Abstract
Time-series generated by complex systems (CS) are often characterized by phenomena such as chaoticity, fractality and memory effects, which pose difficulties in their analysis. The paper explores the dynamics of multidimensional data generated by a CS. The Dow Jones Industrial Average (DJIA) index is selected as a test-bed. The DJIA time-series is normalized and segmented into several time window vectors. These vectors are treated as objects that characterize the DJIA dynamical behavior. The objects are then compared by means of different distances to generate proper inputs to dimensionality reduction and information visualization algorithms. These computational techniques produce meaningful representations of the original dataset according to the (dis)similarities between the objects. The time is displayed as a parametric variable and the non-locality can be visualized by the corresponding evolution of points and the formation of clusters. The generated portraits reveal a complex nature, which is further analyzed in terms of the emerging patterns. The results show that the adoption of dimensionality reduction and visualization tools for processing complex data is a key modeling option with the current computational resources.
Highlights
Complex systems (CS) are composed of several autonomous entities, described by simple rules, that interact with each other and their environment
Information visualization plays a key role in time-series analysis, as it provides an insight into the data characteristics
Each segment translates into a Dow Jones Industrial Average (DJIA) dynamics exhibiting strong memory effects that are captured by the visualization technique with the adopted distance
Summary
Complex systems (CS) are composed of several autonomous entities, described by simple rules, that interact with each other and their environment. Reduction-based schemes try to preserve, in lower-dimensional representations, the information present in the original datasets. They include linear methods, such as classic multidimensional scaling (MDS) [17], principal component [18], canonical correlation [19], linear discriminant [20] and factor analysis [21], as well as nonlinear approaches, such as non-classic MDS, or Sammon’s projection [22], isomap [23], Laplacian eigenmap [24], diffusion map [25], t-distributed stochastic neighbor embedding (t-SNE) [26] and uniform manifold approximation and projection (UMAP) [27].
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