This document discusses unsupervised learning techniques for clustering data, specifically K-Means clustering and Gaussian Mixture Models. It explains that K-Means clustering groups data by assigning each point to the nearest cluster center and iteratively updating the cluster centers. Gaussian Mixture Models assume the data is generated from a mixture of Gaussian distributions and uses the Expectation-Maximization algorithm to estimate the parameters of the mixture components.
Information-theoretic clustering with applicationsFrank Nielsen
Information-theoretic clustering with applications
Abstract: Clustering is a fundamental and key primitive to discover structural groups of homogeneous data in data sets, called clusters. The most famous clustering technique is the celebrated k-means clustering that seeks to minimize the sum of intra-cluster variances. k-Means is NP-hard as soon as the dimension and the number of clusters are both greater than 1. In the first part of the talk, we first present a generic dynamic programming method to compute the optimal clustering of n scalar elements into k pairwise disjoint intervals. This case includes 1D Euclidean k-means but also other kinds of clustering algorithms like the k-medoids, the k-medians, the k-centers, etc.
We extend the method to incorporate cluster size constraints and show how to choose the appropriate number of clusters using model selection. We then illustrate and refine the method on two case studies: 1D Bregman clustering and univariate statistical mixture learning maximizing the complete likelihood. In the second part of the talk, we introduce a generalization of k-means to cluster sets of histograms that has become an important ingredient of modern information processing due to the success of the bag-of-word modelling paradigm.
Clustering histograms can be performed using the celebrated k-means centroid-based algorithm. We consider the Jeffreys divergence that symmetrizes the Kullback-Leibler divergence, and investigate the computation of Jeffreys centroids. We prove that the Jeffreys centroid can be expressed analytically using the Lambert W function for positive histograms. We then show how to obtain a fast guaranteed approximation when dealing with frequency histograms and conclude with some remarks on the k-means histogram clustering.
References: - Optimal interval clustering: Application to Bregman clustering and statistical mixture learning IEEE ISIT 2014 (recent result poster) http://arxiv.org/abs/1403.2485
- Jeffreys Centroids: A Closed-Form Expression for Positive Histograms and a Guaranteed Tight Approximation for Frequency Histograms.
IEEE Signal Process. Lett. 20(7): 657-660 (2013) http://arxiv.org/abs/1303.7286
http://www.i.kyoto-u.ac.jp/informatics-seminar/
Jiawei Han, Micheline Kamber and Jian Pei
Data Mining: Concepts and Techniques, 3rd ed.
The Morgan Kaufmann Series in Data Management Systems
Morgan Kaufmann Publishers, July 2011. ISBN 978-0123814791
Information-theoretic clustering with applicationsFrank Nielsen
Information-theoretic clustering with applications
Abstract: Clustering is a fundamental and key primitive to discover structural groups of homogeneous data in data sets, called clusters. The most famous clustering technique is the celebrated k-means clustering that seeks to minimize the sum of intra-cluster variances. k-Means is NP-hard as soon as the dimension and the number of clusters are both greater than 1. In the first part of the talk, we first present a generic dynamic programming method to compute the optimal clustering of n scalar elements into k pairwise disjoint intervals. This case includes 1D Euclidean k-means but also other kinds of clustering algorithms like the k-medoids, the k-medians, the k-centers, etc.
We extend the method to incorporate cluster size constraints and show how to choose the appropriate number of clusters using model selection. We then illustrate and refine the method on two case studies: 1D Bregman clustering and univariate statistical mixture learning maximizing the complete likelihood. In the second part of the talk, we introduce a generalization of k-means to cluster sets of histograms that has become an important ingredient of modern information processing due to the success of the bag-of-word modelling paradigm.
Clustering histograms can be performed using the celebrated k-means centroid-based algorithm. We consider the Jeffreys divergence that symmetrizes the Kullback-Leibler divergence, and investigate the computation of Jeffreys centroids. We prove that the Jeffreys centroid can be expressed analytically using the Lambert W function for positive histograms. We then show how to obtain a fast guaranteed approximation when dealing with frequency histograms and conclude with some remarks on the k-means histogram clustering.
References: - Optimal interval clustering: Application to Bregman clustering and statistical mixture learning IEEE ISIT 2014 (recent result poster) http://arxiv.org/abs/1403.2485
- Jeffreys Centroids: A Closed-Form Expression for Positive Histograms and a Guaranteed Tight Approximation for Frequency Histograms.
IEEE Signal Process. Lett. 20(7): 657-660 (2013) http://arxiv.org/abs/1303.7286
http://www.i.kyoto-u.ac.jp/informatics-seminar/
Jiawei Han, Micheline Kamber and Jian Pei
Data Mining: Concepts and Techniques, 3rd ed.
The Morgan Kaufmann Series in Data Management Systems
Morgan Kaufmann Publishers, July 2011. ISBN 978-0123814791
The amount of digital data in the new era has grown exponentially in recent years and with the development of new technologies, is growing more rapidly than ever before.
Nevertheless, simply knowing that all these data are out there is easily understandable, utilizing these data to turn a profit is not trivial.
The need of data mining techniques able to extract profitable insight information is the next frontier of innovation, competition and profit.
A data analytic services provider, in order to well-scale and exponentially grow its profit, has to deal with scalability, multi-tenancy and self-adaptability.
In big data applications, machine learning is a very powerful instrument but a bad choice regarding the algorithm and its configuration parameters can easily lead to poor results. The key problem is automating the tuning process without a priori knowledge of the data and without human intervention.
In this research project we implemented and analysed TunUp: A Distributed Cloud-based Genetic Evolutionary Tuning for Data Clustering.
The proposed solution automatically evaluates and tunes data clustering algorithms, so that big data services can self-adapt and scale in a cost-efficient manner.
For our experiments, we considered k-means as clustering algorithm, that is a simple but popular algorithm, widely used in many data mining applications.
Clustering outputs are evaluated using four internal techniques: AIC, Dunn, Davies-Bouldin and Silhouette and an external evaluation: AdjustedRand.
We then performed a correlation t-test in order to validate and benchmark our internal techniques against AdjustedRand.
Defined the best evaluation criteria, the main challenge of k-means is setting the right value of k, that represents the number of clusters, and the distance measure used to compute distances of each pair of points in the data space.
To address this problem we propose an implementation of the Genetic Evolutionary Algorithm that heuristically finds out an optimal configuration of our clustering algorithm.
In order to improve performances, we implemented a parallel version of genetic algorithm developing a REST API and deploying several instances in the Amazon Cloud Computing (EC2) infrastructure.
In conclusion, with this research we contributed building and analysing TunUp, an open solution for evaluation, validation and tuning of data clustering algorithms, with a particularly focused on cloud services.
Our experiments show the quality and efficiency of tuning k-means on a set of public datasets.
The research also provides a Roadmap that gives indications of how the current system should be extended and utilized for future clustering applications, such as: Tuning of existing clustering algorithms, Supporting new algorithms design, Evaluation and comparison of different algorithms.
Mathematics online: some common algorithmsMark Moriarty
Brief overview of some basic algorithms used online and across data-mining, and a word on where to learn them. Prepared specially for UCC Boole Prize 2012.
Conjugate Gradient method for Brain Magnetic Resonance Images SegmentationEL-Hachemi Guerrout
Image segmentation is the process of partitioning the im-
age into regions of interest in order to provide a meaningful represen-
tation of information. Nowadays, segmentation has become a necessity
in many practical medical imaging methods as locating tumors and dis-
eases. Hidden Markov Random Field model is one of several techniques
used in image segmentation. It provides an elegant way to model the
segmentation process. This modeling leads to the minimization of an ob-
jective function. Conjugate Gradient algorithm (CG) is one of the best
known optimization techniques. This paper proposes the use of the non-
linear Conjugate Gradient algorithm (CG) for image segmentation, in
combination with the Hidden Markov Random Field modelization. Since
derivatives are not available for this expression, finite differences are used
in the CG algorithm to approximate the first derivative. The approach
is evaluated using a number of publicly available images, where ground
truth is known. The Dice Coefficient is used as an objective criterion to
measure the quality of segmentation. The results show that the proposed
CG approach compares favorably with other variants of Hidden Markov
Random Field segmentation algorithms.
A review of one of the most popular methods of clustering, a part of what is know as unsupervised learning, K-Means. Here, we go from the basic heuristic used to solve the NP-Hard problem to an approximation algorithm K-Centers. Additionally, we look at variations coming from the Fuzzy Set ideas. In the future, we will add more about On-Line algorithms in the line of Stochastic Gradient Ideas...
Sergei Vassilvitskii, Research Scientist, Google at MLconf NYC - 4/15/16MLconf
Teaching K-Means New Tricks: Over 50 years old, the k-means algorithm remains one of the most popular clustering algorithms. In this talk we’ll cover some recent developments, including better initialization, the notion of coresets, clustering at scale, and clustering with outliers.
Animashree Anandkumar, Electrical Engineering and CS Dept, UC Irvine at MLcon...MLconf
Anima Anandkumar is a faculty at the EECS Dept. at U.C.Irvine since August 2010. Her research interests are in the area of large-scale machine learning and high-dimensional statistics. She received her B.Tech in Electrical Engineering from IIT Madras in 2004 and her PhD from Cornell University in 2009. She has been a visiting faculty at Microsoft Research New England in 2012 and a postdoctoral researcher at the Stochastic Systems Group at MIT between 2009-2010. She is the recipient of the Microsoft Faculty Fellowship, ARO Young Investigator Award, NSF CAREER Award, and IBM Fran Allen PhD fellowship.
The amount of digital data in the new era has grown exponentially in recent years and with the development of new technologies, is growing more rapidly than ever before.
Nevertheless, simply knowing that all these data are out there is easily understandable, utilizing these data to turn a profit is not trivial.
The need of data mining techniques able to extract profitable insight information is the next frontier of innovation, competition and profit.
A data analytic services provider, in order to well-scale and exponentially grow its profit, has to deal with scalability, multi-tenancy and self-adaptability.
In big data applications, machine learning is a very powerful instrument but a bad choice regarding the algorithm and its configuration parameters can easily lead to poor results. The key problem is automating the tuning process without a priori knowledge of the data and without human intervention.
In this research project we implemented and analysed TunUp: A Distributed Cloud-based Genetic Evolutionary Tuning for Data Clustering.
The proposed solution automatically evaluates and tunes data clustering algorithms, so that big data services can self-adapt and scale in a cost-efficient manner.
For our experiments, we considered k-means as clustering algorithm, that is a simple but popular algorithm, widely used in many data mining applications.
Clustering outputs are evaluated using four internal techniques: AIC, Dunn, Davies-Bouldin and Silhouette and an external evaluation: AdjustedRand.
We then performed a correlation t-test in order to validate and benchmark our internal techniques against AdjustedRand.
Defined the best evaluation criteria, the main challenge of k-means is setting the right value of k, that represents the number of clusters, and the distance measure used to compute distances of each pair of points in the data space.
To address this problem we propose an implementation of the Genetic Evolutionary Algorithm that heuristically finds out an optimal configuration of our clustering algorithm.
In order to improve performances, we implemented a parallel version of genetic algorithm developing a REST API and deploying several instances in the Amazon Cloud Computing (EC2) infrastructure.
In conclusion, with this research we contributed building and analysing TunUp, an open solution for evaluation, validation and tuning of data clustering algorithms, with a particularly focused on cloud services.
Our experiments show the quality and efficiency of tuning k-means on a set of public datasets.
The research also provides a Roadmap that gives indications of how the current system should be extended and utilized for future clustering applications, such as: Tuning of existing clustering algorithms, Supporting new algorithms design, Evaluation and comparison of different algorithms.
Mathematics online: some common algorithmsMark Moriarty
Brief overview of some basic algorithms used online and across data-mining, and a word on where to learn them. Prepared specially for UCC Boole Prize 2012.
Conjugate Gradient method for Brain Magnetic Resonance Images SegmentationEL-Hachemi Guerrout
Image segmentation is the process of partitioning the im-
age into regions of interest in order to provide a meaningful represen-
tation of information. Nowadays, segmentation has become a necessity
in many practical medical imaging methods as locating tumors and dis-
eases. Hidden Markov Random Field model is one of several techniques
used in image segmentation. It provides an elegant way to model the
segmentation process. This modeling leads to the minimization of an ob-
jective function. Conjugate Gradient algorithm (CG) is one of the best
known optimization techniques. This paper proposes the use of the non-
linear Conjugate Gradient algorithm (CG) for image segmentation, in
combination with the Hidden Markov Random Field modelization. Since
derivatives are not available for this expression, finite differences are used
in the CG algorithm to approximate the first derivative. The approach
is evaluated using a number of publicly available images, where ground
truth is known. The Dice Coefficient is used as an objective criterion to
measure the quality of segmentation. The results show that the proposed
CG approach compares favorably with other variants of Hidden Markov
Random Field segmentation algorithms.
A review of one of the most popular methods of clustering, a part of what is know as unsupervised learning, K-Means. Here, we go from the basic heuristic used to solve the NP-Hard problem to an approximation algorithm K-Centers. Additionally, we look at variations coming from the Fuzzy Set ideas. In the future, we will add more about On-Line algorithms in the line of Stochastic Gradient Ideas...
Sergei Vassilvitskii, Research Scientist, Google at MLconf NYC - 4/15/16MLconf
Teaching K-Means New Tricks: Over 50 years old, the k-means algorithm remains one of the most popular clustering algorithms. In this talk we’ll cover some recent developments, including better initialization, the notion of coresets, clustering at scale, and clustering with outliers.
Animashree Anandkumar, Electrical Engineering and CS Dept, UC Irvine at MLcon...MLconf
Anima Anandkumar is a faculty at the EECS Dept. at U.C.Irvine since August 2010. Her research interests are in the area of large-scale machine learning and high-dimensional statistics. She received her B.Tech in Electrical Engineering from IIT Madras in 2004 and her PhD from Cornell University in 2009. She has been a visiting faculty at Microsoft Research New England in 2012 and a postdoctoral researcher at the Stochastic Systems Group at MIT between 2009-2010. She is the recipient of the Microsoft Faculty Fellowship, ARO Young Investigator Award, NSF CAREER Award, and IBM Fran Allen PhD fellowship.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Safalta Digital marketing institute in Noida, provide complete applications that encompass a huge range of virtual advertising and marketing additives, which includes search engine optimization, virtual communication advertising, pay-per-click on marketing, content material advertising, internet analytics, and greater. These university courses are designed for students who possess a comprehensive understanding of virtual marketing strategies and attributes.Safalta Digital Marketing Institute in Noida is a first choice for young individuals or students who are looking to start their careers in the field of digital advertising. The institute gives specialized courses designed and certification.
for beginners, providing thorough training in areas such as SEO, digital communication marketing, and PPC training in Noida. After finishing the program, students receive the certifications recognised by top different universitie, setting a strong foundation for a successful career in digital marketing.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Normal Labour/ Stages of Labour/ Mechanism of LabourWasim Ak
Normal labor is also termed spontaneous labor, defined as the natural physiological process through which the fetus, placenta, and membranes are expelled from the uterus through the birth canal at term (37 to 42 weeks
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
2. Unsupervised
Learning
• Supervised
learning
used
labeled
data
pairs
(x, y)
to
learn
a
func=on
f : X→Y
– But,
what
if
we
don’t
have
labels?
• No
labels
=
unsupervised
learning
• Only
some
points
are
labeled
=
semi-‐supervised
learning
– Labels
may
be
expensive
to
obtain,
so
we
only
get
a
few
• Clustering
is
the
unsupervised
grouping
of
data
points.
It
can
be
used
for
knowledge
discovery.
3. K-‐Means
Clustering
Some
material
adapted
from
slides
by
Andrew
Moore,
CMU.
Visit
hMp://www.autonlab.org/tutorials/
for
Andrew’s
repository
of
Data
Mining
tutorials.
5. K-‐Means
Clustering
K-‐Means
(
k
,
X
)
• Randomly
choose
k
cluster
center
loca=ons
(centroids)
• Loop
un=l
convergence
• Assign
each
point
to
the
cluster
of
the
closest
centroid
• Re-‐es=mate
the
cluster
centroids
based
on
the
data
assigned
to
each
cluster
6. K-‐Means
Clustering
K-‐Means
(
k
,
X
)
• Randomly
choose
k
cluster
center
loca=ons
(centroids)
• Loop
un=l
convergence
• Assign
each
point
to
the
cluster
of
the
closest
centroid
• Re-‐es=mate
the
cluster
centroids
based
on
the
data
assigned
to
each
cluster
7. K-‐Means
Clustering
K-‐Means
(
k
,
X
)
• Randomly
choose
k
cluster
center
loca=ons
(centroids)
• Loop
un=l
convergence
• Assign
each
point
to
the
cluster
of
the
closest
centroid
• Re-‐es=mate
the
cluster
centroids
based
on
the
data
assigned
to
each
cluster
8. K-‐Means
Anima=on
Example generated by
Andrew Moore using
Dan Pelleg’s super-
duper fast K-means
system:
Dan Pelleg and Andrew
Moore. Accelerating
Exact k-means
Algorithms with
Geometric Reasoning.
Proc. Conference on
Knowledge Discovery in
Databases 1999.
9. K-‐Means
Objec=ve
Func=on
• K-‐means
finds
a
local
op=mum
of
the
following
objec=ve
func=on:
arg min
S
k
X
i=1
X
x2Si
kx µik2
2
where S = {S1, . . . , Sk} is a partitioning ov
X = {x1, . . . , xn} s.t. X =
Sk
i=1 Si
and µi = mean(Si)
arg min
S
k
X
i=1
X
x2Si
kx µik2
2
where S = {S1, . . . , Sk} is a partitioning over
X = {x1, . . . , xn} s.t. X =
Sk
i=1 Si
and µi = mean(Si)
10. Problems
with
K-‐Means
• Very
sensi=ve
to
the
ini=al
points
– Do
many
runs
of
K-‐Means,
each
with
different
ini=al
centroids
– Seed
the
centroids
using
a
beMer
method
than
randomly
choosing
the
centroids
• e.g.,
Farthest-‐first
sampling
• Must
manually
choose
k
– Learn
the
op=mal
k
for
the
clustering
• Note
that
this
requires
a
performance
measure
11. • How
do
you
tell
it
which
clustering
you
want?
Constrained
clustering
techniques
(semi-‐supervised)
Problems
with
K-‐Means
Same-‐cluster
constraint
(must-‐link)
Different-‐cluster
constraint
(cannot-‐link)
k = 2"