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Level 4: Individual, Networked, Social Interaction with Content (Me to We with Museum)

This is the level where web 2.0 sits. Individuals still do their interacting with the content singly, but their interactions are available for comment and connection by other users. And the architecture promotes these connections automatically. For example, on Netflix, when you rate a movie highly, you don’t just see how others have rated it; Netflix recommends other movies to you based on what like-minded viewers also rated highly. By networking the ratings, tags, or comments individuals place on content, individuals are linked to each other and form relationships around the content. A successful level 4 experience uses social interaction to enhance the individual experience; it gets better the more people use it. The social component is a natural extension of the individual actions. Which means, perhaps, users are ready for…

Level 5: Collective Social Interaction with Content (We in Museum)

This is the holy grail of social discourse, where people interact directly with each other around content. Personal discussions, healthy web bulletin boards and list-servs fall in this category. Healthy level 5 experiences promote respect among users, encourage community development, and support interaction beyond the scope of the content.

So how do we level up?

The good news is that moving up the levels does not require new content. At all levels, the interaction and participation can occur around pre-existing content. A lot of museums top out at level 2 or 3, imagining that offering people heightened opportunities to interact with content, or to create their own content, is enough. Granted, I’m not sure if social engagement is the goal for interactive designers. But with side benefits like deeper connection with the content, greater appreciation for the museum as a social venue, and heightened awareness of other visitors, it deserves a place at the drafting table.

We begin with the
nature of a network itself. In any network, there will be three major
elements:

–        Entities, that is, the things that are connected that
send and receive signals

–        Connections, that is, the link or channel between
entities (may be represented as physical or virtual)

–        Signals, that is, the message sent between entities.
Note that meaning is not inherent in signal and must be interpreted by
the receiver

In an environment of
this description, then, networks may vary according to a certain set of
properties:

–        Density, or how many other entities each entity is
connected to

–        Speed, or how quickly a message moves to an entity (can
be measured in time or ‘hops’)

–        Flow, or how much information an entity processes, which
includes messages sent and received in addition to transfers of messages for
other entities

–        Plasticity, or, how frequently connections created,
abandoned

–        Degree of connectedness – is a function of density,
speed, flow and plasticity

Given this description
of networks, we can identify the essential elements of network
semantics.

First, context,
that is, the localization of entities in a network. Each context is unique


–


entities see the network
differently, experience the world differently. Context is required in order to
interpret signals, that is, each signal means something different depending on
the perspective of the entity receiving it.

Second, salience,
that is, the relevance or importance of a message. This amounts to the
similarity between one pattern of connectivity and another. If a signal creates
the activation of a set of connections that were previously activated, then this
signal is salient. Meaning is created from context and messages via salience.

Third,
emergence, that is, the development of patterns in the network. Emergence
is a process of resonance or synchronicity, not creation. We do not
create emergent phenomena. Rather emergence phenomena are more like
commonalities in patterns of perception. It requires an interpretation to be
recognized; this happens when a pattern becomes salient to a
perceiver.

Fourth, memory
is the persistence of patterns of connectivity, and in particular, those
patterns of connectivity that result from, and result in, salient signals or
perceptions.

Connective semantics is
therefore derived from what might be called connectivist ‘pragmatics’,
that is, that actual use of networks in practice. In our particular
circumstance we would examine how networks are used to support learning. The
methodology employed is to look at multiple examples and to determine what
patterns may be discerned. These patterns cannot be directly communicated. But
instances of these patterns may be communicated, thus allowing readers to (more
or less) ‘get the idea’.

For example, in order
to illustrate the observation that ‘knowledge is distributed’ I have frequently
appealed to the story of the 747. In a nutshell, I ask, “who knows how to make a
747 fly from London to Toronto?” The short answer is that nobody knows
how to do this
–
no one person could design a 747, manufacture
the parts (including tires and aircraft engines), take it off, fly it properly,
tend to the passengers, navigate, and land it successfully. The knowledge is
distributed across a network of people, and the phenomenon of ‘flying a
747’ can exist at all only because of the connections between the constituent
members of that network.

Or, another story: if
knowledge is a network phenomenon, then, is it necessary for all the elements of
a bit of knowledge to be stored in one’s own mind? Karen Stephenson writes, “I store my knowledge in
my friends.” This assertion constitutes an explicit recognition that what we
‘know’ is embedded in our network of connections to each other, to resources, to
the world. Siemens writes,
“Self-organization on a personal level is a micro-process of the larger
self-organizing knowledge constructs created within corporate or institutional
environments. The capacity to form connections between sources of information,
and thereby create useful information patterns, is required to learn in our
knowledge economy.”

This approach to
learning has been captured under the heading of ‘connectivism’.
In his paper of the same name, George Siemens articulates the major
theses:

• 
  

  Learning and knowledge rests in diversity of opinions.
  

  
  
• 
  

  Learning is a process of connecting specialized nodes or information
  sources.

  
  
• 
  

  Learning may reside in non-human appliances.

  
  
• 
  

  Capacity to know more is more critical than what is currently
  known

  
  
• 
  

  Nurturing and maintaining connections is needed to facilitate
  continual learning.

  
  
• 
  

  Ability to see connections between fields, ideas, and concepts is a core
  skill.

  
  
• 
  

  Currency (accurate, up-to-date knowledge) is the intent of all
  connectivist learning activities.

  
  
• 
  

  Decision-making is in
  itself a learning process. Choosing what to learn and the meaning of incoming
  information is seen through the lens of a shifting reality. While there is a
  right answer now, it may be wrong tomorrow due to alterations in the information
  climate affecting the decision.

Is this the definitive
statement of network learning? Probably not. But it is developed in the classic
mold of network learning, through a process of immersion into the network and
recognition of salient patterns. What sort of network? The following list is
typical of what might be called ‘network’ practices online (I won’t draw these
out in detail because there are dozens of papers and presentations that do
this):

Practice: Content
Authoring and Delivery

–        Numerous content authoring
systems on the web…

–        Weblogs – Blogger, Wordpress,
LiveJournal, Moveable Type, more

–        Content Management Systems –
Drupal, PostNuke, Plone, Scoop, and many more…

–        Audio – Audacity – and
audioblogs.com – and Podcasting

–        Digital imagery and video – and
let’s not forget Flickr

–        Collaborative authoring –
Writely, Hula, the wiki

Practice: Organize,
Syndicate Sequence, Deliver

–        Aggregation of content metadata
– RSS and Atom, OPML, FOAF, even DC and LOM

–        Aggregators – NewsGator,
Bloglines – Edu_RSS

–        Aggregation services –
Technorati, Blogdex, PubSub

–        More coming – the Semantic
Social Network

Practice: Identity and
Authorization

–        A raft of centralized (or
Federated) approaches – from Microsoft Passport to Liberty to
Shibboleth

–        Also various locking and
encryption systems

–        But nobody wants
these

–        Distributed DRM – Creative
Commons, ODRL…

–        Distributed Identification
management – Sxip, LID…

Practice: Chatting,
Phoning, Conferencing

–        Bulletin board systems and chat
rooms, usually attached to the aforementioned content management systems such as
Drupal, Plone, PostNuke, Scoop

–        Your students use this, even if
you don’t: ICQ, AIM, YIM, and some even use MSN Messenger

–        Audioconferencing? Skype…Or
NetworkEducationWare…

–        Videoconferencing? Built into
AIM… and Skype

“What happens,” I
asked, “when online learning ceases to be like a medium, and becomes more like a
platform? What happens when online learning software ceases to be a type of
content-consumption tool, where learning is "delivered," and becomes more like a
content-authoring tool, where learning is created?”

The answer turns out to
be a lot like Web 2.0: “The model of e-learning as being a type of content,
produced by publishers, organized and structured into courses, and consumed by
students, is turned on its head. Insofar as there is content, it is used rather
than read— and is, in any case, more likely to be produced by students than
courseware authors. And insofar as there is structure, it is more likely to
resemble a language or a conversation rather than a book or a
manual.”

In the days since this
shift was recognized a growing community of educators and developers has been
gathering around a model of online learning typified by this diagram authored by Scott
Wilson (and remixed by various others since then):

Figure 1: Future
VLE

http://www.cetis.ac.uk/members/scott/blogview?entry=20050125170206

In an environment such
as this, the nature of design changes. In a typical computer program, the design
will be specified with an algorithm or flowchart. Software will be described as
performing a specific process, with specified (and often controlled) inputs and
outputs. In a distributed environment, however, the design is no longer defined
as a type of process. Rather, designers need to characterize the nature of the
connections between the constituent entities.

What are the core principles
that will characterize such a description? The internet itself illustrates a
sound set of principles, grounded by two major characteristics: simple services
with realistic scope. “Simple service or simple devices with realistic scope are
usually able to offer a superior user experience compared to a complex,
multi–purpose service or device.” Or as David Weinberger describes the network:
small pieces, loosely joined.

In practice, these
principles may be realized in the following design principles. It is worth
noting at this juncture that these principles are intended to describe not only
networks but also network learning, to show how network learning differs from
traditional learning. The idea is that each principle confers an advantage over
non-network systems, and that the set, therefore, may be used as a means of
evaluating new technology. This is a tentative set of principles, based
on observation and pattern recognition. It is not a definitive list, and indeed,
it is likely that there cannot be a definitive list.

1. Effective networks
are decentralized. Centralized networks have a characteristic ‘star’
shape, where some entities have many connections while the vast majority have
few. This is typical of, say a broadcast network or the method of a teacher in a
classroom. Decentralized networks, by contrast, form a mesh. The weight of
connections and the flow of information is distributed. This balanced load
results in a more stable network, with no single point of
failure.

2. Effective networks
are distributed. Network entities reside in different physical locations.
This reduces the risk of network failure. It also reduces need for major
infrastructure, such as powerful servers, large bandwidth, and massive storage.
Examples of distributed networks include peer-to-peer networks, such as Kazaa, Gnutella and content syndication networks,
such as RSS. The
emphasis of such systems is on sharing, not copying; local copies, if they
exist, are temporary.

3. Effective networks
disintermediated. That is, they eliminate ‘mediation’, the barrier
between source and receiver. Examples of disintermediation include the bypassing
of editors, replacing peer review prior to publication with recommender systems
subsequent to publication. Or of the replacement of traditional news media and
broadcasters with networks of news
bloggers. And, crucially, the removal of the intermediate teacher that
stands between knowledge and the student. The idea is to, where possible,
provide direct access to information and services. The purpose of mediation, if
any, is to manage flow, not information, to reduce the volume of information,
not the type of information.

4. In effective
networks, content and services are disaggregated. Units of content should
be as small as possible and content should not be ‘bundled’. Instead, the
organization and structure of content and services is created by
the receiver
. This allows the integration of new
information and services with the old, of popular news and services with those
in an individual’s particular niche interests. This was the idea behind learning
objects; the learning object was sometimes defined as the ‘smallest possible
unit of instruction’. The assembly of learning objects into pre-packaged
‘courses’ defeats this, however, obviating any advantage the disaggregating of
content may have provided.

5. In an effective
network, content and services are dis-integrated. That is to say,
entities in a network are not ‘components’ of one another. For example, plug-ins
or required software to be avoided. What this means in practice is that the
structure of the message is logically distinct from the type of entity sending
or receiving it. The message is coded in a common ‘language’ where the code is
open, not proprietary. So no particular software or device is needed to receive
the code. This is the idea of standards, but where standards evolve rather than
being created, and where they are adopted by agreement, not
requirement.

6. An effective network
is democratic. Entities in a network are autonomous; they have the
freedom to negotiate connections with other entities, and they have the freedom
to send and receive information. Diversity in a network is an asset, as it
confers flexibility and adaptation. It also allows the network as a whole to
represent more than just the part. Control of the entities in a network,
therefore, should be impossible. Indeed, in an effective network, even where
control seems desirable, it is not practical. This condition




–




which may be
thought of as the semantic condition – is what distinguishes networks
from groups (see below).

7. An effective network
is dynamic. A network is a fluid, changing entity, because without
change, growth and adaptation are not possible. This is sometimes described as
the ‘plasticity’
of a network. It is through this process of change that new knowledge is
discovered, where the creation of connections is a core
function.

8. An effective network
is desegregated. For example, in network learning, learning is not
thought of as a Separate Domain. Hence, there is no need for learning-specific
tools and processes. Learning is instead thought of as a part of living, of
work, of play. The same tools we use to perform day-to-day activities are the
tools we use to learn. Viewed more broadly, this condition amounts to seeing the
network as infrastructure. Computing, communicating and learning are not
something we ‘go some place to do’. Instead, we think of network resources as
similar to a utility, like electricity, like water, like telephones. The network
is everywhere.

It should be noted that
though some indication of the justification for these methodological principles
has been offered in the list above, along with some examples, this list is in
essence descriptive. In other words, what is claimed here is that
successful networks in fact adhere to these principles. The why of
this is the subject of the next few sections.

But it should be
self-evident that mere organization is not the only determinate of what
constitutes, if you will, 'good' knowledge as opposed to 'bad' (or 'false')
knowledge. Consider public knowledge. People form themselves into communities,
develop common language and social bonds, and then proceed to invade Europe or
commit mass suicide. Nor is personal knowledge any reliable counterbalance to
this. People are as inclined to internalize the dysfunctional as the utile, the
self-destructive as the empowering. Some types of knowledge (that is, some ways
of being organized, whether socially or personally) are destructive and
unstable.

These are examples of
cascade
phenomena. In social sciences the same phenomenon might be referred to as
the bandwagon
effect. Such
phenomena exist in the natural world as well. The sweep of the plague
through medieval society, the failure of one hydro plant after another, the
bubbles in the stock market. Cascade phenomena occur when some event or property
sweeps through the network. Cascade phenomena are in one sense difficult to
explain and in another sense deceptively simple.

The sense in which they
are simple to explain is mathematical. If a signal has more than an even chance
of being propagated from one entity in the network to the next, and if the
network is fully connected, then the signal will eventually propagate to every
entity in the network. The speed at which this process occurs is a property of
the connectivity of the network. In (certain) random and scale free networks,
including hierarchal
networks, it takes very few connections to jump from one side of the network
to the other. Cascade phenomena sweep through densely connected networks very
rapidly.

The sense in which they
are hard to explain is related to the question of why they exist at all. Given
the destructive nature of cascade phenomena, it would make more sense to leave
entities in the network unconnected (much like Newton escaped
the plague by isolating himself). Terminating all the connections would
prevent cascade phenomena. However, it would also prevent any possibility of
human knowledge, any possibility of a knowing society.

Network Semantics
and Connective Learning

If we accept that
something like the network theory of learning is true, then we are faced with a
knowledge and learning environment very different from what we are used to. In
the strictest sense, there is no semantics in network learning, because there is
no meaning in network learning (and hence, the constructivist practice of
‘making
meaning’ is literally meaningless).

Traditionally, what a
sentence ‘means’ is the (truth of falsity of) the state of the world it
represents. However, on a network theory of knowledge, there is no such state of
the world to which this meaning can be affixed. This is not because there is no
such state of the world. The world could most certainly exist, and there is no
contradiction in saying that a person’s neural states are caused by world
events. However, it does mean that there is no particular state of
the world that corresponds with (is isomorphic to) a particular mental state.
This is because the mental state is embedded in a sea of context and
presuppositions that are completely opaque to the state of the
world.

How, then, do we
express ourselves? How do we distinguish between true and false – what, indeed,
does it even mean to say that something is true and false? The answer to
these questions is going to be different for each of us. They will be embedded
in a network of assumptions and beliefs about the nature of meaning, truth and
falsity. In order to get at a response, therefore, it will be necessary to
outline what may only loosely be called ‘network semantics’

As we
examine the emergentist theory of mind we can arrive at five major
implications of this approach for educational theorists:

- first,
knowledge is subsymbolic.
Mere possession of the words does not mean that there is knowledge;
the possession of knowledge does not necessarily result in the
possession of the words (and for much more on this, see Michael
Polanyi's discussion of 'tacit
knowledge' in 'Personal
Knowledge').

- second,
knowledge is distributed. There is no specific 'mental entity' that
corresponds to the belief that 'Paris is the capital of France'. What
we call that 'knowledge' is (an indistinguishable) pattern of
connections between neurons. See, for example, Geoffrey Hinton,
'Learning
Distributed Representations of Concepts'.

- third,
knowledge is interconnected. The same neuron that is a part of 'Paris
is the capital of France' might also be a part of 'My dog is named
Fred'. It is important to note that this is a non-symbolic
interconnection - this is the basis for non-rational associations,
such as are described in the recent Guardian article, 'Where
Belief is Born'

- fourth,
knowledge is personal. Your 'belief' that 'Paris is the capital of
France' is quite literally different from my belief that 'Paris is
the capital of France'. If you think about it, this must be the case
- otherwise Gestalt
tests would be useless; we would all utter the same word when
shown the same picture.

- fifth,
what we call 'knowledge' (or 'belief', or 'memory') is an emergent
phenomenon. Specifically, it is not 'in' the brain itself, or even
'in' the connections themselves, because there is no 'canonical' set
of connections that corresponds with 'Paris is the capital of
France'. It is, rather (and carefully stated), a recognition of a
pattern in a set of neural events (if we are introspecting) or
behavioural events (if we are observing). We infer to mental contents
the same way we watch Donald Duck on TV - we think we see something,
but that something is not actually there - it's just an organization
of pixels.

This set
of features constitutes a mechanism for evaluating whether a
cognitivist theory or a connectivist theory is likely to be true. In
my own mind (and in my own writing, as this was the subject of my
first published paper, ‘Why Equi Fails’), the mechanism
can be summed in one empirical test: context sensitivity.

Postscript:
The Non-Causal Theory of Knowledge

In recent
years we have heard a great deal about evidence based educational
policy. It is an appealing demand: the idea that educational policy
and pedagogy ought to be informed by theory that is empirically
supported. Such demands are typical of causal theories; following the
methodology outlined theorists like Carl
Hempel, they require an assessment of initial conditions, an
intervention, and a measurement of observed difference, as predicted
by a (causal) generalization.

In the
earlier theory, there is a direct causal connection between states of
affairs in the communicating entities; it is, therefore, a causal
theory. But in the latter theory, there is no direct causal
connection; it is what would be called (in the parlance of the new
theory) an emergentist theory (that is, it is based on emergence, not
causality). Calls for "evidence that show this claim is true"
and "studies to substantiate this claim" are, like most
Positivist
and Positivist-inspired theories, reductive
in nature; that is why, for example, we expect to find something like
a reductive entity, 'the message', 'the information', 'the learning',
and the like. They are also aggregationist; the presumption, for
example, is that knowledge is cumulative, that it can be assembled
through a series of transactions, or in more advanced theories,
'constructed' following a series of cues and prompts.

But what
happens, first of all, if the entities we are ‘measuring’
don’t exist?

Even if
there are mental states, it may still be that our descriptions of
them nonetheless commit some sort of category error. Saying that
there are ‘thoughts’ and ‘beliefs’ that
somehow reduce to physical instantiations of, well, something
(a word, a brain state…) is a mistake. These concepts are
relics of an age when we thought the mental came in neat little
atomistic packages, just like the physical. They are an unfounded
application of concepts like 'objects' and 'causation' to phenomena
that defy such explanation; they are, in other words, relics of 'folk
psychology'. Saying 'someone has a belief' is like saying that 'the
Sun is rising' - it is literally untrue, and depends on a mistaken
world view.

But even
more significantly, what happens if we cannot ‘measure’
the phenomena in question at all?

On the
network theory knowledge and learning are emergent phenomena, and it
is necessary to highlight a critical point: emergent phenomena are
not causal phenomena. That is (say) the picture of Richard Nixon does
not 'cause' you to think of the disgraced former president. They
require a perceiver, someone to recognize the pattern being
displayed in the medium. And this recognition depends on a relevant
(but not strictly defined) similarity between one's own mental state
and the pattern being perceived. That's why perception (and
language, etc), unlike strict causation, is context-sensitive.

And there
is no means for a student to 'cause' (strictly speaking) recognition
on the part of, say, an examiner, that he or she 'knows that Paris is
the capital of France'. What is essential (and, I might add,
ineliminable) is that the complex of this person's behaviours be
recognized as displaying that knowledge. As Wittgenstein says, we
recognize that a person believes the ice is safe by the manner in
which he walks on the ice. And because this demonstration is
non-causal, it depends on the mental state of the examiner, and
worse, because (quite literally) we see what we want to see, the
prior disposition of the examiner.

If this is
the case, the very ideas of ‘evidence’ and ‘proof’
are turned on their heads. "Modeling
the brain is not like a lot of science where you can go from one
step to the next in a chain of reasoning, because you need to take
into account so many levels of analysis... O'Reilly likens the
process to weather modeling."

This is a very important
point, because it shows that traditional research methodology, and
for that matter, traditional methods of testing and evaluation, as
employed widely in the field of e-learning, will not be
successful (are high school grades a predictor of college success?
Are LSAT scores? Are college grades a predictor of life success?).
This becomes even more relevant with the recent emphasis on
'evidence-based' methodology, such as the Campbell
Collaboration. This methodology, like much of the same type,
recommends double-blind tests measuring the impacted of individual
variables in controlled environments. The PISA
samples are an example of this process in action.

The
problem with this methodology is that if the brain (and hence
learning) operates as described by O'Reilly (and there is ample
evidence that it does) then concepts such as 'learning' are best
understood as functions applied to a distributed representation, and
hence, will operate in environments of numerous mutually dependent
variables (the value of one variable impacts the value of a second,
which impacts the value of a third, which in turn impacts the value
of the first, and so on).

As I argue in papers like Public
Policy, Research and Online Learning and Understanding
PISA the traditional methodology fails in such environments.
Holding one variable constant, for example, impacts the
variable you are trying to measure. This is because you are not
merely screening the impact of the second variable, you are screening
the impact of the first variable on itself (as transferred through
the second variable). This means you are incorrectly measuring
the first variable.

Environments with numerous mutually
dependent variables are known collectively as chaotic
systems. Virtually all networks are chaotic systems. Classic
examples of chaotic systems are the weather system and the ecology.
In both cases, it is not possible to determine the long-term impact
of a single variable. In both cases, trivial differences in initial
conditions can result in significant long-term differences (the
butterfly
effect).

This was a significant difference between
computation and neural networks. In computation (and computational
methodology, including traditional causal science) we look for
specific and predictable results. Make intervention X and get result
Y. Neural network (and social network) theory does not offer this.
Make intervention X today and get result Y. Make intervention X
tomorrow (even on the same subject) and get result Z.

This
does not mean that a 'science' of learning is impossible. Rather, it
means that the science will be more like meteorology than like
(classical) physics. It will be a science based on modeling and
simulation, pattern recognition and interpretation, projection and
uncertainty. One would think at first blush that this is nothing
like computer science. But as the article takes pains to explain, it
is like computer science - so long as we are studying networks
of computers, like social networks.

Learning
theorists will no longer be able to study learning from the detached
pose of the empirical scientist. The days of the controlled study
involving 24 students ought to end. Theorists will have to, like
students, immerse themselves in their field, to encounter and engage
in a myriad of connections, to immerse themselves, as McLuhan would
say, as though in a warm bath. But it’s a new world in here,
and the water’s fine.

An alternative block model is that of "factions."  Factions
are groupings that have high density within the group, and low density of ties
between groups.  Networks>Subgroups>Factions
fits this block model to one-mode data (for any user-specified number of factions). 
Network>2-Mode>2-Mode Factions fits
the same type of model to two-mode data (but for only two factions).

When we apply the core-periphery model to actor-by-event data (Network>2-Mode>Categorical
Core/Periphery) we are seeking the same idealized "image"
of a high and a low density block along the main diagonal.  But, now the
meaning is rather different.

The "core" consists of a partition of actors that are closely
connected to each of the events in an event partition; and simultaneously a
partition of events that are closely connected to the actors in the core
partition.  So, the "core" is a cluster of frequently
co-occurring actors and events.  The "periphery" consists of a partition of actors who are not
co-incident to the same events; and a partition of events that are disjoint
because they have no actors in common.

The core-periphery structure is an ideal typical pattern that divides both
the rows and the columns into two classes.  One of the blocks on the main
diagonal (the core) is a high-density block; the other block on the main
diagonal (the periphery) is a low-density block.  The core-periphery model is indifferent
to the density of ties in the off-diagonal blocks.

When we apply the core-periphery model to actor-by-actor data (see
Network>Core/Periphery), the model seeks to identify a set of actors who have
high density of ties among themselves (the core) by sharing many events in
common, and another set of actors who
have very low density of ties among themselves (the periphery) by having few
events in common.  Actors in
the core are able to coordinate their actions, those in the periphery are
not.  As a consequence, actors in the core are at a structural advantage in
exchange relations with actors in the periphery.

Often all that we know about actors and events is simple co-presence. 
That is, either an actor was, or wasn't present, and our incidence matrix is
binary.  In cases like this, the scaling methods discussed above can be
applied, but one should be very cautious about the results.  This is
because the various dimensional methods operate on similarity/distance matrices,
and measures like correlations (as used in two-mode factor analysis) can be
misleading with binary data.  Even correspondence analysis, which is more
friendly to binary data, can be troublesome when data are sparse.

An alternative approach is block modeling.  Block modeling works
directly on the binary incidence matrix by trying to permute rows and columns to
fit, as closely as possible, idealized images.  This approach doesn't
involve any of the distributional assumptions that are made in scaling analysis.

In principle, one could fit any sort of block model to actor-by-event
incidence data.  We will examine two models that ask meaningful
(alternative) questions about the patterns of linkage between actors and
events.  Both of these models can be directly calculated in UCINET. 
Alternative block models, of course, could be fit to incidence data using more
general block-modeling algorithms.

For binary data, the use of factor analysis and SVD is not recommended. 
Factoring methods operate on the variance/covariance or correlation matrices
among actors and events.  When the connections of actors to events is
measured at the binary level (which is very often the case in network analysis)
correlations may seriously understate covariance and make patterns difficult to discern.

As an alternative for binary actor-by-event scaling, the method of
correspondence analysis (Tools>2-Mode Scaling>Correspondence)
can be used.  Correspondence analysis (rather like Latent Class
Analysis) operates on multi-variate binary cross-tabulations, and its distributional assumptions are better suited to binary data.

Factor analysis provides an alternative method to SVD to the same
goals:  identifying underlying dimensions of the joint space of
actor-by-event variance, and locating or scaling actors and events in that
space.  The method used by factor analysis to identify the dimensions
differs from SVD. 

Singular value decomposition (SVD) is one method of identifying the factors
underlying two-mode (valued) data.  The method of extracting factors
(singular values) differs somewhat from conventional factor and components analysis, so it is a
good idea to examine both SVD and 2-mode factoring results.

Two-mode data offer some very interesting analytic possibilities for gaining
greater understanding of "macro-micro" relations.  In the Davis
data, for example, we can see how the choices of the individual women
"make" the meaning of the parties by choosing to attend or not. 
We can also see how the parties, as macro structures may affect the choices of
the individual women.

With a little creativity, you can begin to see examples of these kinds of
two-mode, or macro-micro social structures everywhere.  The social world is
one of "nesting" in which individuals (and larger structures) are
embedded in larger structures (and larger structures are embedded in still
larger ones).  Indeed, the analysis of the tension between "structure
and agency" or "macro and micro" is one of the core themes in
sociological theory and analysis.

In this chapter we will take a look at some of the tools that have been
applied (and, in some cases, developed) by social network analysts for examining
two-mode data.  We begin with a discussion of data structures, proceed to
visualization, and then turn our attention to techniques for identifying
quantitative and qualitative patterns in two-mode data.

The cross-product method takes each entry of the row for actor A, and
multiplies it times the same entry for actor B, and then sums the result. 
Usually, this method is used for binary data because the result is a count of
co-occurrence.  With binary data, each product is 1 only if both actors
were "present" at the event, and the sum across events yields the
number of events in common - a valued measure of strength.

Our example is a little more complicated because we've applied the
cross-product method to valued data.  Here, if neither actor donated to an
initiative (0 * 0 = 0), or if one donated and the other did not (0 * -1 or 0 *
+1 = 0), there is no tie.  If both donated in the same direction (-1 * -1 =
1 or +1 * +1 = 1) there is a positive tie.  If both donated, but in
opposite directions (+1 * -1 = -1) there is a negative tie.  The sum of the
cross-products is a valued count of the preponderance of positive or negative
ties.

The minimums method examines the entries for the two actors at each
event, and selects the minimum value.  For binary data, the result is the
same as the cross-product method (if both, or either actor is zero, the minimum
is zero; only if both are one is the minimum one).  For valued data, the
minimums method is essentially saying:  the tie between the two actors is
equal to the weaker of the ties of the two actors to the event.  This
approach is commonly used when the original data are measured as valued.