Spatial Big Data and Moving Objects: A Comprehensive Survey <s> 2) DIMENSION REDUCTION <s> Scientists working with large volumes of high-dimensional data, such as global climate patterns, stellar spectra, or human gene distributions, regularly confront the problem of dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. The human brain confronts the same problem in everyday perception, extracting from its high-dimensional sensory inputs—30,000 auditory nerve fibers or 106 optic nerve fibers—a manageably small number of perceptually relevant features. Here we describe an approach to solving dimensionality reduction problems that uses easily measured local metric information to learn the underlying global geometry of a data set. Unlike classical techniques such as principal component analysis (PCA) and multidimensional scaling (MDS), our approach is capable of discovering the nonlinear degrees of freedom that underlie complex natural observations, such as human handwriting or images of a face under different viewing conditions. In contrast to previous algorithms for nonlinear dimensionality reduction, ours efficiently computes a globally optimal solution, and, for an important class of data manifolds, is guaranteed to converge asymptotically to the true structure. <s> BIB001 </s> Spatial Big Data and Moving Objects: A Comprehensive Survey <s> 2) DIMENSION REDUCTION <s> We present a new methodology for sufficient dimension reduction (SDR). Our methodology derives directly from the formulation of SDR in terms of the conditional independence of the covariate $X$ from the response $Y$, given the projection of $X$ on the central subspace [cf. J. Amer. Statist. Assoc. 86 (1991) 316--342 and Regression Graphics (1998) Wiley]. We show that this conditional independence assertion can be characterized in terms of conditional covariance operators on reproducing kernel Hilbert spaces and we show how this characterization leads to an $M$-estimator for the central subspace. The resulting estimator is shown to be consistent under weak conditions; in particular, we do not have to impose linearity or ellipticity conditions of the kinds that are generally invoked for SDR methods. We also present empirical results showing that the new methodology is competitive in practice. <s> BIB002 </s> Spatial Big Data and Moving Objects: A Comprehensive Survey <s> 2) DIMENSION REDUCTION <s> Assuming that high-dimensional data are generated from intrinsic variables with lower dimensions, several key manifold-learning algorithms can help effectively analyze and visualize such data. <s> BIB003 </s> Spatial Big Data and Moving Objects: A Comprehensive Survey <s> 2) DIMENSION REDUCTION <s> We present several new variations on the theme of nonnegative matrix factorization (NMF). Considering factorizations of the form X = FGT, we focus on algorithms in which G is restricted to containing nonnegative entries, but allowing the data matrix X to have mixed signs, thus extending the applicable range of NMF methods. We also consider algorithms in which the basis vectors of F are constrained to be convex combinations of the data points. This is used for a kernel extension of NMF. We provide algorithms for computing these new factorizations and we provide supporting theoretical analysis. We also analyze the relationships between our algorithms and clustering algorithms, and consider the implications for sparseness of solutions. Finally, we present experimental results that explore the properties of these new methods. <s> BIB004
The complexity of learning problem is another issue in data analysis for moving objects. In case of V2V, the vehicle image can be considered having multiple dimensions. The increase in dimensions results in exponential increase in number of samples. There are several dimension reduction techniques proposed in BIB001 and  . An important method in this context is known as manifold learning BIB003 . The basic idea behind manifold is discovering the low dimensional manifold integrated in high dimensional Euclidean space. The initial inspiration of manifold is to obtain the nonnegative part from the data BIB004 . The other method for dimension reduction is Kernel dimension BIB002 . It uses supervised information to make decision on the dimension reduction. Such methods help to extract very useful information for moving object analysis and help to improve the performance of learningdriven tasks.