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When $i=n,$ write $\mathbb{A}$ in block matrix form $$\mathbb A = \pmatrix{A & B \\ C & D}$$ where $A$ is the $n-1 \times n-1$ matrix obtained by omitting the last row and column of $\mathbb{A},$ $B = C^\prime$ is the first $n-1$ entries in the last column, and $D = \mathbb{A}_{nn}$ is a nonzero number because $\mathbb{A}$ is an invertible ...


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There are reasons why t-sne is not used as a clustering algorithm. First, as you point out yourself, that t-sne does not generate any cluster assignments. Instead, it performs dimensionality reduction, embedding the data into a low dimensional space that is easy to visualize. You could, of course, use a standard clustering algorithm such as k-means on this ...


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This thread may be useful to statisticians and data scientists because it shows how to construct arbitrarily "nasty" functions (that nevertheless are easy to handle mathematically and computationally) for testing algorithms that rely on optimization. One way to construct functions with specified local properties (like local minima) is to assemble them from ...


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My answer is certainly NO for cryptography, and maybe YES sometimes for compression. Artificial neural nets (ANN) can't be trained to decrypt data. The reason is that the inverse problem is too stiff. Encryption In cryptography, by design, encryption transforms input X into output Y=f(X) using a very rough function f(). That's the whole idea of encryption ...


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The slides are about Perceptron algorithm not SVM (although it's quoted maybe mistakenly). First equation is about normal perceptron, and the second is about the kernel version of it. They're equivalent. However, perceptron algorithm only give you a solution, not necessarily the max-margin solution. For having max-margin solution, you need to look at the ...


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Based on your description my best guess is that you looking for a recommender system. You can model that by treating documents as "users" and tags as "items". Then you may have e.g. such a table where a certain document "likes" certain tags. document id | tags | d1 | music, bach | d2 | programming, r | d3 ...


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I have been wondering the same thing. My conclusion is that doing what you propose is valid for say establishing cluster centres but the challenge is that those change as you vary bin width. An interesting exercise is to take your data and produce a series of histograms changing (say linearly) the bin width for each histogram. As width diminishes the ...


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