In order to identify videos on the Internet, a robust video hashing based on key frames and Isometric Feature Mapping (ISOMAP) is proposed in this paper. In this method, key frames extraction and hash generation are two major components. During the video hashing, key frame extraction is achieved by a uniform distribution vector and video tomography analysis, while hash generation is accomplishe...

[1] It is known that the empirical orthogonal function method is unable to detect possible nonlinear structure in climate data. Here, isometric feature mapping (Isomap), as a tool for nonlinear dimensionality reduction, is applied to 1958–2001 ERA-40 sea-level pressure anomalies to study nonlinearity of the Asian summer monsoon intraseasonal variability. Using the leading two Isomap time series...

The problem of multiple surface clustering is a challenging task, particularly when the surfaces intersect. Available methods such as Isomap fail to capture the true shape of the surface near by the intersection and result in incorrect clustering. The Isomap algorithm uses shortest path between points. The main draw back of the shortest path algorithm is due to the lack of curvature constrained...

We propose a dimensionality reduction technique in this paper, named Orthogonal Isometric Projection (OIP). In contrast with Isomap, which learns the low-dimension embedding, and solves problem under the classic Multidimensional Scaling (MDS) framework, we consider an explicit linear projection by capturing the geodesic distance, which is able to handle new data straightforward, and leads to a ...

The problem of tracking an object in an image sequence involves challenges like translation, in-plane and out-of-plane rotations, scaling, variations in ambient light and occlusions. A model of an object to be tracked is built off-line by making a training set with images of the object with different poses. A dimensionality reduction technique is used to capture the variations in the training i...

The IsoMAP uses the multiple linear regression and geostatistical methods to analyze isotope data. Suppose the response variable Y (s) and the vector of independent variable x(s) are observed at a finite number of sites s1, · · · , sn. The multiple linear regression method assumes Y (s) and Y (s′) are independent but the geostatistical method assume they are not. In the following, we will first...

ISOMAP is a new nonlinear algorithm, which was recently developed in the field of data mining, to reduce the dimensionality of a data-set when a low-dimensional embedding manifold exists. In dynamical systems, when the attracting set is embedded in a lower dimensional manifold, we will show how ISOMAP can be useful to reduce the dimensionality of useful models of the system. The major problem o...

This paper considers the problem of finding a meaningful template function that represents the common pattern of a sample of curves. To address this issue, a novel algorithm based on a robust version of the isometric featuring mapping (Isomap) algorithm is developed. Assuming that the functional data lie on an intrinsically low-dimensional smooth manifold with unknown underlying structure, we p...

We describe a novel approach to anchoring symbols in the sensory data of a hybrid autonomous system. Using an autonomous mobile robot as a test platform we show how an Isomap can be used to detect and properly classify time-series of sensory data. In the past, similar approaches have used self-organizing maps (SOMs) for this purpose. Isomap can be regarded as an improved technique for generatin...