En palabras de Marichal Plasencia, descritas en la tesis escrita el año 1999 titulada “Diseño de políticas de identificación y control de robots basadas en redes neuronales y sistemas neuro-fuzzy”, las redes neuronales generalmente han sido implementadas mediante la programación sobre computadoras digitales, sin embargo ya en estos días empiezan a proliferar implementaciones en hardware, ya sea mediante montajes electrónicos o incorporando dispositivos ópticos. Tales ingenios, presentan un paso importante hacia la consecución de mayores velocidades de procesamiento, así como un camino hacia la popularización de las mismas, siendo ésta un área de investigación muy activa. En relación con la clasificación de las redes neuronales podría establecerse una división de las mismas en función de su arquitectura y forma de procesar las señales en tres clases. (1) La primera clase de redes se conoce con el nombre de redes neuronales estáticas. En esta clase se puede encontrar la red Multicapa de Perceptrones, la red de Funciones de Base Radial, Red Neuronal Probabilística. Todas ellas tienen como característica común el no poseer memoria, es decir, sólo son capaces de transformar un conjunto de entradas en un conjunto de salidas, de tal manera que una vez establecidos todos los parámetros de la red las salidas únicamente dependen de las entradas. Este tipo de redes se ha empleado con éxito en muchos problemas de clasificación, como funciones lógicas, así como en el campo de la aproximación funcional. (2) Como segunda clase de redes neuronales figuran las redes neuronales dinámicas. Estas a diferencia de las anteriores permiten establecer una relación entre salidas y entradas o salidas y entradas previas. Esto añade cierta memoria a estas redes. Como ejemplos de este tipo de redes se encuentran la red de Hopfield, la red de retardos en el tiempo, la red de tiempo discreto, etc. Las redes neuronales dinámicas se han revelado útiles en problemas de modelización de la dinámica directa e inversa de sistemas complejos, tales como robots, cohetes, naves espaciales, etc., así como en el modelado de circuitos secuenciales y en la conversión de texto a voz. (3) En este punto se destacan las denominadas redes auto-organizativas, en las cuales los nodos vecinos dentro de la red neuronal compiten en actividad por medio de las interacciones mutuas laterales, y evolucionan adaptativamente hacia detectores específicos de las diferentes señales de entrada. El aprendizaje en este caso se denomina aprendizaje competitivo, no supervisado o autoorganizativo. Estas se han aplicado con éxito en problemas de reconocimiento de patrones, control de procesos e incluso en el procesamiento de información semántica.
Para la comprensión de la red de Hopfield es necesario realizar un breve recorrido acerca de los conceptos que rodean al término “memoria asociativa.” Según Sossa y Barrón, en el artículo escrito el año 2003 titulado “Reconocimiento de objetos por su recuerdo”, una memoria asociativa es un dispositivo electrónico, programa computacional o modelo matemático, que permite recuperar patrones a través de su recuerdo por medio de otros patrones llamados llaves; a los patrones que se recuperan se les llama patrones de información. En una primera etapa, la memoria es construida a través de un conjunto de patrones de información junto con sus llaves respectivas. Al conjunto de asociaciones (llave, patrón) se le llama conjunto de entrenamiento de la memoria asociativa. En una segunda etapa, a la memoria se le presenta una llave. Según Hassoun, en el libro escrito el año 1993 titulado “Memorias neuronales asociativas: Teoria e implementación”, si la memoria asociativa es capaz de recordar todos los patrones del conjunto de entrenamiento, se dice que dicha memoria tiene la capacidad básica de recuerdo o recuperación. A la cantidad de patrones que se pueden almacenar en la memoria sin alterar su capacidad básica de recuerdo se le llama capacidad de la memoria asociativa. En general, las memorias asociativas más eficientes desarrolladas hasta el momento, son capaces de reconocer patrones del conjunto de entrenamiento a través de versiones alteradas de los mismos, pero en presencia de ruido ya sea aditivo o substractivo. El ruido aditivo se caracteriza por alterar un patrón de manera que sus componentes se ven sesgadas hacia valores mayores. El ruido substractivo, por otro lado, altera un patrón de manera que sus componentes se ven sesgadas hacia valores menores. El ruido combinado o mezclado, que es el que se presenta en la realidad, altera un patrón de manera que sus valores se ven cargados en forma aleatoria hacia valores mayores o menores. En resumen, según Ricardo Barrón, en la tesis escrita el año 2006 titulada “Memorias asociativas y redes neuronales morfológicas para la recuperación de patrones”, una memoria asociativa ideal debe tener las siguientes características: (1) Capacidad de almacenamiento ilimitada. (2) Recuperación básica. (3) Recuperación robusta. (4) Soportes de tamaño máximo para cada patrón llave del conjunto de entrenamiento. (5) Una forma de representación sencilla que implique un costo computacional pequeño. Las aplicaciones de las memorias asociativas con características ideales son numerosas. Una de ellas es el reconocimiento de personas a partir de las fotografías. En este caso sería muy interesante recuperar la fotografía de una persona dada, a partir de otra fotografía con o sin lentes, con o sin bigote, por ejemplo.
From simple charts to complex maps and infographics, Brian
Suda's round-up of the best – and mostly free – tools has everything you
need to bring your data to life
One of the most common questions I get asked is how to get
started with data visualisations. Beyond following blogs, you need to
practise – and to practise, you need to understand the tools available.
In this article, I want to introduce you to 20 different tools for
creating visualisations: from simple charts to complex graphs, maps and
infographics. Almost everything here is available for free, and some you
have probably installed already.
Entry-level tools
At the entry level, we'll be looking at unexpected uses for familiar
tools. You might not think of Excel as a visualisation package, for
example – but it's capable of surprisingly complex results. If you are
just getting started, these tools are musts to understand. If you deal
with visualisations every day, you'll quickly find yourself advancing
beyond them, but not everyone will, so you'll always be dealing with
data coming in from sources you'd rather not deal with.
1. Excel
It isn't graphically flexible, but Excel is a good way to explore data: for example, by creating 'heat maps' like this one
You can actually do some pretty complex things with Excel,
from 'heat maps' of cells to scatter plots. As an entry-level tool, it
can be a good way of quickly exploring data, or creating visualisations
for internal use, but the limited default set of colours, lines and
styles make it difficult to create graphics that would be usable in a
professional publication or website. Nevertheless, as a means of rapidly
communicating ideas, Excel should be part of your toolbox.
Excel comes as part of the commercial Microsoft Office suite, so if you don't have access to it, Google's spreadsheets – part of Google Docs and Google Drive – can do many of the same things. Google 'eats its own dog food', so the spreadsheet can generate the same charts as the Google Chart API. This will get your familiar with what is possible before stepping off and using the API directly for your own projects.
2. CSV/JSON
CSV (Comma-Separated Values) and JSON
(JavaScript Object Notation) aren't actual visualisation tools, but
they are common formats for data. You'll need to understand their
structures and how to get data in or out of them. All of the following
toolkits accept at least one of the two formats as input.
Online visualisations
3. Google Chart API
The portion of the toolset for static images has been deprecated, so the Google Chart Tools
site now only offers tools for dynamic charts. They are robust and work
on all browsers supporting SVG, canvas and VML, but one big problem is
that they are generated on the client side, which creates problems for
devices without JavaScript, offline use – or just when saving in
different formats. Static images didn't have the same issues, so I'm
sorry to see them go.
However, the API has just about everything but the kitchen sink, from
bar charts and line graphs to maps and even QR codes. You will probably
find the right visualisation for your needs as long as you are
comfortable with the Google look and not in need of extreme
customisation. As a jumping-off point, it is a great tool to know how to
use.
The portion for static images has been deprecated, but the Google Chart API is a good way to create dynamic visualisations
4. Flot
Flot is a great library for
line graphs and bar charts. It works in all browsers that support canvas
– which means most of the popular ones, with some extra libraries to
get canvas to work as VML in older browsers. It's a jQuery library, so
if you're already familiar with jQuery, it's easy to manipulate the
calls back, styling and behaviour of the graphics.
The nice thing about Flot is that you have access to plenty of callback
functions so you can run your own code and style the results when
readers hover, click, mouseout, and other common events. This gives you
much more flexibility than other charting packages, but there is a
steeper learning curve. Flot is also limited to line and bar charts. It
doesn't have as many options as other libraries, but it performs common
tasks really well.
It's specialised on line and bar charts, but if you know jQuery, Flot is a powerful option
5. Raphaël
Raphaël is another great
JavaScript library for creating charts and graphs. The biggest
difference to other libraries is that it focuses on SVG and VML as
output. This has pros and cons. Since SVG is a vector format, the
results look great at any resolution; but since it creates a DOM node
for each element, it can be slower than creating rasterised images via
canvas. However, the upside is that you can interact with each DOM
element and attach events, just like HTML.
The website includes plenty of demos to show how easily Raphaël can
create common charts and graphs but, because it can also render
arbitrary SVG, it has the ability to create some very complex
visualisations for which you might otherwise have to resort to other
vector tools such as Illustrator or Inkscape.
Raphaël is a great way to create vector-based charts: slower than raster-based tools, but it's capable of complex results
6. D3
D3 (Data-Driven Documents) is another
JavaScript library that supports SVG rendering. The examples go beyond
the simple bar charts and line graphs to much more complicated Voronoi
diagrams, tree maps, circular clusters and word clouds. It's another
great tool to have in your toolbox, but I wouldn't always recommend D3
as the go-to library. It's great for creating very complicated
interactions – but just because you can, it doesn't mean you should.
Knowing when to stay simple is a big part of choosing the right
visualisation tool.
D3 is capable of creating very complex output – but it's best saved for special cases, not everyday use
7. Visual.ly
If you are in need of an infographic rather than a data visualisation, there is a new crop of tools out there to help. Visual.ly
is probably the most popular of these. Although primarily an online
marketplace for infographic designers, its Create option lets you pick a
template, connect it to your Facebook or Twitter account and get some
nice cartoon graphics back. While the results are currently limited,
it's a useful source of inspiration – both good and bad – and a site I
expect to see grow in future, accepting more formats and creating more
interesting graphics.
Visual.ly acts both as an online marketplace and simple creation tool for infographics
Interactive GUI controls
What happens when data visualisations become so interactive they
themselves become GUI controls? As online visualisations evolve,
buttons, drop-downs and sliders are morphing into more complex interface
elements, such as little handles that let you manipulate ranges,
changing the input parameters and the data at the same time. Controls
and content are becoming one. The following tools will help you explore
the possibilities this offers.
8. Crossfilter
As we build more complex tools to enable clients to wade through
their data, we are starting to create graphs and charts that double as
interactive GUI widgets. JavaScript library Crossfilter
can be both of these. It displays data, but at the same time, you can
restrict the range of that data and see other linked charts react.
Crossfilter in action: by restricting the input range on
any one chart, data is affected everywhere. This is a great tool for
dashboards or other interactive tools with large volumes of data behind
them
9. Tangle
The line between content and control blurs even further with Tangle.
When you are trying to describe a complex interaction or equation,
letting the reader tweak the input values and see the outcome for
themselves provides both a sense of control and a powerful way to
explore data. JavaScript library Tangle is a set of tools to do just
this. Dragging on variables enables you to increase or decrease their
values and see an accompanying chart update automatically. The results
are only just short of magical.
Tangle creates complex interactive graphics. Pulling on any
one of the knobs affects data throughout all of the linked charts. This
creates a real-time feedback loop, enabling you to understand complex
equations in a more intuitive way
Mapping
Mapping used to be a really hard task on the web. Then Google Maps came along and blew away every preconceived notion of how an online map should work. Soon after, Google released its Maps API, which allowed any developer to embed maps in their own sites.
Since then, the market has matured a great deal. There are now several
options out there if you are looking to embed custom mapping solutions
in your own data visualisation project, and knowing when to choose one
over the others is a key business decision. Sure, you can probably
shoehorn everything you need into any of these maps, but it's best not
to have a hammer and view every problem as a nail.
10. Modest Maps
Modest Maps is a tiny mapping
library. Weighing in at only 10kB, it is the smallest of options
discussed here. This makes it very limited in its basic form – but don't
let that fool you: with a few extensions, such as Wax, you can really make this library sing. This is a product of Stamen, Bloom and MapBox, so you know it has an interesting track record.
Teamed with additional libraries, such as MapBox's Wax (pictured), the tiny Modest Maps becomes a powerful tool
11. Leaflet
Brought to you by the CloudMade team, Leaflet
is another tiny mapping framework, designed to be small and lightweight
enough to create mobile-friendly pages. Both Leaflet and Modest Maps
are open source projects, which makes them ideal for using in your own
sites: with a strong community backing them, you know they won't
disappear any time soon.
Leaflet is a small, lightweight JavaScript library ideal for mobile-friendly projects
12. Polymaps
Polymaps is another mapping
library, but it is aimed more squarely at a data visualisation audience.
Offering a unique approach to styling the the maps it creates,
analagous to CSS selectors, it's a great resource to know about.
Aimed more at specialist data visualisers, the Polymaps library creates image and vector-tiled maps using SVG
13. OpenLayers
OpenLayers is probably the most
robust of these mapping libraries. The documentation isn't great and the
learning curve is steep, but for certain tasks nothing else can
compete. When you need a very specific tool no other library provides,
OpenLayers is always there.
It isn't easy to master, but OpenLayers is arguably the most complete, robust mapping solution discussed here
14. Kartograph
Kartograph's tag line is 'rethink mapping' and that is exactly what its developers are doing. We're all used to the Mercator projection,
but Kartograph brings far more choices to the table. If you aren't
working with worldwide data, and can place your map in a defined box,
Kartograph has the options you need to stand out from the crowd.
Kartograph's projections breathe new life into our standard slippy maps
15. CartoDB
Finally, CartoDB is a must-know
site. The ease with which you can combine tabular data with maps is
second to none. For example, you can feed in a CSV file of address
strings and it will convert them to latitudes and longitudes and plot
them on a map, but there are many other users. It's free for up to five
tables; after that, there are monthly pricing plans.
CartoDB provides an unparalleled way to combine maps and tabular data to create visualisations
Charting fonts
One recent trend in web development is to merge symbol fonts with
font embedding to create beautifully vectorised icons. They scale and
print perfectly, and look great on newer Retina devices too. A few of
these fonts, such as FF Chartwell and Chartjunk,
have been specially crafted for the purpose of displaying charts and
graphs. They have the usual problem of OpenType not being fully
supported in all browsers, but they're something to consider in the near
future.
Getting serious
If you're getting serious about data visualisations, you need to move
beyond simple web-based widgets onto something more powerful. This
could mean desktop applications and programming environments.
16. Processing
Processing has become the poster
child for interactive visualisations. It enables you to write much
simpler code which is in turn compiled into Java. There is also a Processing.js
project to make it easier for websites to use Processing without Java
applets, plus a port to Objective-C so you can use it on iOS. It is a
desktop application, but can be run on all platforms, and given that it
is now several years old, there are plenty of examples and code from the
community.
Processing provides a cross-platform environment for creating images, animations, and interactions
17. NodeBox
NodeBox is an OS X application for
creating 2D graphics and visualisations. You need to know and understand
Python code, but beyond that it's a quick and easy way to tweak
variables and see results instantly. It's similar to Processing, but
without all the interactivity.
NodeBox is a quick, easy way for Python-savvy developers to create 2D visualisations
Pro tools
At the opposite end of the spectrum from Excel are professional
data-analysis tools. If you are serious about data visualisation, you
need to be at least aware of, if not proficient in, some of these.
Industry-standard tools such as SPSS and SAS
require expensive subscriptions, so only large institutions and
academia have access to them, but there are several free alternatives
with strong communities. The open-source software is just as good, and
the plug-ins and support are better.
18. R
How many other pieces of software have an entire search engine dedicated to them? A statistical package used to parse large data sets, R
is a very complex tool, and one that takes a while to understand, but
has a strong community and package library, with more and more being
produced. The learning curve is one of the steepest of any of these
tools listed here, but you must be comfortable using it if you want to
get to this level.
A powerful free software environment for statistical computing and graphics, R is the most complex of the tools listed here
19. Weka
When you get deeper into being a data scientist, you will need to
expand your capabilities from just creating visualisations to data
mining. Weka is a
good tool for classifying and clustering data based on various
attributes – both powerful ways to explore data – but it also has the
ability to generate simple plots.
A collection of machine-learning algorithms for data-mining tasks, Weka is a powerful way to explore data
20. Gephi
When people talk about relatedness, social graphs and co-relations,
they are really talking about how two nodes are related to one another
relative to the other nodes in a network. The nodes in question could be
people in a company, words in a document or passes in a football game,
but the maths is the same. Gephi, a
graph-based visualiser and data explorer, can not only crunch large data
sets and produce beautiful visualisations, but also allows you to clean
and sort the data. It's a very niche use case and a complex piece of
software, but it puts you ahead of anyone else in the field who doesn't
know about this gem.
Gephi in action. Coloured regions represent clusters of data that the system is guessing are similar
Further reading
A great Tumblr blog for visualisation examples and inspiration: vizualize.tumblr.com
Nicholas Felton's annual reports are now infamous, but he also has a Tumblr blog of great things he finds.
From the guy who helped bring Processing into the world: benfry.com/writing
Stamen Design is always creating interesting projects: stamen.com
Eyeo Festival brings some of the greatest minds in data visualisation together in one place, and you can watch the videos online.
