The Need for Distance Metrics in Machine Learning

In this lesson, we will explore why distance metrics are necessary in machine learning, what a distance metric is exactly, and which types of distance metrics are available. The similarity between amnesty hits can be quantified using a distance metric, and it's essential to understand the properties that a distance metric should satisfy.

The Properties of a Distance Metric

A metric is a function that satisfies three fundamental properties: the triangle inequality, symmetric property, and positivity. The triangle inequality states that the distance between two vectors is the shortest distance along any path. The symmetric property states that the distance between x and y is the same in either direction. Lastly, the distance is positive between two different vectors and in serial from a vector to itself in full dimensional space.

The Euclidean Distance

In this example, we can see how we compute the clear distance between the points P and Q by finding the length of the line segment connecting them. This concept can be generalized to high-dimensional vectors using functions such as list. We can use these functions to compute the clear and distance matrix between the rows of a data matrix.

Plotting the Computed Values

We will plot the computed values using a hid map with each digit labor. The first other examples of digit 8 are the most similar regarding this metric because the color is darker, but that does not happen for the other digits with level 8. Minkowski provided a generalization for the hidden distance, and it's named after the Minkowski distance. When P is equal to one, we call it the Manhattan distance. When P is equal to two, we have the clear on distance. And when P is equal to infinite, it is known as the Chebyshev distance.

Computing Minkowski Distance

We can compute this matrix using the dist function. This code shows how we compute the Minkowski distance of order 3. The Ramon Hutton distance computes the distance that will be traveled from one data point to another if a grid-like path is followed.

Key LD Variance: A Measure of Probability Distribution Difference

The coolbut layer divergence or key LD variance is a measure of how one probability distribution is different from a second one. It's not a strict Patrick science and does not satisfy the symmetric and triangle inequality properties. However, it does indicate that the two distributions are identical when the variance of 0. This distance metric is commonly used to optimize all variants in machine learning.

Computing KL Divergence

To compute the KL divergence, we will use the philanthropy puppets first. We load the puppets and store the last six Emnes records from a mini sample without getting the true labor. To compute the KL variance, we need to sum up the values to one, so we add one to all records to avoid gatina not a number while rescaling.

Generating the Heat Map

We get the Rosen's of its record finally. We will compute the key LD variance using the distance function and generate the corresponding heat map. As you can see, we are doing a much better job of finding the similarities between digits here. All the positions that correspond to the digit 8 are the most similar ones.

Practicing with Emily's Data Set

Now it's time to practice with Emily's data set and compute some similarity or distance matrix to identify

"WEBVTTKind: captionsLanguage: enwelcome to the second video of the course in this lesson we will learn about why we need these tasks metrics what a distance metric is exactly and which types of distance metrics are available the similarity between amnesty hits can be quantified using a distance metric a metric is a function that for any given point the output satisfies the following properties first the triangle inequality which means that the distance between two vectors is the shortest distance along any path second the symmetric property that is the distance between x and y is the same in either direction and third the distance is positive between two different vectors and in serial from a vector to itself in at full dimensional space the clear distance between two points P and Q is the length of the line segment connecting them in this example you can see how we compute the clear and distance between the points P and Q Euclidean distance can be also generalized to high dimensional vectors you can use the function list to compute the clear and distance matrix between the rows of a data matrix let's see how we compute the clear and distance of the last six digits in any sample in the object distances you can see the computed values now we will plot those values using a hid map with each digit labor the first other examples of digit 8 are the most similar regarding this metric because the color is darker but that does not happen for the other digits with level 8 minkowski provided a generalization for the hidden distance it's named for the Minkowski distance arise from the order P of the general formula that we are seeing here when P is equal to one we call it the Manhattan distance when P is equal to 2 they'll clear on distance and when P is equal to infinite it is known as the chebyshev distance in our we can compute this matrix using the dist function this code shows how we compute the Minkowski distance of the order 3 Ramon Hutton distance computes the distance that will be traveled to well from one data point to another if a grid-like path is followed the coolbut layer divergence or key LD variance is a measure of how one probability distribution is different from a second one it is not a strict Patrick science it does not satisfy the symmetric and triangle inequality properties at the variance of 0 indicates that the two distributions are identical it is a common distance metric used to optimize all variants in machine learning like in the case of TS named in the season trees for example it is called information gain to compute the KL divergence in our we are going to use the philanthropy puppets first we load the puppets and store the last 6 Emnes records from a mini sample without getting the true labor to compute the the variants or values need to sum up to one so we are going to normalize the pixel values of each bead first we add one to all records to avoid gatina not a number while rescaling then we get the Rosen's of its record finally we will compute the key LD variance using the distance function and generate the corresponding heat map as you can see we are doing a much better job of finding the similarities between digits here all the positions that correspond to the digit 8 are the most similar ones now it's time to practice with the Emily's data set and compute some similarity or distance matrix to identifywelcome to the second video of the course in this lesson we will learn about why we need these tasks metrics what a distance metric is exactly and which types of distance metrics are available the similarity between amnesty hits can be quantified using a distance metric a metric is a function that for any given point the output satisfies the following properties first the triangle inequality which means that the distance between two vectors is the shortest distance along any path second the symmetric property that is the distance between x and y is the same in either direction and third the distance is positive between two different vectors and in serial from a vector to itself in at full dimensional space the clear distance between two points P and Q is the length of the line segment connecting them in this example you can see how we compute the clear and distance between the points P and Q Euclidean distance can be also generalized to high dimensional vectors you can use the function list to compute the clear and distance matrix between the rows of a data matrix let's see how we compute the clear and distance of the last six digits in any sample in the object distances you can see the computed values now we will plot those values using a hid map with each digit labor the first other examples of digit 8 are the most similar regarding this metric because the color is darker but that does not happen for the other digits with level 8 minkowski provided a generalization for the hidden distance it's named for the Minkowski distance arise from the order P of the general formula that we are seeing here when P is equal to one we call it the Manhattan distance when P is equal to 2 they'll clear on distance and when P is equal to infinite it is known as the chebyshev distance in our we can compute this matrix using the dist function this code shows how we compute the Minkowski distance of the order 3 Ramon Hutton distance computes the distance that will be traveled to well from one data point to another if a grid-like path is followed the coolbut layer divergence or key LD variance is a measure of how one probability distribution is different from a second one it is not a strict Patrick science it does not satisfy the symmetric and triangle inequality properties at the variance of 0 indicates that the two distributions are identical it is a common distance metric used to optimize all variants in machine learning like in the case of TS named in the season trees for example it is called information gain to compute the KL divergence in our we are going to use the philanthropy puppets first we load the puppets and store the last 6 Emnes records from a mini sample without getting the true labor to compute the the variants or values need to sum up to one so we are going to normalize the pixel values of each bead first we add one to all records to avoid gatina not a number while rescaling then we get the Rosen's of its record finally we will compute the key LD variance using the distance function and generate the corresponding heat map as you can see we are doing a much better job of finding the similarities between digits here all the positions that correspond to the digit 8 are the most similar ones now it's time to practice with the Emily's data set and compute some similarity or distance matrix to identify\n"