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Discovery Latinoamérica | Inteligencia Artificial - IBM

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Discovery Latinoamérica | Inteligencia Artificial - IBM

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Discovery Latinoamérica | Inteligencia Artificial - IBM

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The following is an introduction for producing simple graphs with the R Programming Language. Each example builds on the previous one. The areas in bold indicate new text that was added to the previous example. The graph produced by each example is shown on the right.

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Network analysis and visualization with R and igraph

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Network analysis and visualization with R and igraph

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Se trata de un recurso web en el que se presenta un tutorial de análisis y visualización de grafos en R con la librería igraph.

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Network analysis with R and igraph: NetSci X Tutorial

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Discover what actually works in AI. Join millions of builders, researchers, and labs evaluating agents, models, and frontier technology through crowdsourced benchmarks, competitions, and hackathons.

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Determining the optimal number of clusters: 3 must known methods

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Determining the optimal number of clusters: 3 must known methods

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Determining The Optimal Number Of Clusters: 3 Must Know Methods

Determining the optimal number of clusters in a data set is a fundamental issue in partitioning clustering, such as k-means clustering (Chapter @ref(kmeans-clustering)), which requires the user to specify the number of clusters k to be generated.

Unfortunately, there is no definitive answer to this question. The optimal number of clusters is somehow subjective and depends on the method used for measuring similarities and the parameters used for partitioning. A simple and popular solution consists of inspecting the dendrogram produced using hierarchical clustering (Chapter @ref(agglomerative-clustering)) to see if it suggests a particular number of clusters. Unfortunately, this approach is also subjective.

In this chapter, we'll describe different methods for determining the optimal number of clusters for k-means, k-medoids (PAM) and hierarchical clustering.

These methods include direct methods and statistical testing methods:

1. Direct methods: consists of optimizing a criterion, such as the within cluster sums of squares or the average silhouette. The corresponding methods are named elbow and silhouette methods, respectively.

2. Statistical testing methods: consists of comparing evidence against null hypothesis. An example is the gap statistic.

In addition to elbow, silhouette and gap statistic methods, there are more than thirty other indices and methods that have been published for identifying the optimal number of clusters. We'll provide R codes for computing all these 30 indices in order to decide the best number of clusters using the "majority rule".

For each of these methods:

We'll describe the basic idea and the algorithm

We'll provide easy-o-use R codes with many examples for determining the optimal number of clusters and visualizing the output.

Contents:

Related Book:

Elbow method

Recall that, the basic idea behind partitioning methods, such as k-means clustering (Chapter @ref(kmeans-clustering)), is to define clusters such that the total intra-cluster variation [or total within-cluster sum of square (WSS)] is minimized. The total WSS measures the compactness of the clustering and we want it to be as small as possible.

The Elbow method looks at the total WSS as a function of the number of clusters: One should choose a number of clusters so that adding another cluster doesn't improve much better the total WSS.

The optimal number of clusters can be defined as follow:

1. Compute clustering algorithm (e.g., k-means clustering) for different values of k. For instance, by varying k from 1 to 10 clusters.

2. For each k, calculate the total within-cluster sum of square (wss).

3. Plot the curve of wss according to the number of clusters k.

4. The location of a bend (knee) in the plot is generally considered as an indicator of the appropriate number of clusters.

Note that, the elbow method is sometimes ambiguous. An alternative is the average silhouette method (Kaufman and Rousseeuw [1990]) which can be also used with any clustering approach.

Average silhouette method

The average silhouette approach we'll be described comprehensively in the chapter cluster validation statistics (Chapter @ref(cluster-validation-statistics)). Briefly, it measures the quality of a clustering. That is, it determines how well each object lies within its cluster. A high average silhouette width indicates a good clustering.

Average silhouette method computes the average silhouette of observations for different values of k. The optimal number of clusters k is the one that maximize the average silhouette over a range of possible values for k (Kaufman and Rousseeuw 1990).

The algorithm is similar to the elbow method and can be computed as follow:

1. Compute clustering algorithm (e.g., k-means clustering) for different values of k. For instance, by varying k from 1 to 10 clusters.

2. For each k, calculate the average silhouette of observations ( a v g. s i l).

3. Plot the curve of a v g. s i l according to the number of clusters k.

4. The location of the maximum is considered as the appropriate number of clusters.

Gap statistic method

The gap statistic has been published by R. Tibshirani, G. Walther, and T. Hastie (Standford University, 2001). The approach can be applied to any clustering method.

The gap statistic compares the total within intra-cluster variation for different values of k with their expected values under null reference distribution of the data. The estimate of the optimal clusters will be value that maximize the gap statistic (i.e, that yields the largest gap statistic). This means that the clustering structure is far away from the random uniform distribution of points.

The algorithm works as follow:

1. Cluster the observed data, varying the number of clusters from k = 1, ..., k W k.m a x, and compute the corresponding total within intra-cluster variation

2. Generate B reference data sets with a random uniform distribution. Cluster each of these reference data sets with varying number of clusters k = 1, ..., k W k b.m a x, and compute the corresponding total within intra-cluster variation

3. Compute the estimated gap statistic as the deviation of the observed W W k b under the null hypothesis: k value from its expected value \(Gap(k) = \frac{1}{B} \sum\limits_{b=1}^B log(W_{kb}^*) - log(W_k)\) . Compute also the standard deviation of the statistics.

4. Choose the number of clusters as the smallest value of k such that the gap statistic is within one standard deviation of the gap at k+1: G a p( k)≥ G a p( k + 1)− s k + 1.

Note that, using B = 500 gives quite precise results so that the gap plot is basically unchanged after an another run.

Computing the number of clusters using R

In this section, we'll describe two functions for determining the optimal number of clusters:

1. fviz_nbclust() function [in factoextra R package]: It can be used to compute the three different methods [elbow, silhouette and gap statistic] for any partitioning clustering methods [K-means, K-medoids (PAM), CLARA, HCUT]. Note that the hcut() function is available only in factoextra package.It computes hierarchical clustering and cut the tree in k pre-specified clusters.

2. NbClust() function [ in NbClust R package] (Charrad et al. 2014): It provides 30 indices for determining the relevant number of clusters and proposes to users the best clustering scheme from the different results obtained by varying all combinations of number of clusters, distance measures, and clustering methods. It can simultaneously computes all the indices and determine the number of clusters in a single function call.

Required R packages

We'll use the following R packages:

factoextra to determine the optimal number clusters for a given clustering methods and for data visualization.

NbClust for computing about 30 methods at once, in order to find the optimal number of clusters.

To install the packages, type this:

pkgs

Load the packages as follow:

library(factoextra) library(NbClust)

Data preparation

We'll use the USArrests data as a demo data set. We start by standardizing the data to make variables comparable.

# Standardize the data df

## Murder Assault UrbanPop Rape ## Alabama 1.2426 0.783 -0.521 -0.00342 ## Alaska 0.5079 1.107 -1.212 2.48420 ## Arizona 0.0716 1.479 0.999 1.04288 ## Arkansas 0.2323 0.231 -1.074 -0.18492 ## California 0.2783 1.263 1.759 2.06782 ## Colorado 0.0257 0.399 0.861 1.86497

fviz_nbclust() function: Elbow, Silhouhette and Gap statistic methods

The simplified format is as follow:

fviz_nbclust(x, FUNcluster, method = c("silhouette", "wss", "gap_stat"))

x: numeric matrix or data frame

FUNcluster: a partitioning function. Allowed values include kmeans, pam, clara and hcut (for hierarchical clustering).

method: the method to be used for determining the optimal number of clusters.

The R code below determine the optimal number of clusters for k-means clustering:

# Elbow method fviz_nbclust(df, kmeans, method = "wss") + geom_vline(xintercept = 4, linetype = 2)+ labs(subtitle = "Elbow method") # Silhouette method fviz_nbclust(df, kmeans, method = "silhouette")+ labs(subtitle = "Silhouette method") # Gap statistic # nboot = 50 to keep the function speedy. # recommended value: nboot= 500 for your analysis. # Use verbose = FALSE to hide computing progression. set.seed(123) fviz_nbclust(df, kmeans, nstart = 25, method = "gap_stat", nboot = 50)+ labs(subtitle = "Gap statistic method")

## Clustering k = 1,2,..., K.max (= 10): .. done ## Bootstrapping, b = 1,2,..., B (= 50) [one "." per sample]: ## .................................................. 50

Elbow method: 4 clusters solution suggested

Silhouette method: 2 clusters solution suggested

Gap statistic method: 4 clusters solution suggested

According to these observations, it's possible to define k = 4 as the optimal number of clusters in the data.

The disadvantage of elbow and average silhouette methods is that, they measure a global clustering characteristic only. A more sophisticated method is to use the gap statistic which provides a statistical procedure to formalize the elbow/silhouette heuristic in order to estimate the optimal number of clusters.

NbClust() function: 30 indices for choosing the best number of clusters

The simplified format of the function NbClust() is:

NbClust(data = NULL, diss = NULL, distance = "euclidean", min.nc = 2, max.nc = 15, method = NULL)

data: matrix

diss: dissimilarity matrix to be used. By default, diss=NULL, but if it is replaced by a dissimilarity matrix, distance should be "NULL"

distance: the distance measure to be used to compute the dissimilarity matrix. Possible values include "euclidean", "manhattan" or "NULL".

min.nc, max.nc: minimal and maximal number of clusters, respectively

method: The cluster analysis method to be used including "ward.D", "ward.D2", "single", "complete", "average", "kmeans" and more.

To compute NbClust() for kmeans, use method = "kmeans".

To compute NbClust() for hierarchical clustering, method should be one of c("ward.D", "ward.D2", "single", "complete", "average").

The R code below computes NbClust() for k-means:

library("NbClust") nb

The result of NbClust using the function fviz_nbclust() [in factoextra], as follow:

library("factoextra") fviz_nbclust(nb)

## Among all indices: ## =================== ## * 2 proposed 0 as the best number of clusters ## * 10 proposed 2 as the best number of clusters ## * 2 proposed 3 as the best number of clusters ## * 8 proposed 4 as the best number of clusters ## * 1 proposed 5 as the best number of clusters ## * 1 proposed 8 as the best number of clusters ## * 2 proposed 10 as the best number of clusters ## ## Conclusion ## ========================= ## * According to the majority rule, the best number of clusters is 2 .

....

2 proposed 0 as the best number of clusters

10 indices proposed 2 as the best number of clusters.

2 proposed 3 as the best number of clusters.

8 proposed 4 as the best number of clusters.

According to the majority rule, the best number of clusters is 2.

Summary

In this article, we described different methods for choosing the optimal number of clusters in a data set. These methods include the elbow, the silhouette and the gap statistic methods.

We demonstrated how to compute these methods using the R function fviz_nbclust() [in factoextra R package]. Additionally, we described the package NbClust(), which can be used to compute simultaneously many other indices and methods for determining the number of clusters.

After choosing the number of clusters k, the next step is to perform partitioning clustering as described at: k-means clustering (Chapter @ref(kmeans-clustering)).

References

Charrad, Malika, Nadia Ghazzali, Véronique Boiteau, and Azam Niknafs. 2014. "NbClust: An R Package for Determining the Relevant Number of Clusters in a Data Set." Journal of Statistical Software 61: 1-36. http://www.jstatsoft.org/v61/i06/paper.

Kaufman, Leonard, and Peter Rousseeuw. 1990. Finding Groups in Data: An Introduction to Cluster Analysis.

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Comment

Hi, I would like to ask whether elbow method and average silhouette method can be used for hierarchical clustering to choose the optimal number of clusters.

Cheers.

Comment

Yes, for hierarchical clustering, you can use the function hcut() [in factoextra]:

for example:

Code R :

fviz_nbclust(mydata, hcut, method = "wss" )

Comment

Hi, I would like to ask whether other distance methods can be used for hierarchical clustering in fviz_nbclust(). For instance,dissimilarity structure as produced by distHaversine() function.

Comment

Hi

Can any of these methods be used for hkmeans?

Or do you have to estimate it for hierarchical clustering,
and then separately for k-means?

very cool package!!!

Thanks,
-Luigi

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Determining The Optimal Number Of Clusters: 3 Must Know Methods

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Determining The Optimal Number Of Clusters: 3 Must Know Methods Determining the optimal number of clusters in a data set is a fundamental issue in partitioning clustering, such as k-means clustering (Chapter @ref(kmeans-clustering)), which requires the user to specify the number of clusters k to be generated.

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libro que podemos consultar directamente en la web y que incluye recursos en los que se presentan, a nivel introductorio, los principales conceptos teóricos relativos a buena parte de los aspectos cubiertos en este tema

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The best learning investment you'll ever make. For one week only, get unlimited access to DataCamp for one month for just $1. Regular subscription resumes after first month. Running until October 8, 2023, online data science and AI learning platform DataCamp is offering its premium subscription for only $1. With DataCamp Premium, you ... [Read more...]

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R news and tutorials contributed by hundreds of R bloggers

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crantastic_production tagged MultipleBubbles with TimeSeries, nardl with TimeSeries, tibbletime with TimeSeries, tsfknn with TimeSeries, tsibble with TimeSeries, TSrepr with TimeSeries, and TSstudio with TimeSeries (about 12 hours ago)

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The 'main' R mailing list, for discussion about problems and solutions using R, announcements (not covered by 'R-announce' or 'R-packages', see above), about the availability of new functionality for R and documentation of R, comparison and compatibility with S-plus, and for the posting of nice examples and benchmarks.

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Currently, the CRAN package repository features 12412 available packages.

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El paquete estadístico R es uno de los más flexibles, potentes y profesionales que existen actualmente para realizar tareas estadísticas de todo tipo, desde las más elementales, hasta las más avanzadas. En particular, está desarrollado y mantenido por algunos de los más prestigiosos estadísticos actuales. Cuenta, además, con la ventaja de ser gratuito y de descarga e instalación sencillas. La asignatura introduce al alumno al manejo y uso a nivel principiante/medio del paquete de software R. Para ello se introducen tareas sencillas, pero relevantes, relacionadas con el manejo y análisis de datos en el contexto estadístico. Entre ellas se incluye el manejo de datos estadísticos, la simulación de variables aleatorias en los casos univariante y multivariante, la representación gráfica de datos univariantes y multivariantes, y la programación de tareas estadísticas con el lenguaje de programación incluído en R.

Prof. Alberto Muñoz García

Departamento de Estadística
Universidad Carlos III de Madrid

Área: Simulación y Computación Estadística.

Titulación: La asignatura se enmarca dentro de los programas de Licenciado en Ciencias y Técnicas Estadísticas.

Octubre de 2007.

4 horas semanales (teoría y práctica)
Asignatura de 4 créditos (40 horas)

PRERREQUISITOS Y CONOCIMIENTOS PREVIOS RECOMENDADOS

Se recomiendan conocimientos de estadística descriptiva a un nivel básico.

DESCRIPCIÓN GENERAL DE LA ASIGNATURA

El paquete estadístico R es uno de los más flexibles, potentes y profesionales que existen actualmente para realizar tareas estadísticas de todo tipo, desde las más elementales, hasta las más avanzadas. En particular, está desarrollado y mantenido por algunos de los más prestigiosos estadísticos actuales. Cuenta, además, con la ventaja de ser gratuito y de descarga e instalación sencillas. La asignatura introduce al alumno al manejo y uso a nivel principiante/medio del paquete de software R. Para ello se introducen tareas sencillas, pero relevantes, relacionadas con el manejo y análisis de datos en el contexto estadístico. Entre ellas se incluye el manejo de datos estadísticos, la simulación de variables aleatorias en los casos univariante y multivariante, la representación gráfica de datos univariantes y multivariantes, y la programación de tareas estadísticas con el lenguaje de programación incluído en R.

OBJETIVOS: CONOCIMIENTOS Y CAPACIDADES

Al finalizar la asignatura, el alumno será capaz de realizar operaciones de manejo de datos univariantes y multivariantes, incluyendo el almacenamiento, recuperación, creación de estructuras de datos y representación gráfica de los mismos, utilizando el programa R. Además estará capacitado para simular variables aleatorias diversas, programar diversas rutinas estadísticas, y realizar algunas tareas de estadística multivariante.

MATERIAL DOCENTE

Bibliografía obligatoria y recomendada, material de clase relativa al programa estadístico R, incorporando ejemplos prácticos de simulación y tareas estadísticas. Material complementaria consistente en enlaces web relacionados con la temática de la asignatura.

ACTIVIDADES DE EVALUACIÓN O TAREAS PRÁCTICAS

Las principales tareas de (auto)evaluación consisten en leer los tutoriales y/o lecturas complementarias que aparecen a lo largo del curso, así como realizar los ejercicios que se proponen. El nivel de profundización tanto en las (numerosas) lecturas que se proponen depende tanto del nivel de partida del estudiante como de los objetivos que se deseen alcanzar en relación con los conocimientos propuestos en la asignatura.

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El paquete estadístico R es uno de los más flexibles, potentes y profesionales que existen actualmente para realizar tareas estadísticas de todo tipo, desde las más elementales, hasta las más avanzadas. En particular, está desarrollado y mantenido por algunos de los más prestigiosos estadísticos actuales.

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15 aplicaciones del mundo real que emplean algoritmos genéticos

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15 aplicaciones del mundo real que emplean algoritmos genéticos

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Genetic Algorithm: A heuristic search technique used in computing and Artificial Intelligence to find optimized solutions to search problems using techniques inspired by evolutionary biology: mutation, selection, reproduction [inheritance] and recombination.

1. Automotive Design

Using Genetic Algorithms [GAs] to both design composite materials and aerodynamic shapes for race cars and regular means of transportation (including aviation) can return combinations of best materials and best engineering to provide faster, lighter, more fuel efficient and safer vehicles for all the things we use vehicles for. Rather than spending years in laboratories working with polymers, wind tunnels and balsa wood shapes, the processes can be done much quicker and more efficiently by computer modeling using GA searches to return a range of options human designers can then put together however they please.

2. Engineering Design

Getting the most out of a range of materials to optimize the structural and operational design of buildings, factories, machines, etc. is a rapidly expanding application of GAs. These are being created for such uses as optimizing the design of heat exchangers, robot gripping arms, satellite booms, building trusses, flywheels, turbines, and just about any other computer-assisted engineering design application. There is work to combine GAs optimizing particular aspects of engineering problems to work together, and some of these can not only solve design problems, but also project them forward to analyze weaknesses and possible point failures in the future so these can be avoided.

3. Robotics

Robotics involves human designers and engineers trying out all sorts of things in order to create useful machines that can do work for humans. Each robot's design is dependent on the job or jobs it is intended to do, so there are many different designs out there. GAs can be programmed to search for a range of optimal designs and components for each specific use, or to return results for entirely new types of robots that can perform multiple tasks and have more general application. GA-designed robotics just might get us those nifty multi-purpose, learning robots we've been expecting any year now since we watched the Jetsons as kids, who will cook our meals, do our laundry and even clean the bathroom for us!

4. Evolvable Hardware

Evolvable hardware applications are electronic circuits created by GA computer models that use stochastic (statistically random) operators to evolve new configurations from old ones. As the algorithm does its thing in the running model, eventually a circuit configuration will come along that does what the designer wants. Think of reconfigurable circuits in something like a space robot. It could use a built-in GA library and simulator to re-design itself after something like radiation exposure that messes up its normal configuration, or encounters a novel situation in which it needs a function it doesn't already have. Such GAs would enable self-adaptation and self-repair.

5. Optimized Telecommunications Routing

Do you find yourself frustrated by slow LAN performance, inconsistent internet access, a FAX machine that only sends faxes sometimes, your land line's number of 'ghost' phone calls every month? Well, GAs are being developed that will allow for dynamic and anticipatory routing of circuits for telecommunications networks. These could take notice of your system's instability and anticipate your re-routing needs. Using more than one GA circuit-search at a time, soon your interpersonal communications problems may really be all in your head rather than in your telecommunications system. Other GAs are being developed to optimize placement and routing of cell towers for best coverage and ease of switching, so your cell phone and blackberry will be thankful for GAs too.

6. Joke and Pun Generation

Among the linguistic applications of GAs - including a JAPE (automated pun generator) inspired STANDUP program to design communications strategies for people working with children who suffer communications disabilities - are GAs that search for jokes and puns. These come under the heading of "artificial creativity" and AI, but could prove very useful to class clowns and wannabe punsters whose public reputations depend upon being funnier than they actually are. These clever GAs will let you input a word you wish to pun or a subject you'd like to joke about, and will return a variety of solutions that just might lead to a lucrative career on the comedy club circuit!

7. Biomimetic Invention

Biomimicry or biomimetics is the development of technologies inspired by designs in nature. Since GAs are inspired by the mechanisms of biological evolution, it makes sense that they could be used in the process of invention as well. GAs rely primarily on something called implicit parallelism (like to like), using mutation and selection in secondary roles toward a design solution. GA programmers are working on applications that not only analyze the natural designs themselves for a return on how they work, but can also combine natural designs to create something entirely new that can have exciting applications.

8. Trip, Traffic and Shipment Routing

New applications of a GA known as the "Traveling Salesman Problem" or TSP can be used to plan the most efficient routes and scheduling for travel planners, traffic routers and even shipping companies. The shortest routes for traveling. The timing to avoid traffic tie-ups and rush hours. Most efficient use of transport for shipping, even to including pickup loads and deliveries along the way. The program can be modeling all this in the background while the human agents do other things, improving productivity as well! Chances are increasing steadily that when you get that trip plan packet from the travel agency, a GA contributed more to it than the agent did.

9. Computer Gaming

Those who spend some of their time playing computer Sims games (creating their own civilizations and evolving them) will often find themselves playing against sophisticated artificial intelligence GAs instead of against other human players online. These GAs have been programmed to incorporate the most successful strategies from previous games - the programs 'learn' - and usually incorporate data derived from game theory in their design. Game theory is useful in most all GA applications for seeking solutions to whatever problems they are applied to, even if the application really is a game.

10. Encryption and Code Breaking

On the security front, GAs can be used both to create encryption for sensitive data as well as to break those codes. Encrypting data, protecting copyrights and breaking competitors' codes have been important in the computer world ever since there have been computers, so the competition is intense. Every time someone adds more complexity to their encryption algorithms, someone else comes up with a GA that can break the code. It is hoped that one day soon we will have quantum computers that will be able to generate completely indecipherable codes. Of course, by then the 'other guys' will have quantum computers too, so it's a sure bet the spy vs. spy games will go on indefinitely.

11. Computer-Aided Molecular Design

The de novo design of new chemical molecules is a burgeoning field of applied chemistry in both industry and medicine. GAs are used to aid in the understanding of protein folding, analyzing the effects of substitutions on those protein functions, and to predict the binding affinities of various designed proteins developed by the pharmaceutical industry for treatment of particular diseases. The same sort of GA optimization and analysis is used for designing industrial chemicals for particular uses, and in both cases GAs can also be useful for predicting possible adverse consequences. This application has and will continue to have great impact on the costs associated with development of new chemicals and drugs.

12. Gene Expression Profiling

The development of microarray technology for taking 'snapshots' of the genes being expressed in a cell or group of cells has been a boon to medical research. GAs have been and are being developed to make analysis of gene expression profiles much quicker and easier. This helps to classify what genes play a part in various diseases, and further can help to identify genetic causes for the development of diseases. Being able to do this work quickly and efficiently will allow researchers to focus on individual patients' unique genetic and gene expression profiles, enabling the hoped-for "personalized medicine" we've been hearing about for several years.

13. Optimizing Chemical Kinetic Analysis

In the not-so rarified realm of fuels and engines for combustion technologies, GAs are proving very useful toward optimizing designs in transportation, aerospace propulsion and electrical generation. By being able to predict ahead of time the chemical kinetics of fuels and the efficiency of engines, more optimal mixtures and designs can be made available quicker to industry and the public. Some computer modeling applications in this area also simulate the effectiveness of lubricants and can pinpoint optimized operational vectors, and may lead to greatly increased efficiency all around well before traditional fuels run out.

14. Finance and Investment Strategies

In the current unprecedented world economic meltdown one might legitimately wonder if some of those Wall Street gamblers made use of GA-assisted computer modeling of finance and investment strategies to funnel the world's accumulated wealth into what can best be described as dot-dollar black holes. But then again, maybe they were simply all using the same prototype, which hadn't yet been de-bugged. It is possible that a newer generation of GA-assisted financial forecasting would have avoided the black holes and returned something other than bad debts the taxpayers get to repay. Who knows?

15. Marketing and Merchandising

We could think the word 'merchandising' just the way Mel Brooks said it in the "Space Balls" the movie. Space Balls the toilet paper. Space Balls the lunchbox. Space Balls the flame thrower (the kids love this one)... And laugh because it's close enough to reality to be funny. So it shouldn't surprise anyone that GAs are indeed being put to work to help merchandisers to produce products and marketing consultants design advertising and direct solicitation campaigns to sell stuff. Maybe this application of GAs could someday get us out of the financial black hole and get things moving again.

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15 Real-World Applications of Genetic Algorithms - Brainz

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Genetic Algorithm: A heuristic search technique used in computing and Artificial Intelligence to find optimized solutions to search problems using techniques inspired by evolutionary biology: mutation, selection, reproduction [inheritance] and recombination. 1. Automotive Design Using Genetic Algorithms [GAs] to both design composite materials and aerodynamic shapes for race cars and regular means of transportation (including ...

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Redes neuronales aplicadas al reconocimiento de imágenes

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curso sobre sistemas de recomendación donde están disponibles enlaces relativos a sistemas recomendadores y a datasets

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Lecture 2 slides ; Lecture 7 Slides ;Lecture 8 Slides; Lecture 8 mfile Lecture 9 Slides; Lecture 9 mfile Lecture 10 Slides; Lecture 10 mfile Lecture 11 mfile Extra Slides Lecture 7 ; Lecture 7 mfile Lecture 2 mfile Lecture 3 mfile Lecture 4 slides ; Lecture 4 mfile Lecture 5 mfile ; Code to visulalize Jester Data ; Example Data Lecture 6 mfile ; Saving and loading data example file

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elaborado por el Departamento de Estadística e Investigación Operativa de la Universidad de Granad

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Recomendación de productos basada en filtrado colaborativo

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Recomendación de productos basada en filtrado colaborativo

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Sistemas recomendadores basados en contenidos

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Sistemas recomendadores basados en contenidos

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From Socr

This activity demonstrates mixture modeling and expectation maximization (EM) applied to the problem of 2D point cluster segmentation.

Background

It may be useful to review the mathematics of Expectation Maximization and Mixture Modeling. In this activity, we will demonstrate how the EM and mixture modeling may be used to obtain cluster classification of points in 2D. There are problems where such segmentation is very important for solving a practical problem. 1D and 3D applications of the EM mixture modeling are also included at the end.

Exercise 1: SOCR Charts Activity

This exercise demonstrates the applications of expectation maximization and mixture modeling for cluster classification of points in 2D. Go to SOCR Charts and select Line Charts --> SOCR EM MixtureModelChart. The image below demonstrates the overall look-and-feel of the SOCR EM Mixture Model applet. Try adding several clusters of points and select different number of the kernels/mixtures you want to fit to this data. Notice the adaptive behavior of this iterative algorithm - the kernels will dynamically adjust to fit the data. The image below shows the main widgets/controls of this applet and the results of fitting a mixture of 3 kernels to the defaults data.

Data: You can enter data (paired X,Y observations) either via the Data-Tab, using copy-and-paste, or via the add random points button (RandomPts). This applet was designed specifically so that you may enter your own paired observations in tabular form. If you are not interested in data analysis, but want to explore more the properties of the EM mixture model, you may try the second SOCR applet (SOCR Experiments, select Mixture Model EM Experiment from the drop down list of SOCR Experiments on the top-left), which allows you to manually add points by clicking on the graphing canvas. At the end of this document, the step-by-step protocol is included for running the algorithm on any dataset.

Applet Specifications: You can fit one of two models to your data (Linear or elliptical Gaussian), see the GaussianMix button. Linear model will only show the main direction of variation for a sub-cluster. A Gaussian model will illustrate additional information, including the scope of the kernel coverage. The Normal button allows you to choose Slow, Normal or Fast speed for the iterative EM estimation. The ClearPts will remove all data and reset the applet. The InitKernels button re-initializes the kernels (location and size) and is useful for shaking the EM algorithm to escape the local minimum. A kernel is roughly a weighting function used in non-parametric techniques. Kernel locations are generally non trivial to choose - we use random initial kernel locations (InitKernels button). The drop-down list on the top-right allows you to select the number of kernels you want to fit to this data. There is no exact method for determining this number in all situations (manually or automatically). Typically, one uses the physical or biological properties of the studied data/process to determine the appropriate integer value. On the top, the Step, Run and Stop buttons have the natural functions associated with driving the iterative EM algorithm. The Segment button allows labeling/classification of the points once the EM algorithm has converged or stopped.

Segmentation Results: Once the EM algorithm converges to a visually satisfactory result you should stop the iterative process (Stop button) and click on the Segment button. You will obtain a color classification of all points in 2D based on which of the kernels is most likely to contain the point in its neighborhood. In addition to this visual classification, the Data tab-panel will contain a couple of result columns that contain the complete analytical description of the kernels (as 2D Gaussian), the mixture-model weight coefficients, the log-likelihood function (quantifying the match between the mixture model and the data), and color-coded membership of all data points to one of the kernels.

Exercise 2: 1D and 3D Examples of SOCR EM Mixture Modeling

You may also see the action of the same SOCR EM Mixture modeling algorithm for analyzing 1D or 3D data.

For 1D data, you can see the EM mixture model fitting used by the SOCR Modeler to fit a polynomial, spectral or distribution model for randomly sampled or observed data. To see this, go to SOCR Modeler and select MixedFit_Modeler from the drop-down list of models on the top-left. The figure below shows the result of fitting a 3-kernel Mixture of Normal (Gaussian) distributions to the histogram of a random sample of 100 Cauchy random variables.

A demonstration of a 3D data analysis using the SOCR EM Mixture model is included in the LONI Viz Manual. This shows how 3D brain imaging data may be segmented into three tissue types (White Matter, Gray Matter and Cerebra-spinal Fluid). This is achieved by LONI Viz (Dinov et al., 2006) sending the segmentation tasks to SOCR and SOCR returning back the 3D segmented volumes, which are superimposed dynamically on top of the initial anatomical brain imaging data in real time. The figure below illustrates this functionality. Other external computational tools could also invoke SOCR statistical computing resources directly by using the SOCR JAR binaries and the SOCR Documentation.

How stable is the EM algorithm in finding a solution? Does this solution appear to be unique?

What affects the convergence properties of the EM algorithm (data characteristics, number and properties of the starting initial kernel(s), etc.)?

Step-by-Step Data Analysis Protocol

The following 10 steps show the protocol for entering and analyzing new data using the SOCR EM Mixture model Chart tool.

Go to: http://www.socr.ucla.edu/htmls/SOCR_Charts.html --> Line Charts --> SOCR EM Mixture Chart.

ClearPnts (remove default data).

Data-Tab: Click the top-left cell & paste in your data (in two column tabular format) using the paste button.

Mapping Tab: Map the two columns (C1 and C2) accordingly to X & Y axes.

Click UpdateChart button.

Select Number of Kernels (drop-down list of integers on the top-right).

InitKernels (choose an appropriate starting configuration - could be arbitrary)

Use the Step or Run buttons to go one iteration or continuously in the EM Mixture algorithm.

Use Stop button to stop (for continuous running).

Click the Segment button to find point association to kernels.

Finally, you can right-click on the SOCR Graph to adjust the display or save/print the result.

Your quantitative results will be stored as new columns in the data table ( Data Tab).

Manual Kernel Initialization

Note that you can manually initialize the Gaussian kernels as follows: To add (up to 9) kernels manually, hold down the ALT key, click and drag the mouse to select a rectangle for each of the kernels. While holding the ALT key, you can repeat this to add more manually chosen kernels (up to 9). There will be 2 new buttons that appear in this manual kernel-selection mode. The removeLastKernel button will remove the last manually added kernel, and the autoInitKernel button will switch back to the auto kernel-selection mode, where kernels are randomly chosen. The figure below illustrates the manual kernel selection process

Data Import Format

Remember that in the 2D mixture modeling applet you only need 2D data (2 columns). If you have more remove the unnecessary columns first (e.g., using Excel), or load all columns but later specify which 2 columns shoud be considered as X and Y. When File-importing data, note that your data must be in CSV format. If you have a header Column, it must start with a hashtag (#), like this:

#X	Y
11	73
20	88
19	73
15	65
21	57
26	101
24	117
35	106
37	96

The easiest way is to copy-paste only the values (no headers) into the applet by clicking on the first cell (1,1) and clicking the paste button (do not paste in data using short keys), and then follow the step-by-step protocol to generate the plot. Remember after you paste in (or File-load in) the data, you need to go to the Mapping Tab to select your 2 columns (X,Y), click " Update Chart ", etc., according to the step-by-step protocol.

Try this protocol with the SOCR Knee Pain dataset.

References

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socr edumaterials activities 2d pointsegmentation em mixture

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socr edumaterials activities 2d pointsegmentation em mixture

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ap statistics curriculum 2007 estim mom mle

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SOCR EduMaterials Activities 2D PointSegmentation EM Mixture

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This activity demonstrates mixture modeling and expectation maximization (EM) applied to the problem of 2D point cluster segmentation. It may be useful to review the mathematics of Expectation Maximization and Mixture Modeling. In this activity, we will demonstrate how the EM and mixture modeling may be used to obtain cluster classification of points in 2D.

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Ampliación de Análisis de Datos Multivariantes del Departamento de Estadística e Investigación Operativa de la Universidad de Granada

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K-means mediante un ejemplo de cartas de póker

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K-means mediante un ejemplo de cartas de póker

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Wiki de Técnicas de Aprendizaje Estadístico

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Wiki de Técnicas de Aprendizaje Estadístico

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Uno de los datos de evaluación que muestra Weka en las salidas de los algoritmos de clasificación es el área ROC.

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Curva ROC - Wikipedia, la enciclopedia libre

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El análisis de la curva ROC, o simplemente análisis ROC, proporciona herramientas para seleccionar los modelos posiblemente óptimos y descartar modelos subóptimos independientemente de (y antes de especificar) el coste de la distribución de las dos clases sobre las que se decide.

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La contribución de las reglas de asociación a la minería de datos

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La contribución de las reglas de asociación a la minería de datos

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Weka is a collection of machine learning algorithms for data mining tasks. It contains tools for data preparation, classification, regression, clustering, association rules mining, and visualization.

Found only on the islands of New Zealand, the Weka is a flightless bird with an inquisitive nature. The name is pronounced like this, and the bird sounds like this.

Weka is open source software issued under the GNU General Public License.

We have put together several free online courses that teach machine learning and data mining using Weka. The videos for the courses are available on Youtube.

Weka supports deep learning!

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Weka 3 - Data Mining with Open Source Machine Learning Software in Java

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Weka is a collection of machine learning algorithms for data mining
tasks. It contains tools for data preparation, classification, regression, clustering, association
rules mining, and visualization.

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Welcome to the UC Irvine Machine Learning Repository!

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Welcome to the UC Irvine Machine Learning Repository!

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We currently maintain 398 data sets as a service to the machine learning community. You may view all data sets through our searchable interface. Our old web site is still available, for those who prefer the old format. For a general overview of the Repository, please visit our About page.

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WEKA

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Abstract

The technology for building knowledge-based systems by inductive inference from examples has been demonstrated successfully in several practical applications. This paper summarizes an approach to synthesizing decision trees that has been used in a variety of systems, and it describes one such system, ID3, in detail. Results from recent studies show ways in which the methodology can be modified to deal with information that is noisy and/or incomplete. A reported shortcoming of the basic algorithm is discussed and two means of overcoming it are compared. The paper concludes with illustrations of current research directions.

Key words

classification induction decision trees information theory knowledge acquisition expert systems

References

Pearl, J. (1978a). Entropy, information and rational decisions (Technical report). Cognitive Systems Laboratory, University of California, Los Angeles.

© Kluwer Academic Publishers 1986

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The technology for building knowledge-based systems by inductive inference from examples has been demonstrated successfully in several practical applications. This paper summarizes an approach to synthesizing decision trees that has been used in a variety of systems, and it describes one such system, ID3, in detail.

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Programación Avanzada

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Programación básica