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کاربرد نگاشت با حفظ تنکی در شناسایی چهره
Introduction to DRs
روش های کاهش ابعاد یا DRs یک راه حل اصلی برای انجام عملیات پردازشی بر روی داده هایی که دارای ابعاد بالایی هستند (از جمله تصاویر چهره) می باشند. روش های زیادی برای کاهش ابعاد تا به حال معرفی شده اند که از بین آنها می توان به روش LPP و روش NPE اشاره کرد.
یکی از این روش ها روش SPP است. در این روش با کمک ذخیره رابطه بین داده ها و نمایش تنک آنها می توان علاوه بر کاهش ابعاد که به دنبال آن پیچیدگی محاسباتی نیز کاهش می یابد، اطلاعات جداکننده گروه ها بدون هیچ برچسبی نیز حفظ شود. یکی از ویژگی های ممتاز در این روش، مقاوم بودن آن در برابر چرخش ، تغییر مقیاس و تبدیل داده است.
DRs methods
The supervised DRs
Linear Discriminant Analysis(LDA)
Marginal Fisher Analysis(MFA)
Maximum Margin Criterion(MMC)
The unsupervised DRs
Principal Component Analysis(PCA)
Locality Preserving Projections(LPP)
The semi-supervised DRs
Semi-supervised Dimensionality Reduction(SSDR)
Semi-supervised Discriminant Analysis(SDA)
In this paper, we only focus on unsupervised scenario
Manifold Learning
In the unsupervised DRs, PCA seems to be the most popular one.
PCA may fail to discover essential data structures that are nonlinear. Although the kernel-based techniques such as KPCA can implicitly deal with nonlinear DR problems.How to select kernel and assign optimal kernel parameter is generally difficult and unsolved fully in many practical applications.
Some desirable virtues the traditional PCA possesses are not inherited. 1) a research has shown that nonlinear techniques perform well on some artificial data sets, but do not necessarily outperform the traditional PCA for real-world tasks yet
2) it is generally difficult to select suitable values for the hyper-parameters (e.g., the neighborhood size) in such models. One effective approach to overcome the above limitations is approximating the nonlinear DRs using linear ones.
Characteristics of SPP
SPP shares some advantages of both LPP and many other linear DRs. For example, it is linear and defined everywhere, thus the “out-of-sample” problem is naturally solved. In addition, the weight matrix is kept sparse like in most locality preserving algorithms, which is beneficial to computational tractability.
SPP does not have to encounter model parameters such as the neighborhood size and heat kernel width incurred in LPP and NPE, etc, which are generally difficult to set in practice. Although cross-validation technique can be used in these cases, it is very time-consuming and tends to waste the limited training data. In contrast, SPP does not need to deal with such parameters, which makes it very simple to use in practice.
Although SPP belongs to global methods in nature, it owns some local properties due to the sparse representation procedure.
This technique proposed here can be easily extended to supervised and semi-supervised scenarios based on the existing dimensionality reduction framework.
PCA
LPP
NPE