It is a list of probability values that it could be a part of multiple distributions, it could be in the middle, it could be 60% likely this class and 40% likely of this class. Sometimes we want the maximum probability like: This is going to be 70% likely that it’s a part of this class but we also want the probability that it’s going to be a part of other classes. In a lot of cases we just want that hard assignment but in a lot of cases it’s better to have a soft assignment. This means that the k-means algorithm gives you a hard assignment: it either says this is going to be this data point is a part of this class or it’s a part of this class. i.e K-means calculates distance and GM calculates weights. The reason that standard deviation is added into this because in the denominator the 2 takes variation into consideration when it calculates its measurement but K means only calculates conventional Euclidean distance. It uses the same optimization strategy which is the expectation maximization algorithm. It is very similar to the k-means algorithm.
we want to maximize the likelihood that X belongs to a particular class or we want to find a class that this data point X is most likely to be part of. Now, we would like to find the maximum likelihood estimate of X (the data point we want to predict the probability) i.e. Once we have that huge continuous curve then for the given data points, it can tell us the probability that it is going to belong to a specific class. What we really want is a single continuous curve that consists of multiple bell curves. If we were to plot multiple Gaussian distributions, it would be multiple bell curves. Once we multiply the probability distribution function of d-dimension by W, the prior probability of each of our gaussians, it will give us the probability value X for a given X data point. The probability distribution function of d-dimensions Gaussian Distribution is defined as: It is a probability distribution that consists of multiple probability distributions and has Multiple Gaussians. In other words we can say that, if we have three Gaussian Distribution as GD1, GD2, GD3 having mean as µ1, µ2,µ3 and variance 1,2,3 than for a given set of data points GMM will identify the probability of each data point belonging to each of these distributions. But if there are Multiple Gaussian distributions that can represent this data, then we can build what we called a Gaussian Mixture Model. There are two peak points and the data seems to be going up and down twice or maybe three times or four times. It will look like there are multiple peaks happening here and there. It does not always have one peak, and one can notice that by looking at the data set. Sometimes our data has multiple distributions or it has multiple peaks. This is a function of a continuous random variable whose integral across an interval gives the probability that the value of the variable lies within the same interval. So, for any X value, we can calculate the probability of that X value being a part of the curve or being a part of the dataset. Y values are the probabilities for those X values. It looks like it follows a kind of bell curve the frequencies go up as the speed goes up and then it has a peak value and then it goes down again, and we can represent this using a bell curve otherwise known as a Gaussian distribution.įor a given point X, we can compute the associated Y values.
We can notice how this follows, the frequency goes up and then it goes down. Here, we can see that a cyclist reaches the speed of 1 Km/h four times, 2Km/h nine times, 3 Km/h and so on. We have a data table that lists a set of cyclist’s speeds. A distribution is a listing of outcomes of an experiment and the probability associated with each outcome. This constitutes a form of unsupervised learning.Ī Gaussian is a type of distribution, and it is a popular and mathematically convenient type of distribution. It allows the model to learn the subpopulations automatically. The advantage of Mixture models is that they do not require which subpopulation a data point belongs to. Gaussian Mixture models are used for representing Normally Distributed subpopulations within an overall population. It is also called Expectation-Maximization Clustering or EM Clustering and is based on the optimization strategy. It is a universally used model for generative unsupervised learning or clustering. Gaussian Mixture Model or Mixture of Gaussian as it is sometimes called, is not so much a model as it is a probability distribution. Why do we use the Variance-Covariance Matrix?Ĭontributed by: Gautam Solanki Introduction.
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