## Three similarity measures between one

As a result, those terms, concepts, and their usage went way beyond the minds of the data science beginner.

Who started to understand them for the very first time. So today we wrote this post to give more clear and very intuitive definitions for similarity. Before going to explain different similarity distance measures. Let me explain the effective key term similarity in data mining or machine learning. If the distance is small, the features are having a high degree of similarity.

Whereas a large distance will be a low degree of similarity. Similarity measure usage is more in the text related preprocessing techniquesAlso the similarity concepts used in advanced word embedding techniques. We can use these concepts in various deep learning applications. Uses the difference between the image for checking the data created with data augmentation techniques.

The similarity is subjective and is highly dependent on the domain and application. For example, two fruits are similar because of color or size or taste. The relative values of each element must be normalized, or one feature could end up dominating the distance calculation. In the machine learning world, this score in the range of [0, 1] is called the similarity score. In most cases when people say about distance, they will refer to Euclidean distance.

Euclidean distance is also known as simply distance. When data is dense or continuous, this is the best proximity measure. The Euclidean distance between two points is the length of the path connecting them. The Pythagorean theorem gives this distance between two points. Manhattan distance is a metric in which the distance between two points is calculated as the sum of the absolute differences of their Cartesian coordinates.

Suppose we have two points A and B. If we want to find the Manhattan distance between them, just we have, to sum up, the absolute x-axis and y-axis variation. This means we have to find how these two points A and B are varying in X-axis and Y-axis.

## Similarity and distance in data: Part 1

In a more mathematical way of saying Manhattan distance between two points measured along axes at right angles. The Minkowski distance is a generalized metric form of Euclidean distance and Manhattan distance. The cosine similarity metric finds the normalized dot product of the two attributes. By determining the cosine similarity, we would effectively try to find the cosine of the angle between the two objects. It is thus a judgment of orientation and not magnitude.

Whereas two vectors diametrically opposed having a similarity of -1, independent of their magnitude. Cosine similarity is particularly used in positive space, where the outcome is neatly bounded in [0,1].Part 2.

We can, of course, set other expectations, but this is the bare minimum any measure of similarity should satisfy. Because of these properties, similarity measures are often obtained by simply using the inverse of a distance metric. The more similar the objects are, the closer they are and the smaller the distance between them is. Again, if it sounds too mathematical, just take a deep breath and focus on the concepts. You should choose the appropriate one according to wether or not your data can be represented as points in a Euclidean space.

Your common two-dimensional or three-dimensional coordinate systems are examples for such spaces. Also known as city block distanceCanberra distancetaxicab metric or snake distancethis is definitely the distance measure with the coolest name s.

Since it takes the absolute distances in each dimension before we sum them up, the Manhattan distance will always be bigger or equal to the Euclidean distance, which we can imagine as the linear distance between the two points.

The maximum distance looks at the distance of two points in each dimension and selects the biggest one. This one is pretty straightforward, but we can express it as a fancy formula anyway:.

The maximum distance is equal to the biggest distance in any dimension. What would the Euclidean distance, symbolizes by the orange line, be? Amazing what can be done with a little trigonometry, right? The Cosine distance is defined by the angle between two vectors. As we know from basic linear algebra, the dot product of two vectors is defined by. If you take a look at what we expected from a similarity measure, then the cosine meets our demands rather well.

If we need to construct a distance measure from here, we can just take the inverse, as we learned before. So the cosine distance is defined as. If the vectors in question are actual real values, the cosine distance is Euclidean.

Like with the cosine distance and similarity, the Jaccard distance is defines by one minus the Jaccard similarity. To compare two objects, it looks at the elements they have in common the intersection and divides it by the number of elements the two objects have in total the union.

Written out as a formula, that definition looks like this. With this definition, the similarity is only equal to one if all elements are the same and only becomes zero if all elements are different. Perfect for a similarity measure, but the wrong way around for a distance measure. This is easily solved by defining the Jaccard distance to be. The sentences have 6 words in common and 10 unique words in total. Their Jaccard distance is 1 — 0.

A nice way to represent objects you want to compute the Jaccard similarity of is in the form of a Boolean matrixa matrix with only ones and zeroes. To compute the Jaccard similarity over the columns, all we have to do is count the rows where both objects have ones 6 and divide it by the total number of rows One way to do that is the edit distance.

You made it through all of the math and learned a lot about some ways to measure distance and similarity in your data.Many real-world applications make use of similarity measures to see how two objects are related together. We can use these measures in the applications involving Computer vision and Natural Language Processing, for example, to find and map similar documents.

One important use case here for the business would be to match resumes with the Job Description saving a considerable amount of time for the recruiter. Another important use case would be to segment different customers for marketing campaigns using the K Means Clustering algorithm which also uses similarity measures. Similarities are usually positive ranging between 0 No Similarity and 1 Complete Similarity. We will specifically discuss two important similarity metric namely euclidean and cosine along with the coding example to deal with Wikipedia articles.

Do you remember Pythagoras Theorem?? Pythagoras Theorem is used to calculate the distance between two points as indicated in the figure below. In the figure, we have two data points x1,y1 and x2,y2 and we are interested in calculating the distance or closeness between these two points. To find the distance, we need to first go horizontally from x1 to x2 and then go vertically up from y1 to y2.

This makes up a right-angled triangle. We are interested in calculating hypotenuse d which we can calculate easily using the Pythagoras theorem. This completes our euclidean distance formula for two points in two-dimensional space. Python Function to define euclidean distance. Here x and y are the two vectors. You can also use sklearn library to calculate the euclidean distance. This function is computationally more efficient. Greater the distance, lower the similarity between the two objects; Lower the distance, higher the similarity between the two objects.

To convert this distance metric into the similarity metric, we can divide the distances of objects with the max distance, and then subtract it by 1 to score the similarity between 0 and 1. We will look at the example after discussing the cosine metric.

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This is another metric to find the similarity specifically for the documents. This metric is a measure of the angle between x and y as indicated in the diagram and is used when the magnitude of the vector does not matter.

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Cosine Formula for dot Product:. Here we are interested in measuring the similarity between v and w. This dot product formula is derived from the same Law of Cosine which you have studied in your schools.

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These two vectors have low similarity explained by the value of 0. This value is close to 0 which means that the angle between x and y is close to 90 degrees. If the value would have been close to 1, then this would be very similar objects with an angle close to 0 degrees. Dividing x and y by their lengths normalizes its length to 1 making it what is known as Unit Vector. This tells that cosine similarity does not take into account the magnitude of x and y.

When we need to take into account the magnitude, euclidean might be a better option. If we already have vectors with a length of 1, cosine similarity can be easily calculated using simple dot product.In statistics and related fields, a similarity measure or similarity function is a real-valued function that quantifies the similarity between two objects.

Machine Learning - Similarity Measures

Although no single definition of a similarity measure exists, usually such measures are in some sense the inverse of distance metrics : they take on large values for similar objects and either zero or a negative value for very dissimilar objects. Cosine similarity is a commonly used similarity measure for real-valued vectors, used in among other fields information retrieval to score the similarity of documents in the vector space model.

In machine learningcommon kernel functions such as the RBF kernel can be viewed as similarity functions. In spectral clusteringa similarity, or affinity, measure is used to transform data to overcome difficulties related to lack of convexity in the shape of the data distribution. Similarity matrices are used in sequence alignment. Higher scores are given to more-similar characters, and lower or negative scores for dissimilar characters. Nucleotide similarity matrices are used to align nucleic acid sequences.

A more complicated matrix would give a higher score to transitions changes from a pyrimidine such as C or T to another pyrimidine, or from a purine such as A or G to another purine than to transversions from a pyrimidine to a purine or vice versa.

Matrices for lower similarity sequences require longer sequence alignments. Amino acid similarity matrices are more complicated, because there are 20 amino acids coded for by the genetic codeand so a larger number of possible substitutions. Therefore, the similarity matrix for amino acids contains entries although it is usually symmetric. The first approach scored all amino acid changes equally.

A later refinement was to determine amino acid similarities based on how many base changes were required to change a codon to code for that amino acid. This model is better, but it doesn't take into account the selective pressure of amino acid changes. Better models took into account the chemical properties of amino acids. One approach has been to empirically generate the similarity matrices. The Dayhoff method used phylogenetic trees and sequences taken from species on the tree.

This approach has given rise to the PAM series of matrices. PAM matrices are labelled based on how many nucleotide changes have occurred, per amino acids. From Wikipedia, the free encyclopedia. For the linear algebra concept, see Matrix similarity.Great Open Access tutorials cost money to produce. Join the growing number of people supporting The Programming Historian so we can continue to share knowledge free of charge.

The first question many researchers want to ask after collecting data is how similar one data sample—a text, a person, an event—is to another. Non-computational assessments of similarity and difference form the basis of a lot of critical activity. And conversely, knowing that a certain text is very different from others in an established genre might open up productive new avenues for criticism. Statistical measures of similarity allow scholars to think computationally about how alike or different their objects of study may be, and these measures are the building blocks of many other clustering and classification techniques.

In text analysis, the similarity of two texts can be assessed in its most basic form by representing each text as a series of word counts and calculating distance using those word counts as features.

In this lesson, you will learn when to use one measure over another and how to calculate these distances using the SciPy library in Python. Though this lesson is primarily geared toward understanding the underlying principles of these calculations, it does assume some familiarity with the Python programming language.

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Code for this tutorial is written in Python3. For the text processing tasks, you will also use scikit-learn v0. You will need to install Python3 as well as the SciPy, Pandas, and scikit-learn libraries, which are all available through the Anaconda Distribution. For more information about installing Anaconda, see their full documentation. You can run our three common distance measures on almost any data set that uses numerical features to describe specific data samples more on that in a moment.

For the purposes of this tutorial, you will use a selection of texts, all published infrom the EarlyPrint project. Begin by downloading the zipped set of text files. Similarity is a large umbrella term that covers a wide range of scores and measures for assessing the differences among various kinds of data.

In fact, similarity refers to much more than one could cover in a single tutorial. The class of similarity covered in this lesson takes the word-based features of a set of documents and measures the similarity among documents based on their distance from one another in Cartesian space. Specifically, this method determines differences between texts from their word counts. Measuring distance or similarity first requires understanding your objects of study as samples and the parts of those objects you are measuring as features.

For text analysis, samples are usually texts, but these are abstract categories. Samples and features can be anything. A sample could be a bird species, for example, and a measured feature of that sample could be average wingspan.

The mathematical principles will work regardless of the number of features and samples you are dealing with. You can label your two texts austen and wharton.

In Python, they would look like the following:.Try to approach each game as a blank slate taking advantage of huge overreactions in the market.

A common mistake from first time NFL bettors is to not factor in the difference between numbers like 2. Successful Field Goals are a huge factor in Point Spread betting. Always be aware that the difference between those records often comes down to one or two great or terrible plays in each game, a bad refereeing decision or just old-fashioned good or bad luck. In any season there will be a couple of exceptional teams and a couple of completely hopeless ones.

The rest will be separated by very fine margins. Teams play only 16 regular season games.

### Five most popular similarity measures implementation in python

Compare that with Premier League football at 38, or Major League Baseball at 162. This means the handicap line (spread) is so important when placing bets. A lot of people will miss -2.

Be sure to browse the NFL markets on Matchbook and check out the alternative point spreads. Led by the irrepressible Tom Brady the Patriots are almost always a well backed Favourite. One trend I do believe in is backing big underdogs in divisional games, where the familiarity between the two teams helps coaches to game plan and nullify talent disparity. Todd Furhman: Like any sport set aside money you can afford to lose. Spend some time familiarizing yourself with US geography and the teams before you take big swings in the market.

I personally went through a three year learning curve when I started studying the EPL and the NFL, aside from no relegation, offers similar challenges to new bettors. Nick Goff: Learn the Quarterbacks and gradually develop opinions on all 32 of them.

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I remember going an entire season betting on JaMarcus Russell when there was an ongoing discussion as to whether his throwing motion was the worst in the history of the game. This is actually the greatest angle in the history of NFL betting. Tony Dungy is an idiot. He usually tips up games on ESPN. The more he likes a team, the more you should bet the other way. While you should be very wary of any long-term trends in NFL betting there are some reliable signals you can follow to find some decent value bets and our panel have a few to get you going.

Although Nick Goff offers a word of caution. Brad Allen: LA Chargers QB Philip Rivers is one to back as a dog: His record against the spread as of October last year: Underdog: 41-24 (63.

Brad Allen loves to back the Chargers and their QB Philip Rivers as underdogs. The main point appears to be look to the skies, in more ways than one. Travel and time zone factors are also a huge consideration. For exampleif the 49ers are playing a 1pm game in the Eastern Time Zone, their bodies are on a 9am time clock and this is generally worth about 2pts to the home team. Brad Allen: I like the weather angles.

Wind is a big one that is underrated by the market. Per a 2014 study, wind speeds of 10 mph are estimated to reduce quarterback ratings by 1. According to Pinnacle research, in the 50 games in recent years when average wind speed was 20 mph or greater, the average total was 38.

Wind makes passing the ball so much harder and therefore sends points totals lower, whereas snow actually slows down defensive players as much as offensive ones and sometimes markets overreact.Neva, Canada Scenic Fjords of Norway, June 2014 The location of hotels so close to trains was excellent.

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