Dimension reduction is one of the most important research directions in the fields of machine learning. Especially in recent years, `high dimensional and large volume data is generated in an uncontrolled manner.The study of dimension reduction once again becomes the focus of attention. We have to face curse of dimensionality which has challenged the pattern recognition and data analysis on high-dimensional data. At the same time,the blessings of dimensionality shows that the abundance information of the high-dimensional data set means the new feasibility. How to express the high-dimensional data in the low-dimensional space and discover the intrinsic structure is the pivotal problem of high-dimensional information processing.Thereinto,dimensional reduction as the availability method to overcome the curses of dimensionality has arouse the broad notice. The correlative research is in the ascendant. Two different paradigms in machine learning: global learning and local learning. Global learning focuses on describing a phenomenon or modeling data in a global way. On the other hand , local learning does not intend to summarize a phenomenon, but builds learning systems by concentrating on some local parts of data. According to the different characteristics of local learning, local learning algorithms are divided into three types. Robustness in statistical inference means that when the real data depart from an assumed sample distribution, there will be little perturbation in the results of the algorithm and remarkable prediction performance of the algorithm. The research methods of statistical robustness are introduced into dimensional reduction. neighborhood weighted estimation algorithm, which is a kind of local learning, can converge to Bayes optimal estimation in the case of large amounts of samples. At the same time, nearest neighbor estimation algorithm is a kind of robust algorithm under the converge condition. In addition, their experimental results on synthetic and real-world data sets are also given. The generalization performance of this algorithm can be guaranteed when the model is affected by some outliers. In boosting algorithm complex natural model is approximated by the linear combination of weak learners. Due to its excellent interpretability and prediction power, boosting has become an intensive focus among computer science field. However, it is only considered as an optimizing procedure with a specific loss function. In essence, a statistic...
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