Gait and Posture 13 (2001) 49–66 Review A review of analytical techniques for gait data. Part 1: fuzzy, statistical and fractal methods Tom Chau a,b, * a Blooriew MacMillan Centre, 350 Rumsey Road, Toronto, Ontario, Canada M4G 1R8 b Institute of Biomaterials and Biomedical Engineering, Uniersity of Toronto, Toronto, Ontario, Canada Received 7 May 2000; received in revised form 26 June 2000; accepted 16 October 2000 Abstract In recent years, several new approaches to gait data analysis have been explored, including fuzzy systems, multivariate statistical techniques and fractal dynamics. Through a critical survey of recent gait studies, this paper reviews the potential of these methods to strengthen the gait laboratory’s analytical arsenal. It is found that time-honoured multivariate statistical methods are the most widely applied and understood. Although initially promising, fuzzy and fractal analyses of gait data remain largely unknown and their full potential is yet to be realized. The trend towards fusing multiple techniques in a given analysis means that additional research into the application of these two methods will benefit gait data analysis. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Multivariate analysis; Automatic data processing; Fuzzy clustering; Fractals; Gait analysis www.elsevier.com/locate/gaitpost 1. Introduction The analysis of quantitative gait data has tradition- ally been a challenging endeavour. From a technical standpoint, the main challenges can be summarized as follows. High -dimensionality. A gait data set may consist of kinematic, kinetic, electromyographic (EMG), metabolic and anthropometric variables. In addition to measured quantities, the use of inverse dynamics yields additionally derived parameters such as joint angles, velocities, moments and powers. The need for data reduction is critical. Due to the curse of dimensionality [1], typical statistical analysis methods such as density estimation become intractable beyond five variables [2]. Further, human visual interpretation is limited to three- dimensions. In terms of data reduction, there are few guiding rules for determining which variables actually contain useful information within a particular clinical context. Further, traditional reduction methods such as factor analysis naively assume linear relationships among gait variables. New, standardized presentation methods are needed to better summarize massive gait time series [3] and to allow quantitative identification of important correlations [4]. Temporal dependence. Data collected during walking at a self-selected pace has a quasi-periodic temporal dependence. The resulting gait time series is difficult to model, as the traditional assumption of stationarity does not hold [5]. For the sake of computational feasi- bility, the temporal curves are usually parameterized, for example with peak amplitude, time-to-peak, mean value or value at the occurrence of a gait event such as heel-strike. In so doing, explicit time dependence is discarded, possibly along with potentially valuable time-dependent patterns. Moreover, gait parameters defined on the basis of able-bodied gait signals can be difficult to extract from pathological gait signals [6]. High ariability. Gait recordings exhibit intrasubject, intersubject, within-trial and between-trial variabilities as well as variability due to marker alignment and instrumentation. Several recent studies have attempted * Tel.: +1-416-4256220, ext. 3515; fax: +1-416-4251634. E-mail address: ttkchau@ieee.org (T. Chau). 0966-6362/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII:S0966-6362(00)00094-1