Kernel relative principal component analysis for pattern recognition

模式识别的核相对主成分分析

• 批准号: 15500101
• 负责人: YAMASHITA Yukihiko
• 金额: $ 2.3万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15500101/
• 关键词: Pattern recognition; Kernel relative principal component analysis; Kernel sample space method; Suppressed kernel sample space method; Kernel principal component analysis; Hilbert space; Banach space; Linear functional; KRPCA; KSP; SKSP

Since the accuracy of pattern recognition is not enough, this research is done for making pattern recognition more accurate by applying the kernel method, which can realize complicated discrimination boundary with a non-linear mapping, to the relative principal component analysis, which is proposed by our research group and can extract principal components under the effect of another signal which has to be suppressed.The results of this research are as follows.1) The theorem of the kernel principal component analysis (KRPCA) was established and its closed form that can provide the solution of KRPCA with a kernel function and samples were obtained.2) A simple closed form of KRPCA for a non-singular kernel Gram matrix was provided. Then, KRPCA can be realized by computer more simply.3) By computer simulation with standard recognition problems, the advantages of KRPCA were shown.4) The kernel sample space method and the one with suppression feature that are the KRPCAs in a special case were proposed. Its closed forms were provided. Although they are restricted version of KRPCA, they achieved similar performance to KRPCA. Since their solution are very simple, the theory of additive learning for them was provided.5) The existing kernel method uses a kind of nonlinear function. By extending it, we proposed the theory of asymmetric kernel method that uses two kinds of nonlinear functions. It will be a basis for future progress of kernel method. A classifier by using it was constructed and its advantages were shown.6) For other researches, we provided a new theory of subband filter bank, showed its advantage in image coding, and researches a computer architecture for recognition and signal processing.

由于模式识别的准确性还不够，因此通过应用内核方法来使模式识别更准确，该方法可以通过非线性映射实现复杂的歧视边界，以实现相对主成分分析，这是由相对主成分分析所提出的我们的研究小组，可以在必须抑制的另一个信号的效果下提取主要成分。该研究的结果如下。1）建立了内核主成分分析（KRPCA）的定理，其封闭形式可以提供KRPCA的解决方案，并获得样品。2）提供了一种简单的krpca krpca，用于非偏线核克矩阵。然后，可以通过计算机更简单地实现KRPCA。3）通过具有标准识别问题的计算机模拟，显示了KRPCA的优势。4）内核样本空间方法和具有抑制功能的krpcas在特殊情况下是建议的。提供了封闭式的表格。尽管它们是KRPCA的受限版本，但他们的性能与KRPCA相似。由于他们的解决方案非常简单，因此为他们提供了添加学习的理论。5）现有的内核方法使用一种非线性函数。通过扩展它，我们提出了使用两种非线性函数的不对称核法理论。这将是内核方法未来进步的基础。构建了使用它的分类器，并显示了其优势。6）对于其他研究，我们提供了一个新的子带滤网理论，显示了其在图像编码方面的优势，并研究了计算机架构以识别和信号处理。

项目成果

Kernel relative component analysis for pattern recognition

模式识别的内核相关成分分析

• 发表时间: 2004
• 期刊: Structural, Syntactic and Statistical Pattern Recognition
• 作者: Y.Washizawa;K.Hikida;T.Tanaka;Y.Yamashita
• 通讯作者: Y.Yamashita

Kernel Sample Space Projection Classifier for Pattern Recognition

用于模式识别的内核样本空间投影分类器

• 发表时间: 2004
• 期刊: Proc.of 17th International Conference on Pattern Recognition 2
• 作者: Yoshikazu Washizawa;Yukihiko Yamashita
• 通讯作者: Yukihiko Yamashita

Generalized weighted rules for principal components tracking

• DOI: 10.1109/tsp.2005.843698
• 发表时间: 2005-04
• 期刊: IEEE Transactions on Signal Processing
• 影响因子: 5.4
• 作者: Toshihisa Tanaka

カーネル理論の拡張と非対称カーネルサポートベクタマシン

核理论和非对称核支持向量机的扩展

• 发表时间: 2004
• 期刊: 第7回情報論的学習理論ワークショップ
• 作者: 柳森;山下幸彦
• 通讯作者: 山下幸彦

A time-varying subband transform with projection-based reconstruction

具有基于投影的重建的时变子带变换

• 发表时间: 2003
• 期刊: IEICE Trans. Fundamentals E86-A
• 作者: T.Tanaka;T.Saito;Y.Yamashita
• 通讯作者: Y.Yamashita