Euclidean distance, Hausdorff distance and SSP distance are discussed, and SSP distance is used to improve Isomap algorithm. Two methods are put forward for improving Isomap algorithm. One is aligning input data of original Isomap algorithm, the other is modifying Isomap algorithm itself. SSP distance is used to search neighbors and compose neighborhood graph, and the plot for each dimension of...

The Isomap method has demonstrated promising results in finding a low dimensional embedding from samples in the high dimensional input space. The crux of this method is to estimate geodesic distance with multidimensional scaling for dimensionality reduction. Since the Isomap method is developed based on the reconstruction principle, it may not be optimal from the classification viewpoint. We pr...

Chemical data related to illicit cocaine seizures is analyzed using linear and nonlinear dimensionality reduction methods. The goal is to find relevant features that could guide the data analysis process in chemical drug profiling, a recent field in the crime mapping community. The data has been collected using gas chromatography analysis. Several methods are tested: PCA, kernel PCA, isomap, sp...

Isometric feature mapping (Isomap) is a promising manifold learning method. However, Isomap fails to work on data which distribute on clusters in a single manifold or manifolds. Many works have been done on extending Isomap to multi-manifolds learning. In this paper, we proposed a new multi-manifolds learning algorithm (M-Isomap) with the help of a general procedure. The new algorithm preserves...

Recently, the Isomap algorithm has been proposed for learning a parameterized manifold from a set of unorganized samples from the manifold. It is based on extending the classical multidimensional scaling method for dimension reduction, replacing pairwise Euclidean distances by the geodesic distances on themanifold.A continuous version of Isomap called continuum Isomap is proposed. Manifold lear...

In this paper, a system based on the MDM-Isomap (Minimax Distance Metric-based neighborhood selection algorithm for Isomap) is proposed to improve the performance of protein subcellular localization prediction. First of all, the protein sequences are quantized into a high dimension space using an effective sequence encoding scheme. However, the problems caused by such representation are computa...

One of the most widely-used nonlinear data embedding methods is ISOMAP. Based on a manifold learning framework, ISOMAP has a parameter k or ǫ that controls how many edges a neighborhood graph has. However, a suitable parameter value is often difficult to determine because of a time-consuming optimization process based on certain criteria, which may not be clearly justified. When ISOMAP is used ...

Isomap is a well-known nonlinear dimensionality reduction method that highly suffers from computational complexity. Its complexity mainly arises two stages; a) embedding full graph on the data in ambient space, and b) complete eigenvalue decomposition. Although of graphing stage has been investigated by processing methods, decomposition remains bottleneck problem. In this paper, we propose Low-...

Recently, the Isomap algorithm has been proposed for learning a nonlinear manifold from a set of unorganized high-dimensional data points. It is based on extending the classical multidimensional scaling method for dimension reduction. In this paper, we present a continuous version of Isomap which we call continuum isomap and show that manifold learning in the continuous framework is reduced to ...