features on the gait classification performance by SVM classifier. Besides, we also compared the generalization performance of our proposed algorithm with those of SVM-based classification algorithm. This paper is organized as follows: Section Ⅱ presents the procedure of the gait data acquisition. In Section Ⅲ, we briefly introduce manifold learning algorithm for the gait features extraction. In section Ⅳ, we evaluate the effective of our proposed technique via experiments. Discussions and conclusions are given in the section Ⅴ. II. GAIT DATA ACQUISTION The kinetic gait data including the thirty healthy young and thirty normal elderly subjects were acquired because these gait data contain more relevant information about the intrinsic non-
linear dynamics of human movement. Each subject was asked to walk on the straight laboratory walkway of approximately 10 m at a self-determined pace. When a foot stepped on the middle of the strain gauge force platform embedded in the walkway, the foot-ground reaction forces(GRF) were recorded during walk. Here, the sampling frequency was set to 400 Hz. In order to avoid the individual difference, the acquired forces and the occurrence of their corresponding times were normalized by subjects’ weight and by gait cycle respectively. Thus, we can represent a gait pattern as 101 dimensions vector by sampling at each 1% in a time normalized stance phase. Here, the vertical GRF gait data, as shown in Fig.1, was selected to analyze. Figure.1. The foot–ground reaction forces along the vertical directions during a normalized stance phase III. MANIFOLD LEARNING ALGORITHM FOR NONLINEAR GAIT FEATURE EXTRACTION To obtain the significance low-dimensional embedding associated with the human gait function in high-dimensional input space, the manifold learning algorithm was applied to perform dimensionality reduction. Presently, there are three usual manifold embedding algorithm for dimensionality reduction: Isomap, Locally-Linear Embedding(LLE), Laplacian Eigenmaps(LE). In this study, considering the effective utilization of the global relationship between all gait variables, we selected the Isomap algorithm to perform dimensionality reduction for the actual discovery of the intrinsic nonlinear structure of the analyzed gait data. Isomap algorithm is a global geometric framework for nonlinear dimensionality reduction, and it can effectively use the measured geodesic distance and classical multidimensional scaling(MDS) technique to find the intrinsic geometry of data(i.e. the low-dimensional embedding in the highdimensional input space). In the algorithm, the geodesic manifold distances between all pairs of data points can be obtained by constructing the graph, and the geodesic distance can be estimated by finding the shortest path in the graph representation of the manifold. Here, we firstly determined the neighboring points by Euelidean distance d ( ) i j X , between the arbitrary pointsi, j in the gait data input space X , and then we can obtain the neighboring relation by selecting the k neighboring points. Thus, we can construct the weighted graph G with edges connecting neighboring point on the manifold M . Next step, we can estimate the geodesic distances d ( ) i j M , by finding the shortest paths d ( ) i j G , between all pairs of points in the constructed graph . Finally, we can use the graph distance d ( ) i j G , replace the distance in MDS, and we can find the low-dimensional embedding by minimizing the following cost function: ()() E DG DY = τ −τ (1) where τ is an operator for efficient optimization of the determined distance matrix D by converting the distances to inner products. The detailed procedure of solution for finding the low-dimensional embedding can be found in[7]. IV. EXPERIMENTS AND RESULTS After The gait nonlinear features can be obtained from gait data by using ISOMAP algorithm to perform dimensionality reduction according to its algorithm step in section 3. As a result, the nonlinear information feature of gait can be obtained easily by a simple transformation for the projected data. In this experiment, in order to evaluate the ability of the extraction of nonlinear gait features, ISOMAP and linear principal component analysis (PCA)