Fuzzy cognitive map reconstruction - dynamics vs. History

This paper proposes a fuzzy cognitive map scheme for real-time online data prediction. The fuzzy cognitive maps (FCMs) are constructed on the basis of abstracting a numerical time series into a limited number of nodes (concepts), and used as a modeling tool for predicting time series. By representing time series in terms of information granules constructed in the space of amplitude and change of amplitude of the time series, a fuzzy cognitive map is dynamically constructed by using the set of information granule, where the particle swarm optimization (PSO) is utilized to study the parameters. In order to find better weights in the global search process, each parameter of the particle swarm algorithm (PSO) is not set to a fixed value but adaptively changes. In this paper, a dynamic fuzzy C-means clustering algorithm is used to online adjust the cluster center and weight according to the impact of the incoming data at the current moment such that the model can capture real-time changes in the data information. The proposed approach is illustrated in detail by a series of experiments using a collection of publicly available data.

The problem of time series prediction based on fuzzy cognitive maps (FCMs) is unresolved. Although many methods have been proposed to cope with this issue, the performance of these methods is far from satisfactory. Traditional FCM-based predictors have three limitations. First, current feature extraction operators are incapable of learning good representations of original time series. Second, current methods use just the output of FCMs to predict the next value; they do not directly utilize the important information of the latent features. Third, current FCM-based predictors optimize each component individually, thereby leading to low prediction accuracy. For example, these methods first optimize the feature extraction operator and then learn the FCMs from the latent features; they do not simultaneously optimize the whole prediction model. In this article, we develop a framework based on a sparse autoencoder (SAE) and a high-order FCM (HFCM) to address the time series prediction problem; we refer this framework as SAE-FCM. To overcome the first limitation of current methods, an SAE is employed to extract features from original time series. Unlike current FCM-based predictors, our method combines the output of both the SAE and the HFCM to calculate the predicted value, thereby overcoming the second limitation of traditional FCM-based predictors. In an application of the idea of “fine tuning” in deep learning, the weights of SAE-FCM can be updated by the batch gradient descent method if the prediction errors are great. Thus, we can optimize SAE-FCM as a whole and overcome the third limitation. We validate the performance of SAE-FCM on ten datasets. Compared with the experimental results obtained by using state-of-the-art methods, the experimental results obtained by using SAE-FCM demonstrate the effectiveness of our method. Extensive experiments also show that SAE-FCM can effectively overcome the above limitations.

With the burgeoning of IoE (Internet of Everything), massive numbers of IoT devices in entensive fields are continuously producing huge number of time series, named as streaming time series (STS). The high dimensionality and dynamic uncertainty of STS lead to the main challenge on traditional time series data mining research. Accordingly, time series representation methods could not only reduce the original high dimensionality of streaming time series, but also contain the main temporal features of raw time series. More importantly, time series representation has been regarded as an necessary preprocessing tool to provide data support for the smooth progress of follow-up research. In this paper, we propose a novel online time series representation approach called continuous segmentation and diversified representation framework (CSDRF) for streaming time series, which contains two different types of time series representation results. The subsequent experiments have been conducted to demonstrate that CSDRF could not only provide the corresponding results to meet the diverse needs of different users, but also provide the corresponding qualified symbolic representation results for time series clustering.

Long-term prediction of time series using fuzzy cognitive maps

Validation of synthetic daily Landsat NDVI time series data generated by the improved spatial and temporal data fusion approach

Time series (TS) data are ubiquitous across various application areas, rendering time series forecasting (TSF) a fundamental task. With the astounding advances in large language models (LLMs), a variety of methods have been developed to adapt LLMs for time series forecasting. Despite unlocking the potential of LLMs in comprehending TS data, existing methods are inherently constrained by their shallow integration of TS information, wherein LLMs typically access TS representations at shallow layers, primarily at the input layer. This causes the influence of TS representations to progressively fade in deeper layers and eventually leads to ineffective adaptation between textual embeddings and TS representations. In this paper, we propose the Multi-layer Steerable Embedding Fusion (MSEF), a novel framework that enables LLMs to directly access time series patterns at all depths, thereby mitigating the progressive loss of TS information in deeper layers. Specifically, MSEF leverages off-the-shelf time series foundation models to extract semantically rich embeddings, which are fused with intermediate text representations across LLM layers via layer-specific steering vectors. These steering vectors are designed to continuously optimize the alignment between time series and textual modalities and facilitate a layer-specific adaptation mechanism that ensures efficient few-shot learning capabilities. Experimental results on seven benchmarks demonstrate significant performance improvements by MSEF compared with baselines, with an average reduction of 31.8% in terms of MSE. The code is available at https://github.com/One1sAll/MSEF.

Time series classification is one of the most active research topics in time series data mining, because it covers a broad range of applications in many different domains. Representation for time series is a technique that converts time series to feature vectors representing the characteristics of time series. The performance of classifying time series depends on this representation. Chaotic time series analyses have been well-studied. Moreover, recurrence plotting underlying chaos theory is one of the most robust representation for time series. In this study, we propose a new time series representation utilising the recurrence plot technique. Moving average convergence divergence (MACD) histogram is the acceleration of time that can represent local-variation in time series. Therefore, a recurrence plot that is made from MACD histogram, which is called a MACD-histogram-based recurrence plot (MHRP), can handle time series very well. Recurrence plots are referred to as grey-scale images and we utilise stacked auto-encoders as a classifier for MHRPs. To evaluate the performance of the proposed classifier, experiments using the UCR time series classification archive was conducted. The experimental results showed that the proposed classifier outperforms other methods.

The article analyzes consecutive phases of time series modelling with Fuzzy Cognitive Maps. The subject of interest are features determining models of good quality. First, we present the procedure: design phase, learning phase, and in the end — application. The discussion is illustrated with experiments on two synthetic time series. We have shown that the design phase determines qualitative and quantitative effectiveness of modelling. We have addressed effects of misdesigns: too large, too small or unfit at all maps on modelling quality.

Modeling time series is a well investigated area for a long period. During last years fuzzy cognitive maps have been successfully employed for this purpose. Easy interpretation of relations and dependencies in an information space raised by time series is an important aspect of latest researches, which brought time series processing from an elementary, numerical, level to a space of concepts created by a given time series. In this paper we investigate time series modeling with fuzzy cognitive maps at a concept level. Discussion is focused on constructions of fuzzy cognitive maps for a given time series which is transformed to a level of concepts. Attention is payed on objective functions, which are employed to training and quality evaluating of fuzzy cognitive maps. Several types of objective functions are proposed, discussed and tested. Objective functions studied in this paper are based on mean square error and maximal square error.

Rare earth elements price forecasting by means of transgenic time series developed with ARIMA models

Machine learning and deep learning models for time series classification generally require a large volume of data to achieve superior performance. However, due to the lack of a sufficient amount of time series in many real-world applications, particularly health care, training these models is more challenging than expected. This paper introduces the Random Frequency Butchering (RFB) method to enhance the generalization performance of classification tasks on limited time series in health care. This approach generates a number of filters with random cutoff frequencies in the frequency domain. The concatenation of time series representations from these filters stacked with the original time series is then used to train an arbitrary time series classifier. The experimental results on the standard medical time series datasets show that the RFB time series representation can significantly enhance the classification performance of the MiniRocket, Inception-Net, and ResNet classifiers.

In the era of uncertainty and chaos, the decision making is a complex process especially when it is related with the future prediction. The decision making process is fully dependent on the level of accuracy in forecasting. It is obvious that forecasting activities play a vital role in our daily life. The classical time series methods can not deal with forecasting problems in which, the values of time series are linguistic terms represented by fuzzy sets [1, 2]. Therefore, Song and Chissom [4] presented the theory of fuzzy time series to overcome the drawback of the classical time series methods. Time series prediction is a very important practical application with a diverse range of applications including economic and business planning, inventory and production control, weather forecasting, signal processing and control, Pattern matching etc. Based on the theory of fuzzy time series, Song presented some forecasting methods [4,5,6] to forecast the enrollments of the University of Alabama. Chen [8] presented a method to forecast the enrollments of the University of Alabama based on fuzzy time series. It has the advantage of reducing the calculation time and simplifying the calculation process. Hwang [10], used the differences of the enrollments to present a method to forecast the enrollments of the University of Alabama based on fuzzy time series. Huang extended Chen’s work presented in [9] and used simplified calculations with the addition of heuristic rules to forecast the enrollments. Chen [12] presented a forecasting method based on high order fuzzy time series for forecasting the enrollments of the University of Alabama. Chen [13] and Hwang presented a method based on fuzzy time series to forecast the temperature.

Multivariate time series data often have a very high dimensionality. Classifying such high dimensional data poses a challenge because a vast number of features can be extracted. Furthermore, the meaning of the normally intuitive term similar needs to be precisely defined. Representing the time series data effectively is an essential task for decision-making activities such as prediction, clustering and classification. In this paper we propose a feature-based classification approach to classify real-world multivariate time series generated by drilling rig sensors in the oil and gas industry. Our approach encompasses two main phases: representation and classification. For the representation phase, we propose a novel representation of time series which combines trend-based and value-based approximations (we abbreviate it as TVA). It produces a compact representation of the time series which consists of symbolic strings that represent the trends and the values of each variable in the series. The TVA representation improves both the accuracy and the running time of the classification process by extracting a set of informative features suitable for common classifiers. For the classification phase, we propose a memory-based classifier which takes into account the antecedent results of the classification process. The inputs of the proposed classifier are the TVA features computed from the current segment, as well as the predicted class of the previous segment. Our experimental results on real-world multivariate time series show that our approach enables highly accurate and fast classification of multivariate time series.

A large part of the information emitted by contemporary technological devices comes in the form of time series. The massive commercialization of these kinds of devices has made the study of time series feature extraction techniques acquire a vital relevance in last years. Two main things are essential when applying feature extraction techniques to time series: to reduce the dimensionality so it occupies the least amount of storage memory possible, and to make features that contain the relevant information regarding the nature of the data set and the goals to be achieved. For this purpose, we propose in this work a brand new technique called the State Changes Representation for Time Series (SCRTS), which relies on the relevant data associated with the conditional probabilities of the time series (also known in the literature as Markov model’s features), and the distribution of its values. This method is length-independent, which means that we can apply it to time series of different dimensions obtaining the same number of features for each one. Also, it provides a visual representation of the input data, so it is possible to interpret what makes a certain time series different from the other. After explaining how it works, we apply it to 3 different wearable accelerometer data sets. This algorithm reduces the original dimension of the time series considerably (in the best case from 5499 values to 31), having a good performance in the classification results (in the best chance with an accuracy of 98%).

Similarity or distance measures between two time series play an important role in analysis and retrieval of time series database, which is a fundamental problem in time series data mining. Mathematical model is widely used as a representation of time series, but few papers discuss it in similarity measure of time series. In this paper, we propose a Markov model based technique for similarity/distance measures of variable-length time sequences. State space of Markov model is partitioned by hierarchical clustering method, and the information of state-transition is used to represent a time series. The similarity/distance measures of time sequences can be defined as various functions of the difference between their state-transition information, and some widely used distance measures can be considered as our specific cases. In addition, in modeling procedure, the vector sequence in reconstructed phase space is used instead of the original time sequence, which more effectively reflects the dynamical property of time series. Experimental results show that it works well under the strong noise environment, and it is versatile for various applications by its flexible definition.