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Use Algorithm 1 from this paper. The rest of paper is more about the analysis of algorithm and theoretical background which is very nice but not necessary for your purpose. Implementation of the algorithm in Python or R is pretty straightforward. Hope it helps :)

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I don't have a full answer to your question, but I wanted to help (and would love to know a complete answer). In a simpler case when you have one source $m=i=1$, it seems to me you are describing a scenario that resembles a hidden Markov model which uses a EM algorithm-based solution (Baum–Welch algorithm) – that is if you make the further hypothesis that a ...

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You're right and you're wrong. The objective/loss function of K-Means algorithm is to minimize the sum of squared distances Yes, absolutely. written in a math form, it looks like this: $$J(X,Z) = min\ \sum_{z\in Clusters}\sum_{x \in data}||x-z||^2$$ Err... sort of. This is definitely the most popular formulation of kmeans, but a more appropriate ...

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Not all the parameters (e.g., the assignment parameters) for a Gaussian mixture model are smoothly differentiable, thus can not be fit with gradient descent. Other use cases for the expectation–maximization (EM) algorithm are: Clustering Latent variable estimation Missing data estimation

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At the beginning of the algorithm, you are taking an initial guess for the relevant parameters. Then in each iteration, in the E-step you are computing the responsibilities for all the given datapoints and in the M-step you are computing the weighted means and variances. Since you are clustering the datapoints there is not training or test set. You just ...

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1. The simplest and most common way is to use AIC or BIC. You would pick a model with the minimum AIC/BIC value. AIC/BIC work well here because you have a likelihood function. Bayesian model selection is another possibility. It's more advances than AIC or BIC, but you get chance to add your own prior distribution. Section 5.3 in Machine Learning - A ...

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You are right that $p(e)$ is the probability of the English sentence. Estimating the probability of a sentence is achieved by a language model. This kind of machine translation model is known as the noisy channel model. The noisy channel model says that given a french sentence $f$, its best English translation is $$e^* = \arg\max_{e\in E} p(e)p(f|e)$$ In ...

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Convert your key-Value Table to a table in wide format (1 row per person) , then calculate the distance matrix using the Jaccard Distance (which can convert categorical values into numeric values) library(dummies) dummy_dat <- dummy.data.frame(my_data) jaccard_dist <- dist(dummy_dat, method = "binary") # Distance Matrix jaccard_dist

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Yes, the mean is crucial. If you just plug in another distance function instead of the sum-of-squares, the algorithm may fail to converge (and will not find a local optimum). The k-means algorithm relies on both steps (reassignment and mean recomputation) to optimize the same function. If they optimize different functions, you can get an infinite loop on ...

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