Active cluster replacement algorithm as a tool to assess bifurcation early-warning signs for von Karman equations

Abstract

The paper deals with a novel algorithm used to improve identification quality of clusters generated by predictive clustering algorithm as a tool to identify states preceding to bifurcations for a system governed by von Karman equations. To construct bifurcation precursors, solutions (of the equations) observed on bifurcation paths are clustered; centers of the clusters constitute a set of bifurcation precursors. To decrease identification error rate, quality of each precursor is assessed with the employment of an additional, validation set. The paper concerns with two approaches to this procedure; the first one employs a single number to assess identification value of a cluster in order to delete those with low identification values. The second approach uses proposed knowledge extraction procedure to ascertain rules of replacement of the precursors chosen by the algorithm (active) by more efficient one. A wide-ranging simulation reveals that the best variant (provided that the Wishart clustering algorithm is utilized) is the replacement of the active cluster in conjunction local normalization of data. The optimal parameters values for both algorithms, arriving at essentially decreased identification errors.

Prediction after a Horizon of Predictability: Nonpredictable Points and Partial Multistep Prediction for Chaotic Time Series

“…Algorithms used to make a one-step-ahead prediction employ nearly all felds of data mining and machine learning, such as (i) Support vector regression and its modifcations [9] (ii) Multilayer perceptron [12] (iii) Clustering algorithms in predictive clustering [13][14][15][16] (iv) LSTM neural networks [10] (v) Voronoi diagrams [17] (vi) Ridge polynomial neural networks [18] (vii) Wavelet neural networks [19,20] (viii) Dilated convolution networks [21] Another factor of fundamental importance is a strategy that "assembles" one-step-ahead predictions into a multistep-ahead one. It involves two basic strategies of MSAP, the iterated (recursive) and direct strategies [22,23].…”

“…add η (α) L to 􏽢 S t+i (15) end if (16) end for (17) if point t + i is predictable then (18) calculate 􏽢 y t+h using corresponding algorithm (19) end if (20) end for (21) end procedure ALGORITHM 2: Te prediction procedure. 8 Complexity…”