Legal Analytics Course - Class 9 - Clustering Algorithms (K-Means & Hierarchical Clustering) - Professor Daniel Martin Katz + Professor Michael J Bommarito
Legal Analytics Course - Class 9 - Clustering Algorithms (K-Means & Hierarchical Clustering) - Professor Daniel Martin Katz + Professor Michael J Bommarito
Application of Clustering in Data Science using Real-life Examples Edureka!
Clustering data into subsets is an important task for many data science applications. It is considered as one of the most important unsupervised learning technique. Keeping this in mind, we have come with a free webinar ‘Application of Cluster in Data Science using Real-life examples.’
Webinar : Introduction to R Programming and Machine LearningEdureka!
'Business Analytics with 'R' at Edureka will prepare you to perform analytics and build models for real world data science problems. It is the world’s most powerful programming language for statistical computing and graphics making it a must know language for the aspiring Data Scientists. 'R' wins strongly on Statistical Capability, Graphical capability, Cost and rich set of packages.
The topics covered in the presentation are:
1.What is R
2.Domains and Companies in which R is used
3.Characteristics of R
4.Get an Overview of Machine Learning
5.Understand the difference between supervised and unsupervised learning
6.Learn Clustering and K-means Clustering
7.Implement K-means Clustering in R
8.Google Trends in R
Machine Learning Interview Questions and Answers | Machine Learning Interview...Edureka!
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This Machine Learning Interview Questions and Answers PPT will help you to prepare yourself for Data Science / Machine Learning interviews. This PPT is ideal for both beginners as well as professionals who want to learn or brush up their concepts in Machine Learning core-concepts, Machine Learning using Python and Machine Learning Scenarios. Below are the topics covered in this tutorial:
1. Machine Learning Core Interview Question
2. Machine Learning using Python Interview Question
3. Machine Learning Scenario based Interview Question
Check out our playlist for more videos: http://bit.ly/2taym8X
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Application of Clustering in Data Science using Real-life Examples Edureka!
Clustering data into subsets is an important task for many data science applications. It is considered as one of the most important unsupervised learning technique. Keeping this in mind, we have come with a free webinar ‘Application of Cluster in Data Science using Real-life examples.’
Webinar : Introduction to R Programming and Machine LearningEdureka!
'Business Analytics with 'R' at Edureka will prepare you to perform analytics and build models for real world data science problems. It is the world’s most powerful programming language for statistical computing and graphics making it a must know language for the aspiring Data Scientists. 'R' wins strongly on Statistical Capability, Graphical capability, Cost and rich set of packages.
The topics covered in the presentation are:
1.What is R
2.Domains and Companies in which R is used
3.Characteristics of R
4.Get an Overview of Machine Learning
5.Understand the difference between supervised and unsupervised learning
6.Learn Clustering and K-means Clustering
7.Implement K-means Clustering in R
8.Google Trends in R
Machine Learning Interview Questions and Answers | Machine Learning Interview...Edureka!
** Machine Learning Training with Python: https://www.edureka.co/python **
This Machine Learning Interview Questions and Answers PPT will help you to prepare yourself for Data Science / Machine Learning interviews. This PPT is ideal for both beginners as well as professionals who want to learn or brush up their concepts in Machine Learning core-concepts, Machine Learning using Python and Machine Learning Scenarios. Below are the topics covered in this tutorial:
1. Machine Learning Core Interview Question
2. Machine Learning using Python Interview Question
3. Machine Learning Scenario based Interview Question
Check out our playlist for more videos: http://bit.ly/2taym8X
Follow us to never miss an update in the future.
Instagram: https://www.instagram.com/edureka_learning/
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LinkedIn: https://www.linkedin.com/company/edureka
Slides for the first meeting of the course 'Big Data and Automated Content Analysis' at the Department of Communication Science, University of Amsterdam
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Legal Analytics Course - Class 5 - Quantitative Legal Prediction + Data Drive...Daniel Katz
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AWS re:Invent 2016: Blockchain on AWS: Disrupting the Norm (GPST301)Amazon Web Services
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Artificial Intelligence and Law - A Primer Daniel Katz
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Slides for the first meeting of the course 'Big Data and Automated Content Analysis' at the Department of Communication Science, University of Amsterdam
Machine Learning has become a must to improve insight, quality and time to market. But it's also been called the 'high interest credit card of technical debt' with challenges in managing both how it's applied and how its results are consumed.
Legal Analytics Course - Class 5 - Quantitative Legal Prediction + Data Drive...Daniel Katz
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AWS re:Invent 2016: Blockchain on AWS: Disrupting the Norm (GPST301)Amazon Web Services
Recent interest in leveraging distributed ledgers across multiple industries has elevated blockchain from mere theory and into the spotlight of real world use. Learn why some partners have a vested interest in it and how blockchain can be used with AWS. In this session, we explore the AWS services needed for a successful deployment and dive deep into a partner's blockchain journey on AWS.
Artificial Intelligence and Law - A Primer Daniel Katz
Artificial Intelligence in Law (and beyond) including Machine Learning as a Service, Quantitative Legal Prediction / Legal Analytics, Experts + Crowds + Algorithms
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We focus on the goals of prediction, optimization, and risk management to enable holistic organizational changes that empower legal decision-making.
These changes span people and processes, software and data, and execution and education.
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Similar to Legal Analytics Course - Class 9 - Clustering Algorithms (K-Means & Hierarchical Clustering) - Professor Daniel Martin Katz + Professor Michael J Bommarito
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This Edureka k-means clustering algorithm tutorial will take you through the machine learning introduction, cluster analysis, types of clustering algorithms, k-means clustering, how it works along with an example/ demo in R. This Data Science with R tutorial is ideal for beginners to learn how k-means clustering work. You can also read the blog here: https://goo.gl/3aseSs
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Legal Analytics Course - Class 9 - Clustering Algorithms (K-Means & Hierarchical Clustering) - Professor Daniel Martin Katz + Professor Michael J Bommarito
1. Class 9
K-Means & Hierarchical Clustering
Legal Analytics
Professor Daniel Martin Katz
Professor Michael J Bommarito II
legalanalyticscourse.com
5. Task = Can We Determine to Which
Group the Agent Belongs?
Clustering (Unsupervised Learning)
f( )
Group?
Cluster
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12. “Similar” is the Key Idea (but it is a slippery concept)
Clustering is a Method of Grouping Similar Objects
Clustering is typically Unsupervised Learning
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13. There are a variety of methods used in this area
(Agglomerative versus Divisive Methods)
“Similar” is the Key Idea (but it is a slippery concept)
Clustering is a Method of Grouping Similar Objects
Clustering is typically Unsupervised Learning
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14. There are a variety of methods used in this area
(Agglomerative versus Divisive Methods)
Remember real data is n-dimensional
(which makes implementation / accuracy challenging)
“Similar” is the Key Idea (but it is a slippery concept)
Clustering is a Method of Grouping Similar Objects
Clustering is typically Unsupervised Learning
access more at legalanalyticscourse.com
21. in clustering, we are interested in trying
to formalize the idea of ‘similarity’
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22. A typical approach is to project
n-dimensional data into
a unidimensional ‘similarity index’
f( )
dimension 1
dimension 2
dimension 3
.
.
.
.
dimension n
similarity
or
distance function
similarity
index
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23. everything in its own cluster
(i.e. everyone is a special snowflake)
everything in one cluster
unidimensional similarity spectrum
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24. everything in its own cluster
(i.e. everyone is a special snowflake)
everything in one cluster
unidimensional similarity spectrum
as we slide across this spectrum is where the groupings become interesting
0% similarity threshold
hard question is where to stop as move from left to right
100% similarity threshold
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25. The Heavy Lifting is the
develop/apply the optimal
similarity/distance function
for the substantive problem at issue
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27. Goal for Any Clustering Method:
Achieve High Within Cluster Similarity
Achieve Low Cross Cluster Similarity
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28. We Want to Develop a Notion
of Distance Between Objects
Similarity is inversely related to distance
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33. K Means
How do we find the clusters in the data shown below?
We select K clusters in advance
Iteratively seek to min sum of
squared distances
Iteratively seek to min sum of
squared distances
34. K Means Optimization
We start with K clusters with unknown centers
We are attempting to min the sum of squared distances
(i.e. the objective function shown below)
Tricky Part is that this minimization problem
cannot be solved analytically
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35. Stuart Lloyd proposed a simple heuristic solution
“Lloyd’s algorithm” aka “k-means” is a good candidate solution
K Means Optimization
from
FlachText
Page 248
37. K-Means
where k = 2
Adapted from Example by Piyush Rai
initialization step
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38. K-Means
where k = 2
Adapted from Example by Piyush Rai
First Iteration - Assigning Points
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39. K-Means
where k = 2
Adapted from Example by Piyush Rai
First Iteration - Recalculate the Center of the Cluster
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40. K-Means
where k = 2
Adapted from Example by Piyush Rai
Second Iteration - Assigning Points
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41. K-Means
where k = 2
Adapted from Example by Piyush Rai
Second Iteration - Recalculate the Center of the Cluster
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42. K-Means
where k = 2
Adapted from Example by Piyush Rai
Third Iteration - Assigning Points
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43. K-Means
where k = 2
Adapted from Example by Piyush Rai
Third Iteration - Recalculate the Center of the Cluster
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44. K Means Clustering
Fast Method But Leads to Local Minimum
Should repeat from different starting conditions
(must then figure best heuristic to find global min)
Important Weakness is it often not clear what value of K
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48. Hierarchical Clustering
Partitions can be visualized using a tree structure (a dendrogram)
Does not need the number of clusters as input
Possible to view partitions at different levels of granularities
(i.e., can refine/coarsen clusters) using different K
DescriptionVia: Piyush Rai
50. Agglomerative: This is a "bottom up" approach: each
observation starts in its own cluster, and pairs of
clusters are merged as one moves up the hierarchy.
Divisive: This is a "top down" approach: all
observations start in one cluster, and splits are
performed recursively as one moves down the
hierarchy.
Agglomerative versus Divisive Methods
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62. Hierarchical Clustering
“(1) Start by assigning each item to a cluster, so that if you have
N items, you now have N clusters, each containing just one item.
Let the distances (similarities) between the clusters the same as
the distances (similarities) between the items they contain.
(2) Find the closest (most similar) pair of clusters and merge
them into a single cluster, so that now you have one cluster less.
(3) Compute distances (similarities) between the new cluster and
each of the old clusters.
(4) Repeat steps 2 and 3 until all items are clustered into a single
cluster of size N. (*)”
S. C. Johnson (1967): "Hierarchical Clustering Schemes" Psychometrika, 2:241-254
63. Hierarchical Clustering
There are a variety of different approaches to Step 3
(3) Compute distances (similarities) between the new
cluster and each of the old clusters.
single-linkage clustering
complete-linkage clustering
average-linkage clustering
centroid linkage clustering
(see pages 253-258 of Flach)
79. Legal Analytics
Class 9 - K-Means & Hierarchical Clustering
daniel martin katz
blog | ComputationalLegalStudies
corp | LexPredict
michael j bommarito
twitter | @computational
blog | ComputationalLegalStudies
corp | LexPredict
twitter | @mjbommar
more content available at legalanalyticscourse.com
site | danielmartinkatz.com site | bommaritollc.com