an additional mutual information confidence interval from a short-range correlated, tenth-order autoregressive model. We reproduce the previously described Hurst phenomenon (H>0.5) in the analytical amplitude of alpha frequency band oscillations, in EEG microstate sequences, and in fMRI signals, but we show that the Hurst phenomenon occurs without long-range memory in the information-theoretical sense. We find that the mutual information function of neurophysiological data behaves differently from fractional Gaussian noise (fGn), for which the Hurst phenomenon is a sufficient condition to prove long-range memory. Two other well-characterized, short-range correlated stochastic processes (Ornstein-Uhlenbeck, Cox-Ingersoll-Ross) also yield H>0.5, whereas their mutual information functions lie within the Markovian confidence intervals, similar to neural signals. In these processes, which do not have long-range memory by construction, a spurious Hurst phenomenon occurs due to slow relaxation times and heteroscedasticity (time-varying conditional variance). In summary, we find that mutual information correctly distinguishes long-range from short-range dependence in the theoretical and experimental cases discussed. Our results also suggest that the stationary fGn process is not sufficient to describe neural data, which seem to belong to a more general class of stochastic processes, in which multiscale variance effects produce Hurst phenomena without long-range dependence. In our experimental data, the Hurst phenomenon and long-range memory appear as different system properties that should be estimated and interpreted independently.

Classificação de disfonias por meio da análise de medidas não lineares e de quantificação de recorrência

In recent years techniques of digital processing of speech signals have been used as an auxiliary tool in the evaluation of vocal deviations, providing the patient with greater comfort low cost and objectivity when compared to the techniques traditionally employed, such as perceptual-auditory analysis. The evaluation of vocal quality, through acoustic analysis of voice signals, is becoming a very popular clinical practice for the detection of vocal disorders that in some cases can be caused by laryngeal lesions or vocal abuse. In this research, we used some traditional non-linear measures combined with measures of recurrence quantification for the discriminative analysis of vocal deviations, breathiness, roughness and strain. The characteristics of the non-linear dynamic analysis,used in the classification process, were the Reconstruction Step (τ), the First Minimum of the Mutual Information Function (PM) and the Correlation Dimension (D2). The quantification measures employed were: Determinism (Det), Shannon entropy (Entr), Mean length of diagonal lines (Lmed), Maximum length of vertical lines (Vmax) and Transitivity (Trans). Through these statistical tests, the potential of each characteristic to discriminate the types of voice signals was evaluated. In the classification process, the neural network MLP (Multilayer Perceptron) was used, with supervised learning algorithm Graded Conjugate Gradient (SCG). There was an average accuracy of 90% in the discrimination between healthy and deviant voices. In the classification between healthy and strained voices, an average accuracy of 76% was obtained with the combined measures Trans, τ , Vmax, Lmed, Det and D2. In the detection of the roughness deviation, an average accuracy of 89% was obtained with the Lmed, Entr, Trans and D2 measures and in the distinction between healthy and breathy voices, 91.17% of accuracy was obtained with only two combined measures, Trans and τ , showing the promising character of the used technique.

On the Design of Channel Shortening Demodulators for Iterative Receivers in Linear Vector Channels

We consider designing demodulators for linear vector channels that use reduced-size trellis descriptions for the received signal. We assume an iterative receiver and use interference cancellation (IC) with soft-information provided by an outer decoder to mitigate the signal part that is not covered by a reduced-size trellis description. In order to reach a trellis description, a linear filter is applied as a front end to compress the signal structure into a small trellis. This process requires three parameters to be designed: 1) the front-end filter; 2) the feedback filter through which the IC is done; and 3) a target response which specifies the trellis. Demodulators of this form have been studied before under the name channel shortening (CS), but the interplay between CS, IC, and the trellis-search processes has not been adequately addressed in the literature. In this paper, we analyze two types of CS demodulators that are based on the Forney and Ungerboeck detection models, respectively. The parameters are jointly optimized with a generalized mutual information (GMI) function. We also introduce a third type of CS demodulator that is, in general, suboptimal, which has closed-form solutions. Furthermore, signal-to-noise ratio asymptotic properties are analyzed, and we show that the third CS demodulator asymptotically converges to the optimal CS demodulator in the sense of GMI maximization.

A new hybrid expansion function based mutual information for a multilayer neural networks optimization

Function expansion was used to expand initial features based on a non linear transformation. Many known expansion functions are found such the trigonometric, the polynomial, the Legendre polynomial, the power series, the exponential and the logarithmic transformation. This paper present a comparison between different expansion functions based on mutual information and different performance functions. We propose a new expansion process able to improve the correspondent mutual information and the final performance. The process was tested; using different benchmark databases, and shows his ability to improve results of classification problems

Сравнительный анализ методов оценки ненаправленной связанности между внутричерепными отведениями ЭЭГ коры головного мозга крыс-моделей абсансной эпилепсии

Studying coupling between brain areas from its electromagnetic activity is one of the key approaches in epilepsy research now, since epileptic activity has been considered to be a result of pathological synchronization in the brain. Often, research is conducted on animal models, because this allows to perform intracranial measurement, and to get rid of interference caused by the skull and to receive signals from deeper regions of the brain such as thalamus or hippocampus. In this study, the intracranial recordings from the frontal and parietal areas of cortex are investigated with a nonlinear correlation coefficient and a mutual information function in a sliding time window. The coupling estimates obtained were subjected for statistical analysis for significance using surrogate data. The dynamics of connectivity between the frontal cortex and the parietal cortex was shown to vary from seizure to seizure and from animal to animal. Therefore, estimates of the significant change in connectivity associated with initiation of the absense seizure, found previously based on averaging over a large number of animals and a large number of seizures for an each animal, can be a result of contribution of a relatively small number of seizures (less than a half of considered), for which the changes are significant.

Information-theoretical analysis of resting state EEG microstate sequences - non-Markovianity, non-stationarity and periodicities

We present an information-theoretical analysis of temporal dependencies in EEG microstate sequences during wakeful rest. We interpret microstate sequences as discrete stochastic processes where each state corresponds to a representative scalp potential topography. Testing low-order Markovianity of these discrete sequences directly, we find that none of the recordings fulfils the Markov property of order 0, 1 or 2. Further analyses show that the microstate transition matrix is non-stationary over time in 80% (window size 10 s), 60% (window size 20 s) and 44% (window size 40 s) of the subjects, and that transition matrices are asymmetric in 14/20 (70%) subjects. To assess temporal dependencies globally, the time-lagged mutual information function (autoinformation function) of each sequence is compared to the first-order Markov model defined by the classical transition matrix approach. The autoinformation function for the Markovian case is derived analytically and numerically. For experimental data, we find non-Markovian behaviour in the range of the main EEG frequency bands where distinct periodicities related to the subject's EEG frequency spectrum appear. In particular, the microstate clustering algorithm induces frequency doubling with respect to the EEG power spectral density while the tail of the autoinformation function asymptotically reaches the first-order Markov confidence interval for time lags above 1000 ms. In summary, our results show that resting state microstate sequences are non-Markovian processes which inherit periodicities from the underlying EEG dynamics. Our results interpolate between two diverging models of microstate dynamics, memoryless Markov models on one side, and long-range correlated models on the other: microstate sequences display more complex temporal dependencies than captured by the transition matrix approach in the range of the main EEG frequency bands, but show finite memory content in the long run.

THE IMPACT OF MATCHING FUNCTIONAL ON ATROPHY MEASUREMENT FROM GEODESIC SHOOTING IN DIFFEOMORPHISMS.

Longitudinal registration has been used to map brain atrophy and tissue loss patterns over time, in both healthy and demented subjects. However, we have not seen a thorough application of the geodesic shooting in diffeomorphisms framework for this task. The registration model is complex and several choices must be made that may significantly impact the quality of results. One of these decisions is which image matching functional should drive the registration. We investigate four matching functionals for atrophy quantification using geodesic shooting in diffeomorphisms. We check if the choice of matching functional has an impact on the correlation of atrophy scores with clinical variables. We also check the impact of matching functional choice on estimates of the N80 sample size for hypothetical clinical trials that test for slowing of brain atrophy. We find that the mutual information function, which has primarily been used for linear and multi-modal registration, achieves comparable correlation with clinical variables to other matching functionals while yielding better sample size estimates.

Assessment of several nonlinear methods in forecasting suspended sediment concentration in streams

In this paper, the use of nonlinear nearest trajectory based on phase space reconstruction along with several data-driven methods, including two types of perceptron artificial neural networks with Levenberg–Marquardt (ANN-LM) and particle swarm optimization learning algorithms (ANN-PSO), adaptive neuro-fuzzy inference system (ANFIS) and gene expression programming for forecasting suspended sediment concentration (SSC) dynamics in streamflow is studied. The nonlinearity of the series was tested using the method of surrogate data at 0.01 significance level as well as correlation exponent method. The proper time delay is calculated using the average mutual information function. Obtained results of different models are compared using root mean square error (RMSE), Pearson's correlation coefficient (PCC) and Nash–Sutcliffe efficiency with logarithmic values (Eln). Of the applied nonlinear methods, ANFIS generates a slightly better fit under whole daily SSC values (the least amount of RMSE = 10.5 mg/l), whereas ANN-PSO shows superiority based on the Eln criterion (the highest amount of Eln = 0.885). According to the non-parametric Mann–Whitney test, all data-driven models represent the same forecasted results and are significantly superior to the nearest trajectory-based model at the 99% confidence level.

Changes in corticocortical and corticohippocampal network during absence seizures in WAG/Rij rats revealed with time varying Granger causality.

Spike-and-wave discharges (SWDs) recorded in the cortical EEGs of WAG/Rij rats are the hallmark for absence epilepsy in this model. Although this type of epilepsy was long regarded as a form of primary generalized epilepsy, it is now recognized that there is an initiation zone - the perioral region of the somatosensory cortex. However, networks involved in spreading the seizure are not yet fully known. Previously, the dynamics of coupling between different layers of the perioral cortical region and between these zones and different thalamic nuclei was studied in time windows around the SWDs, using nonlinear Granger causality. The aim of the present study was to investigate, using the same method, the coupling dynamics between different regions of the cortex and between these regions and the hippocampus. Local field potentials were recorded in the frontal, parietal, and occipital cortices and in the hippocampus of 19 WAG/Rij rats. To detect changes in coupling reliably in a short time window, in order to provide a good temporal resolution, the innovative adapted time varying nonlinear Granger causality method was used. Mutual information function was calculated in addition to validate outcomes. Results of both approaches were tested for significance. The SWD initiation process was revealed as an increase in intracortical interactions starting from 3.5s before the onset of electrographic seizure. The earliest preictal increase in coupling was directed from the frontal cortex to the parietal cortex. Then, the coupling became bidirectional, followed by the involvement of the occipital cortex (1.5s before SWD onset). There was no driving from any cortical region to hippocampus, but a slight increase in coupling from hippocampus to the frontoparietal cortex was observed just before SWD onset. After SWD onset, an abrupt drop in coupling in all studied pairs was observed. In most of the pairs, the decoupling rapidly disappeared, but driving force from hippocampus and occipital cortex to the frontoparietal cortex was reduced until the SWD termination. Involvement of multiple cortical regions in SWD initiation shows the fundamental role of corticocortical feedback loops, forming coupling architecture and triggering the generalized seizure. The results add to the ultimate aim to construct a complete picture of brain interactions preceding and accompanying absence seizures in rats.

Chaos and complexity in mine grade distribution series detected by nonlinear approaches

In this article, the underlying dynamics of treating grade distribution is interpreted as a chaotic system instead of a stochastic system for a better understanding. Here, we study the behavior of grade distribution spatial series acquired at the Chadormalu mine in Bafgh city of Iran to distinguish the possible existence of low‐dimensional deterministic chaos. This work applies a variety of nonlinear techniques for detecting the chaotic nature of the grade distribution spatial series and adopts a nonlinear prediction method for predicting the future of the grade distributions. First, the delay time dimension is computed using auto mutual information function to reconstruct the strange attractors. Then, the dimensionality of the trajectories is obtained using Cao's method and, correspondingly, the correlation dimension method is adopted to quantify the embedding dimension. The low embedding dimensions achieved from these methods show the existence of low dimensional chaos in the mining data. Next, the high sensitivity to initial conditions is evaluated using the maximal Lyapunov exponent criterion. Positive Lyapunov exponents obtained demonstrate the exponential divergence of the trajectories and hence the unpredictability of the data. Afterward, the nonlinear surrogate data test is done to further verify the nonlinear structure of the grade distribution series. This analysis provides considerable evidence for the being of low‐dimensional chaotic dynamics underlying the mining spatial series. Lastly, a nonlinear prediction scheme is carried out to predict the grade distribution series. Some computer simulations are presented to illustrate the efficiency of the applied nonlinear tools. © 2016 Wiley Periodicals, Inc. Complexity 21: 355–369, 2016

Concealment of time delay signature of chaotic output in a slave semiconductor laser with chaos laser injection

An improved chaotic laser system, which has a slave semiconductor laser (SL) injected by a master SL with double optical feedback (DOF), is proposed, so that the time delay (TD) signature can be successfully concealed from both intensity and phase chaos via choosing appropriate parameters. The TD signature is investigated by employing autocorrelation function (ACF) and mutual information (MI) function. Through analyzing the influence on TD signature in the region of injection current and injection strength for the slave SL, we find that, for both intensity chaos and phase chaos, the TD signature can be easily concealed under weak injection strength. When the injection strength is strong, we can not only successfully conceal TD signature, but also improve the bandwidth of chaotic laser output by choosing the optimal detuning frequency.

Genomic signatures in viral sequences by in-frame and out-frame mutual information

In order to understand the unique biology of viruses, we use the Mutual Information Function (MIF) to characterize 792 viral sequences comprising 458 viral whole genomes. A 3-base periodicity (3-bp) was observed only in DNA-viruses whereas RNA-viruses showed irregular patterns. The correlation of MIF values at frequencies of 3-bp (in-frame) with frequencies of 4 and 5bps (out-frame), turned out to be useful to distinguish viruses according to their respective taxonomic order, and whether they pertain to any of the three different kingdoms, Eubacteria, Archaea and Eukarya. The clustering of viruses was carried out by the use of a new statistics, namely, the pair of in- and out-frame values of the MIF. The clustering thus obtained turned out to be entirely consistent with the current viral taxonomy. As a result we were able to compare in a single plot both viral and cellular genomes unlike any given phylogenetic reconstruction.

Quantitative methods in electroencephalography to access therapeutic response.

Pharmacometrics or Quantitative Pharmacology aims to quantitatively analyze the interaction between drugs and patients whose tripod: pharmacokinetics, pharmacodynamics and disease monitoring to identify variability in drug response. Being the subject of central interest in the training of pharmacists, this work was out with a view to promoting this idea on methods to access the therapeutic response of drugs with central action. This paper discusses quantitative methods (Fast Fourier Transform, Magnitude Square Coherence, Conditional Entropy, Generalised Linear semi-canonical Correlation Analysis, Statistical Parametric Network and Mutual Information Function) used to evaluate the EEG signals obtained after administration regimen of drugs, the main findings and their clinical relevance, pointing it as a contribution to construction of different pharmaceutical practice. Peter Anderer et. al in 2000 showed the effect of 20mg of buspirone in 20 healthy subjects after 1, 2, 4, 6 and 8h after oral ingestion of the drug. The areas of increased power of the theta frequency occurred mainly in the temporo-occipital - parietal region. It has been shown by Sampaio et al., 2007 that the use of bromazepam, which allows the release of GABA (gamma amino butyric acid), an inhibitory neurotransmitter of the central nervous system could theoretically promote dissociation of cortical functional areas, a decrease of functional connectivity, a decrease of cognitive functions by means of smaller coherence (electrophysiological magnitude measured from the EEG by software) values. Ahmad Khodayari-Rostamabad et al. in 2015 talk that such a measure could be a useful clinical tool potentially to assess adverse effects of opioids and hence give rise to treatment guidelines. There was the relation between changes in pain intensity and brain sources (at maximum activity locations) during remifentanil infusion despite its potent analgesic effect. The statement of mathematical and computational aspects in the use of clinical data is frequent and elucidation of these aspects we use PhysioNet https://www.physionet.org/, Clinical Database online supported by the National Institutes of Health (National Institutes of Health of United States of America/NIH-USA) for the acquisition of EEG data and the Matlab program to do the simulations with the methods and thus create opportunities greater understanding.

Using Modified Sample Entropy to Characterize Aging-Associated Microvascular Dysfunction.

Cutaneous microvascular function can be assessed by skin blood flow (SBF) response to thermal stimuli. Usually, the activities of the regulatory mechanisms are quantified by means of spectral analysis of the response. However, spectral measures are unable to characterize the nonlinear dynamics of SBF signal. Sample entropy (SampEn) is a commonly used nonlinear measure of the degree of regularity of time series. However, SampEn value depends on the relationship between the frequency of the studied dynamics and sampling rate. Hence, when time series data are oversampled, SampEn may give misleading results. We modified the definition of SampEn by including a lag between successive data points of the vectors to be compared to address the oversampled issue. The lag could be chosen as the first minimum of the auto mutual information function of the time series. We tested the performance of modified SampEn using simulated signals and SBF data in the young and old groups. The results indicated that modified SampEn yields consistent results for different sampling rates in simulated data, but SampEn cannot. Blood flow data showed a higher degree of regularity during the maximal vasodilation period as compared to the baseline in both groups and a higher degree of regularity in the older group as compared to the young group. Furthermore, our results showed that during the second peak the more regular behavior of blood flow oscillations (BFO) is mainly attributed to enhanced cardiac oscillations. This study suggests that the modified SampEn approach may be useful for assessing microvascular function.

Assessment of Nociceptive Responsiveness Levels during Sedation-Analgesia by Entropy Analysis of EEG

The level of sedation in patients undergoing medical procedures is decided to assure unconsciousness and prevent pain. The monitors of depth of anesthesia, based on the analysis of the electroencephalogram (EEG), have been progressively introduced into the daily practice to provide additional information about the state of the patient. However, the quantification of analgesia still remains an open problem. The purpose of this work was to analyze the capability of prediction of nociceptive responses based on refined multiscale entropy (RMSE) and auto mutual information function (AMIF) applied to EEG signals recorded in 378 patients scheduled to undergo ultrasonographic endoscopy under sedation-analgesia. Two observed categorical responses after the application of painful stimulation were analyzed: the evaluation of the Ramsay Sedation Scale (RSS) after nail bed compression and the presence of gag reflex (GAG) during endoscopy tube insertion. In addition, bispectrum (BIS), heart rate (HR), predicted concentrations of propofol (CeProp) and remifentanil (CeRemi) were annotated with a resolution of 1 s. Results showed that functions based on RMSE, AMIF, HR and CeRemi permitted predicting different stimulation responses during sedation better than BIS.

Impact of complexity on daily and multi-step forecasting of streamflow with chaotic, stochastic, and black-box models

Despite significant research advances achieved during the last decades, seemingly inconsistent forecasting results related to stochastic, chaotic, and black-box approaches have been reported. Herein, we attempt to address the entropy/complexity resulting from hydrological and climatological conditions. Accordingly, mutual information function, correlation dimension, averaged false nearest neighbor with E1 and E2 quantities, and complexity analysis that uses sample entropy coupled with iterative amplitude adjusted Fourier transform were employed as nonlinear deterministic identification tools. We investigated forecasting of daily streamflow for three climatologically different Swedish rivers, Helge, Ljusnan, and Kalix Rivers using self-exciting threshold autoregressive (SETAR), k-nearest neighbor (k-nn), and artificial neural networks (ANN). The results suggest that the streamflow in these rivers during the 1957–2012 period exhibited dynamics from low to high complexity. Specifically, (1) lower complexity lead to higher predictability at all lead-times and the models’ worst performances were obtained for the most complex streamflow (Ljusnan River), (2) ANN was the best model for 1-day ahead forecasting independent of complexity, (3) SETAR was the best model for 7-day ahead forecasting by means of performance indices, especially for less complexity, (4) the largest error propagation was obtained with the k-nn and ANN and thus these models should be carefully used beyond 2-day forecasting, and (5) higher number input variables except for the dominant variables made insignificant impact on forecasting performances for ANN and k-nn models.