3
votes
2answers
146 views

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 ...
0
votes
1answer
84 views

vector subspaces of $(\mathbb Z/2\mathbb Z)^3$

How many possible vector subspaces of $(\mathbb Z/2\mathbb Z)^3$ are there? My idea was, to proove this as follow: $$U_b := ...
1
vote
0answers
33 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 ...
0
votes
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 ...
1
vote
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 ...
1
vote
0answers
201 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 ...
3
votes
0answers
42 views

Symmetrizing a sequence of vectors

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 ...
1
vote
3answers
727 views

Is it wrong to use Binary Vector data in Cosine Similarity?

I am doing Information Retrieval using Cosine Similarity. My data is binary vector. Since most of all reference I read is using non-binary vector (non-binary matrix) data, I am wondering if it is ...