what is algorithm

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What is Algorithm
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Definition

• An algorithm is a collection of instructions for
  performing a specific computation or operation.
  Algorithms originated in mathematics the word
  algorithm. It comes from the Arabic writer
  Muhammad ibn Ms al-Khwrizm. An algorithm is a
  simple, unambiguous definition of what needs to
  be done. An algorithm generates a specific set of
  results. It could return the greater of the two
  numbers, an all-uppercase version of a phrase, or
  a sorted list of numbers. An algorithm is
  guaranteed to finish and generate a result after
  a finite amount of time. If an algorithm could
  run indefinitely, it would be useless because you
  would never get a response. 

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Examples

• There are a few algorithms that appear over and
  over again. Well look at three of the most
  popular in this tutorial searching, sorting and
  adding to/removing from a linked list.
  Understanding these three examples will help us
  lay a stable basis on which we can confidently
  tackle potential algorithm problems!

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Binary search

• Binary search is a simple search algorithm that
  takes a sorted array as input and returns the
  index of the value were looking for. We
  accomplish this by taking the following
  stepsFind the sorted arrays midpoint.
• Compare the midpoint to the interest rate.
• Perform a binary check on the right half of the
  array if the midpoint is greater than the value.
• Perform a binary check on the left half of the
  array if the midpoint is less than the value.
• Repeat these steps until the midpoint value
  equals the value of interest or until we know the
  value isnt in the array.
• The time complexity of the binary search is
  O(logn). We know this because we only need one
  more iteration of our algorithm to get to our
  final answer if we double our input array size.
  This is why binary search is such an essential
  computer science algorithm.

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Merge Sort

• To sort arrays efficiently, merge sort uses a
  similar divide and conquer technique. To see
  how merge sort is implemented, follow the steps
  below.Return true if the array has only one
  element and is already sorted.
• Divide the list into halves until it can no
  longer be divided.
• Until we have our original sorted array, combine
  smaller arrays in sorted order.
• Two methods will be specified to implement merge
  sort. One will deal with breaking up the array,
  while the other will deal with combining two
  unsorted arrays into a single sorted array.
  Recursively, we call the dividing-up method
  (merge sort) until our array has only one
  element. After that, we combine them again and
  return our sorted list. Merge Sort has an
  O(nlogn) time complexity, which is the highest
  time complexity possible for a sorting algorithm. 

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Adding and Removing From a Linked List

• The linked list is a basic data structure in
  computer science that is especially useful for
  its constant-time insertion and deletion. We can
  perform certain processes much more quickly with
  nodes and pointers than we could with an array. A
  linked list consists of nodes, each containing
  data and a pointer to the next node. We can
  remove items from the center of a set with a
  linked list instead of moving the remainder of
  the data structure in memory, as we would with an
  array. We will achieve optimum productivity by
  selecting the right data structure for our needs!

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Use of algorithm

• Algorithms have the ability to save lives, make
  things smoother, and bring order to chaos.
  However, experts are concerned that they may
  place too much power in the hands of companies
  and governments, perpetuating prejudice, creating
  filter bubbles, limiting options, innovation, and
  serendipity, and possibly leading to increased
  unemployment. The overall effect of ubiquitous
  algorithms is currently incalculable. All of our
  extended thinking systems (algorithms power the
  software and communication that allow extended
  thinking systems) necessitate more thinking, not
  less, and a broader perspective than we have
  previously been able to achieve. Expanding data
  collection and analysis and the application of
  that data will cure illnesses, alleviate poverty,
  provide timely solutions to people and places in
  need, and dispel decades of bias and mistaken
  assumptions.

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Maths behind algorithms

• Machine learning algorithms are built so that
  they learn from their mistakes and enhance their
  performance as they consume more data. Every
  algorithm learns and predicts data in its own
  unique way. The workings of several machine
  learning algorithms and some of the mathematical
  equations used in such algorithms aid learning.

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Linear Regression

• By fitting the best line on the data points,
  linear regression is used to predict a continuous
  variables outcome. A relationship between the
  dependent and independent variables is described
  by the best-fitted line (s). The algorithm seeks
  out the best-fitting line for predicting the
  target variables value. The best-fit line is
  found by minimizing the number of squared
  differences between the data points and the
  regression line. Equation Y c m1X1 m2X2
  .. mnXn
• Y ? Dependent Variable or Target Variable
• m ? Slope
• c ? Intercept
• X ? Independent Variables

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Logistic Regression

• The classification algorithm logistic regression
  is used to predict a categorical variable based
  on the independent variables. It fits the data to
  a logistic function to estimate the likelihood of
  an occurrence occurring. Maximizing the
  probability function optimizes the coefficients
  of the independent variables in the logistic
  function. The cost function is minimized by
  optimizing a decision boundary. Gradient Descent
  may be used to reduce the cost function. (THE
  EQUATION COULD NOT BE WRITTEN)

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Naive Bayes

• The Bayes Theorem is the basis for the Naive
  Bayes classification algorithm. This algorithm
  assumes that the independent variables have no
  association. i.e., the existence of one feature
  in a class does not imply the presence of another
  feature in that class. We make a frequency table
  for all predictors against the groups (distinct
  values of the target variable) and measure their
  probability. The posterior likelihood for each
  class is determined using the Naive Bayes
  equation. The class with the highest probability
  of all the class probabilities would be the Naive
  Bayes Classifiers product. (THE EQUATION COULD
  NOT BE WRITTEN)

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Decision Trees

• Decision Trees are typically used to solve
  classification problems, but they can also solve
  regression problems. We divide the dataset into
  two or more homogeneous sets using this algorithm
  based on the attribute that divides the dataset
  the most effectively. Calculating Entropy and
  Information Gain is one approach for selecting
  the attribute that will break the dataset. The
  sum of impurity in the variable is captured by
  entropy. The Information Gain is equal to the
  parent nodes entropy minus the number of the
  child nodes entropies. For splitting, the
  attribute with the highest Information Gain is
  chosen. We may also break the dataset using the
  Gini Index as an impurity criterion. (THE
  EQUATION COULD NOT BE WRITTEN)

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Random Forests

• Random Forests are made up of many Decision Trees
  that work together to form an ensemble. An
  Ensemble, rather than a single model, is a set of
  models used to predict the result. Each decision
  tree predicts a class outcome in random forests,
  and the class outcome with the most votes becomes
  the prediction of random forests. The Decision
  Trees should be least associated with each other
  for accurate predictions.

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k-NN (k Nearest Neighbors)

• This algorithm is applied to both regression and
  classification problems. By calculating its
  distance from all data points, the algorithm
  finds the k nearest neighbors of data points.
  Among the k neighbors, the data point is assigned
  to the class with the most points (voting
  process). It calculates the mean of the k closest
  neighbors in the case of Regression.

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K-Means

• K-Means is an unsupervised learning algorithm
  used to build data clusters. The clusters should
  be constructed so that the data points within
  each cluster are as close as possible while the
  clusters themselves are as distinct as possible.
  It chooses K positions at random, each of which
  serves as the clusters centroid. The data points
  are allocated to the clusters that are closest to
  them. After the data points have been allocated,
  each clusters centroid is calculated, and the
  data points are assigned to the closest clusters
  once more. Furthermore, this method is repeated
  until all of the data points are in the same
  cluster, or the cluster centroids do not change
  between iterations.

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• Apriori Algorithm
• The Apriori Algorithm is a rule-based algorithm
  that finds the most common item sets in a
  database. A frequent itemset is one whose support
  value exceeds a certain threshold (support).
• XGBoost
• XGBoost is a decision tree-based Gradient
  Boosting algorithm. It consists of a group of
  weak learners who work together to make
  remarkably accurate predictions. Boosting, in
  other terms, receives the previous models errors
  and attempts to develop the model by learning
  from them.

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Support Vector Machine (SVM)

• SVM is a supervised learning algorithm. It solves
  problems like classification and regression. SVM
  seeks to find the best hyperplane in
  N-dimensional space (N refers to the number of
  features) to distinguish the various groups.
  Using the Hinge loss function, it finds the ideal
  hyperplane by maximizing the margin distance
  between the groups observations. The dimension
  of the hyperplane is N-1 if the number of
  features is N.

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When to choose which algorithm in Machine
Learning

• The response to which Machine Learning algorithm
  to use depends on a variety of factors, including
  the problem statement and the type of output you
  want, the type and size of the data, the
  computing time available, the number of features,
  and the number of observations in the data, to
  name a few. Here are some important factors to
  consider when selecting an algorithm.

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Size of the training data

• To get accurate forecasts, it is better to
  collect a large amount of data. However, data
  availability is often a constraint. Choose
  algorithms with high bias/low variance if the
  training data is small or the dataset has fewer
  observations and a higher number of features,
  such as genetics or textual data. If the training
  data is large enough and the number of
  observations is greater than the number of
  features, low bias/high variance algorithms may
  be used.

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The number of characteristics/features

• There may be many features in the dataset, but
  not all of them are important and meaningful.
  When dealing with certain types of data, such as
  genetics or text, the number of features relative
  to the number of data points can be very high.
  Some learning algorithms can become clogged by a
  large number of features, making training time
  unfeasible. SVM operates best with data that has
  a wide feature space but few observations. To
  minimize dimensionality and pick essential
  features, PCA and feature selection techniques
  should be used. When choosing an algorithm for a
  machine learning task, efficiency could be the
  most obvious metric. However, performance isnt
  enough to determine which algorithm is best for
  the job. Additional parameters, such as memory
  specifications, training and prediction times,
  interpretability, and data format, must be met by
  your model.