A low rank approximation $\hat{X}$ of $X$ can be decomposed into a matrix square root as $G=U_{r}\lambda_{r}^\frac{1}{2}$ where the eigen decomposition of $X$ is $U\lambda U^T$, thereby reducing the ...

Spectral coherence, if used correctly would do it. Coherence is computed at each frequency-and hence is a vector. Hence, a sum of a weighted coherence would be a good measure. You would typically want ...

There you go- Gibbs Sampler: The burning period is to reach some stationarity in the samples burning_period=5000 iterations=1000 y=matrix(nrow=(burning_period+iterations),ncol=3) a=matrix(nrow=...

Use Laplacian Eigenmaps, Locally Linear Embedding or Local Tangent Space Alignment. These methods map the distances in a low-dimensional space non-linearly, thereby preserving the local neighborhood/ ...

Apply a lag operator on one time series, with the other fixed, and calculate the coherence of the cross-spectrum achieved against each lag. Find the lag that gives you the maximum coherence and ...

The following are the issues that I summarize succinctly in sequence, as each of them are an interesting problem in itself and then follow it up with my solutions: i) How to unlag two time-series so ...

You need to do the sum of the absolute value of eigen values i.e, sum(abs(Eg$values)) and compare it with the sum of the singular values. They would be equal. The reason is that if you multiply the ... View answer 4 votes Nystrom Approximation based large scale SVD and Column sampling based SVD are used in this scenario. Check out sections 3.1, 3.2 and 3.3 in "Large-Scale Manifold Learning" by Ameet Talwalkar, Sanjiv ... View answer 4 votes Comparison: "Metric MDS gives the SAME result as PCA"- procedurally- when we look at the way SVD is used to obtain the optimum. But, the preserved high-dimensional criteria is different. PCA uses a ... View answer 3 votes In an RKHS framework, any function$f(\cdot)$can be minimized with a hilbert-norm minimizing solution, just by a linear combination of the kernels evaluated at the rest of the data points and$x$... View answer Accepted answer 3 votes A specific case, where the p-values are generated from$\chi ^2$tests over frequency tables were used as similarities and multidimensional scaling was applied in this paper: http://www.biomedcentral.... View answer 3 votes See Matthias Scholz's site for the MATLAB code (the homepage includes references). View answer 3 votes The autocorrelation function(acf) of a random white noise signal will have an inpulse at zero, and the acf will be zero at other times meaning there is no periodicity or correlation at time lags. The ... View answer 2 votes You can use the DCOR function in the 'energy' package to compute a measure of non-linear dependency called distance correlation and plot as above. The issue with Pearson's correlation is that it can ... View answer 2 votes This problem is called Distance Metric Learning. Every distance metric can be represented as$\sqrt{(x-y)^tA(x-y)}$where$A$is positive semi-definite. Methods under this sub-area, learn the optimal ... View answer 2 votes Yes-dependent on where the optimal cross-validated value of$\lambda$lies-which is dependent on the true joint distribution that generates the features and the response (interpret as problem ... View answer 2 votes You should be estimating the optimal value of mtry and sampsize by minimizing the out of sample "cross-validated error" over a grid of different mtry, sampsize parameters, for any corresponding ... View answer 2 votes Distance covariance and distance Correlation do not satisfy the triangular inequality. Pearson's correlation itself on centered data or otherwise, does not satisfy the inequality, and hence is known ... View answer 2 votes Cross correlation is used in time-frequency analysis and is a inner product with a lag-parameter obtained between two functions varying over time, where one function is evaluated at time$t$and the ... View answer 1 votes You may try the method of target estimation to reduce bias, if you have the expectation function estimated either computationally or through closed form expressions or closed form von-mises expansion ... View answer 1 votes A sample from a k-determinantal point process models a distribution over subsets that encourages diversity, such that similar items are less likely to occur together in the sample. Refer to K-... View answer 1 votes Plackett-Luce ranking models deal with this problem and are a likelihood based technique where the likelihood is maximized using a majorization-maximization routine, which is similar to Expectation ... View answer Accepted answer 1 votes I have understood this far- recently-looking for the difference between$\mathbb{E}[ \max_j \sum_{j=1}^T x_j(t) - G_A(T) ]$and$\max_j \mathbb{E}[ \sum_{j=1}^T x_j(t) - G_A(T) ]$obviously, the ... View answer 1 votes Unlike PCA- Laplacian eigenmaps uses the generalized eigen vectors corresponding to the smallest eigenvalues. It skips the eigen vector with the smallest eigen value (could be zero), and uses the ... View answer 1 votes This is exactly the focus of active learning. Do watch this video by Sanjoy Dasgupta, John Langford: http://videolectures.net/icml09_dasgupta_langford_actl/ to understand the framework. In a way, it ... View answer 1 votes "Exponential Random Graph Models" - precisely deal with the first case in your question. View answer 1 votes Have you tried a correction- by adding a small$\epsilon\$ perturbation to the diagonal of the matrix you are trying to invert. This is a standard processing routine used to defer the singularity issue ...