Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
SIAM Journal on Scientific Computing
Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements
Journal of Mathematical Imaging and Vision
Impartial trimmed k-means for functional data
Computational Statistics & Data Analysis
Functional Clustering and Functional Principal Points
KES '07 Knowledge-Based Intelligent Information and Engineering Systems and the XVII Italian Workshop on Neural Networks on Proceedings of the 11th International Conference
k-mean alignment for curve clustering
Computational Statistics & Data Analysis
Non parametric estimation of the structural expectation of a stochastic increasing function
Statistics and Computing
Semiparametric Curve Alignment and Shift Density Estimation for Biological Data
IEEE Transactions on Signal Processing
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The problem of finding a template function that represents the common pattern of a sample of curves is considered. To address this issue, a novel algorithm based on a robust version of the isometric featuring mapping (Isomap) algorithm is developed. When the functional data lie on an unknown intrinsically low-dimensional smooth manifold, the corresponding empirical Frechet median function is chosen as an intrinsic estimator of the template function. However, since the geodesic distance is unknown, it has to be estimated. For this, a version of the Isomap procedure is proposed, which has the advantage of being parameter free and easy to use. The feature estimated with this method appears to be a good pattern for the data, capturing the inner geometry of the curves. Comparisons with other methods, with both simulated and real datasets, are provided.