Dimensionality Reduction(维数约简/降维)是机器学习中的一种重要手段,旨在降低数据的维数,同时保留数据的关键特征。
PCA要做的事情,就是把我们原始的数据投影到具有最大方差的方向。 其实PCA在做的就是上面例子中的,从第二个例子到第三个例子的过程。 First PC:具有最大信息量的方向 Second PC:具有第二大信息量的方法,并且它一定与第一个方向相互正交 Others 维度也和前面的维度在方向上都相互正交 接下来,我们来看看PCA是怎...
原数据降维后的新数据为XPXP,降维的数据还原为(XP)PT(XP)PT。 PCA对线性的数据的降维效果是比较好的。 kPCA (kernel PCA) A method combining PCA and kernel tricks. Non-negative Matrix Factorization, NMF like PCA, except the coeffients in the linear combination must be non-negative. It will conv...
它研究了线性技术PCA [36]和LDA [23],以及十种非线性技术:多维缩放(MDS)[15],[43],Isomap [69],[70],内核PCA [52],[63] ,扩散图[45],[53],多层自动编码器[19],[34],局部线性嵌入(LLE)[59],拉普拉斯特征图[4],Hessian LLE [20],局部切线空间分析(LTSA) [83]和本地线性协调(LLC)[68]。我们...
PCA是一种成功的降维方法,当然也可以用它来Visualize高维空间的数据。但是它也有一些局限的地方,比如有些研究称它是一种映射方法,映射后新的特征就变成了原来特征的线性组合,这样它的解释性就没有那么强。比如,你跟医生合作,如果你说线性组合,他们可能根本不关心,他们更想知道的是原来的特征。
We can picture PCA as a technique that finds the directions of maximal variance: In contrast to PCA, LDA attempts to find a feature subspace that maximizes class separability (note that LD 2 would be a very bad linear discriminant in the figure above). ...
Dimensionality reduction technique involves finding out the transformation matrix that maps from the random vector in the higher dimensional space to the lower dimensional space. This is obtained by identifying the orthonormal basis using PCA, LDA, KLDA, and ICA. In PCA, the basis vectors are ...
线性方法(PCA,ICA,LDA)--->非线性方法(LE,LLE,LPP,NPE)--->GE(SGE,SGDA,SLGDA,GDA-SS)--->张量方法(MPCA,STM,TLPP,MTLPP) 对噪声鲁棒,低秩特性被广泛用于图像和视频处理。RPCA--->LRR--->IPRCA(克服解决新样本的缺点)--->LRE LRE缺点: ...
Independent Component Analysis (ICA) is based on information theory and is one of the most widely used dimensionality reduction techniques. The major difference between PCA and ICA is that PCA looks for uncorrelated factors while ICA looks for independent factors. ...
Conceptual and empirical comparison of dimensionality reduction algorithms (PCA, KPCA, LDA, MDS, SVD, LLE, ISOMAP, LE, ICA, t-SNE) 2021, Computer Science Review Show abstract High-dimensional and large-scale anomaly detection using a linear one-class SVM with deep learning 2016, Pattern Recognit...