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I have seen this term "reconstruction error" in the context of PCA before. I will skim over most of the details of PCA, but I recommend you become adequately familiar with diagonalization and SVD in the context of standard linear algebra (if you are not already). One of the things that PCA provides is a transformation of the data in the form of a ...


3

The purpose of clustering is to arrange items into groups. Non-negative factorization (NNMF) does not return group labels for the entries in the original matrix. However, just like with principal component analysis (PCA), the clustering step can be performed afterwards using k-means or some other clustering technique. Hence NNMF might be a useful step, but ...


1

Suppose $X$ is mean-centered (you have subtracted the mean of each column) with the columns storing the features and the rows storing the observations. PCA is the eigendecomposition of the covariance matrix $\Sigma = \frac{1}{n-1}X^T X$. There is a deep relationship between PCA and SVD. In fact, you can use SVD to compute PCA. See: Relationship between SVD ...


1

Since a minimal sufficient statistic$$T:\mathcal X\longmapsto \mathbb R^p$$is (i) sufficient and (ii) a function of every sufficient statistic$$S:\mathcal X\longmapsto \mathbb R^q$$that is, there exists $$t:\mathbb R^p\longmapsto \mathbb R^q$$ such that$$T(x)=t(S(x))$$it is necessary that$$p\le q$$Otherwise, if $p>q$, since $T(X)$ belongs to the $q$-...


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