# Tagged Questions

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### Relationship between the singular value decomposition (SVD) and the principal component analysis (PCA). A radical result(?)

I was wondering if I could get a mathematical description of the relationship between the singular value decomposition (SVD) and the principal component analysis (PCA). To be more specific I have ...
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How many possible vector subspaces of $(\mathbb Z/2\mathbb Z)^3$ are there? My idea was, to proove this as follow: $$U_b := ... 0answers 34 views ### Predict binary occupancy vector from history of vectors I have a set of binary vectors where each vector represents one day of occupancy in a house and consists of 48 elements (each element for 30 minutes of the day). Each element can be 1 meaning that ... 1answer 37 views ### Vector similarity for prediction I have vectors of same length consisting of 1 and 0. I am trying to find out how similar they are. So far I am using hamming distance that I calculate sum of one vector then sum of second vector and ... 2answers 1k views ### Expected value of the inner product of two random vectors X=[x_1, x_2,...x_n] Y = [y_1, y_2,...y_n] If x_i, y_i are both random variables with P(x=1) = .5  P(x=2) = .5  P(y=1)=.5 P(y=2)=.5 How would I find the expected value of the inner ... 0answers 203 views ### Gradient Descent for Primal Kernel SVM with Soft-Margin(Hinge) Loss Given the primal objective$$F({\bf a})=L\sum_{i,j}a_{i}a_{j}k(x_i,x_j) + \sum_{i}max(0, 1-y_i \sum_{j}a_jk(x_i,x_j) for the soft margin SVM, where ${\bf a}=(a_1,...,a_N)$, N being the number of ...
Given a finite set of real numbers $X_1, \ldots, X_n$, we can compute the first $n$ power sums of these numbers. From the power sums, the set $\{X_1, \ldots, X_n\}$ can be recovered. Essentially we ...