3.1 Model Construction with Visualization
There are three basic assumptions that need to be set out in a visual model for online
self-directed learning. First, the model should be constructed in such a way that
learners are given the freedom to develop their own programs, rather than having a
uniform curriculum set by teachers or colleges. This is because the latter do not
differentiate learning programs to meet the needs of different types of students.
Therefore, allowing learners to choose their own resources will increase flexibility
and enthusiasm for learning. Secondly, the learning environment should uphold the
principle of autonomy. Instead of the school fixing the learning environment for students,
students should build the environment for their learning and learn independently in
it. Third, to ensure the effectiveness of students’ self-learning while opening up
free learning, rules and systems should be introduced to regulate activities in order
to achieve a semi-structured teaching and learning design. Finally, the model should
build a technological bridge for students to communicate with each other with the
help of visualization technology in order to facilitate communication and discussion
of students’ online learning. Fig. 1 shows a diagram of the online self-directed learning process.
Fig. 1. Sketch map of online autonomous learning teaching process.
Fig. 2. Schematic diagram of five elements.
The three-tiered structure of the online, self-directed learning process includes
the topic planning tier, the program strategy tier, and the operational reflection
tier. The three tiers are formed by a combination of five elements: learners, learning
content, learning tools, learning activities, and learning objectives. The theme plan
layer is responsible for defining the learning objectives and decomposing them; the
solution strategy layer is responsible for combining the learning activities to achieve
the learning objectives set out in the theme plan layer. The operational reflection
layer is responsible for combining the three elements of learning content, learning
tools, and learners to form a complete learning activity. The three-tier structure
presented in Fig. 1 can be seen as progressively refined and is broken down from left to right, thus
providing an effective guide to student learning behavior. The five elements also
create a differentiated learning environment because of the multiple ways in which
they converge. Fig. 2 illustrates the relationships among the five elements.
Learners denote the group of students involved in a learning activity. Because online
independent learning emphasizes the active nature of learning, students are no longer
just passive recipients but managers and creators of learning activities as well as
commentators and consumers of teaching and learning practices. The reasonableness
of learning objectives is directly related to the outcomes that learners ultimately
achieve. The reasonableness of learning objectives is reflected in their operability
and consistency with learners’ internal values. From the perspective of content, learning
objectives can be categorized as knowledge-based, skills-based, and affective; from
the perspective of difficulty, learning objectives can be categorized as growth-based
and maintenance-based. Learning activities can only be carried out if objectives are
well formulated. Online independent learning greatly enriches the range of activities,
enabling learners to personalize and differentiate their learning. For example, activities
can be divided into research, collaborative, and thematic learning. Online self-directed
learning broadens the concept of learning content. As a result, learning content is
no longer confined to the strictly organized and logical scope of traditional teaching
and learning, but extends to the vast resources available throughout the Internet.
Learning tools are responsible for helping learners carry out their activities, and
are divided into two categories: specialized tools and generic tools. Fig. 3 shows a schematic of the technology used to visualize the online independent learning
process.
Fig. 3. Schematic of online autonomous learning visualization technology.
Fig. 3 shows that visualization of the online, self-directed learning process is structured
in four layers; from top to bottom: the data input layer, the visual coding layer,
the logical recommendation layer, and the view presentation layer. The data input
layer includes role data, such as learners, teachers, and teaching assistants; learning
content data, such as forum statements and student assignments; and work data, such
as learning progress and learning contexts. These three types of data are communicated
to form the learning data, and are used to reflect the current state of learning.
The visualization and coding layer is responsible for analyzing the data, using statistical
techniques, text visualization techniques, or human-computer interaction techniques
to code the input data in order to visualize them. The logical recommendation layer
provides students with references to learning solutions based on learner characteristics,
learning tasks, and knowledge networks, helping them to build a personalized learning
environment. The view presentation layer is related to visualization of the content
space, and is used to present information such as views of the learning network or
a list of learning activities.
3.2 Optimization of Immersive Networks with the U-Net Algorithm and a 3D Layout
Due to the overwhelming size of the teaching data, this research first designed a
visual enhancement algorithm based on the U-Net neural network in order to enhance
visualization of the network data and improve the user’s visual and other sensory
experiences. Then, based on this algorithm, this study proposes an immersive, network
topology visualization layout technique reflecting a 3D immersion effect. Fig. 4 shows a schematic of the U-Net neural network structure.
Fig. 4. The U-Net neural network structure.
As seen in Fig. 4, the network consists of an encoder unit, a decoder unit, and a hop-level connection
unit. The encoder and decoder units are symmetrical. Both are formed by a convolution
module. The function of the convolution module is to capture the deeper features of
the visual image. The role of the hopping connection unit is to enhance details of
the image based on deep feature information in the visual image. Eq. (1) is the mathematical expression used for smoothing and denoising in this network.
In Eq. (1), $y'$ is the median grey value of an image pixel point; $med$denotes the median calculation
function; $I(\alpha _{g},\beta _{g})$denotes a pixel point; $a$ denotes an arbitrary
integer; $g$ denotes the number of rows of pixel points; and $(\alpha _{g},\beta _{g})$,
$\alpha _{g}$, and$\beta _{g}$ represent the position coordinates, abscissa, and ordinate
of the pixel points, respectively.
Eq. (2) is the mathematical expression for image edge sharpening:
In Eq. (2), $a$, $c$, and $e$ all represent arbitrary constants; and $grad$ denotes the vector
field gradient. Eq. (3) represents the expression for the gradient corresponding to the vectorially defined
coordinates:
In Eq. (3), $grad\left[I(\alpha ,\beta )\right]$ is the gradient value corresponding to pixel
$I(\alpha ,\beta )$. In terms of dimensionality, the network topology can be divided
into three types: a one-dimensional layout, a two-dimensional layout, and a three-dimensional
layout. One-dimensional layouts have the advantage of establishing the overall relevance
of the network, but weaken the relationships between information within the community.
Given the increasing complexity of the network structure and its strong, time-varying
nature, two-dimensional layouts also make it difficult to meet practical needs. Therefore,
this study uses an edge aggregation strategy to extend the two-dimensional layout
to a three-dimensional layout.
Suppose the number of network nodes is $n$, the number of network edges is$m$, and
the degree corresponding to any node $v$ is $D_{v}$. The network can be considered
undirected graph adjacency matrix $A$, whereupon the modular degree can be expressed
by Eq. (4):
In Eq. (4), $Q$ indicates the module degree, and $\delta _{ij}$ indicates whether the nodes
belong to the same community. The purpose of using the module degree is to divide
the network, and when the module degree iterates to the maximum value, it indicates
the end of network division. In order to avoid confusion in the layout of network
nodes and to avoid a crossover problem for network edges, this study introduces an
energy model to simulate the network layout process once the network communities are
determined. Eq. (5) is the mathematical expression of the energy model:
In Eq. (5), $d(i,j)$ represents node spacing; $s(i,j)$ represents the spring model length; $k$
and $r$ represent the elasticity coefficient and electrostatic force constant, respectively;
and $w$ denotes the inter-node weights. Let the set of supernodes for the 3D network
be $C$\textcolor{color-6}{.} The coordinates of the supernodes, $C_{i}$, after the
energy model layout are $(x_{i},y_{i},z_{i})$. In order to reduce the loss of community
structure features, the network needs to be laid out twice with the supernodes as
coordinate centers. Then, the spatial translation change matrix at this point is Eq.
(6):
In Eq. (6), $(t_{x},t_{y},t_{z})$ is the spatial translation vector. After quadratic layout,
the nodes’ flush coordinate matrix in 3D space can be obtained with Eq. (7):
In Eq. (7), $T$ represents the spatial translation change matrix; $\left[x_{i} y_{i} z1\right]$
denotes a one-dimensional chi-square coordinate matrix; $\left[x_{i} y z1\right]^{T}$denotes
a two-dimensional chi-square coordinate matrix; and $\left[x y z1\right]^{T}$denotes
a three-dimensional chi-square coordinate matrix. Afterwards, the study uses an edge
aggregation strategy to implement an immersive 3D edge-bound layout. The strategy
consists of four basic rules, shown as a schematic diagram in Fig. 5.
Fig. 5. Schematic of the four basic rules in the edge aggregation strategy.
Rule 1 is a directionally compatible strategy with the mathematical expression in
Eq. (8):
In Eq. (8),$C_{a}(P,Q)$ denotes the directional compatibility size, $\alpha $ represents the
angle between two edges, while $P$ and $Q$ represent the two edges. If the directional
compatibility size is 1, the two edges are perpendicular, and if the directional compatibility
size is 0, the two edges are parallel. Rule 2 is the size compatibility strategy;
the mathematical expression is Eq. (9):
In Eq. (9), $C_{s}(P,Q)$ indicates the size of the dimensional compatibility, and $l_{avg}$
is the average length of the two edges. If the compatibility size is 1, the two edges
are of equal length; if the compatibility size is 0, the two edges are in a size-incompatible
relationship. Rule 3 is a positional compatibility policy with its mathematical expression
in Eq. (10):
In Eq. (10), $P_{m}$ and $Q_{m}$ represent the midpoints of the two edges, $P$ and $Q$. When
the position compatibility size is 1, the two edges intersect; when the position compatibility
size is 0, the two edges never intersect. Rule 4 represents the visual compatibility
policy for which the mathematical expression is Eq. (11):
in which $V(P,Q)=\max (1-2\left\| P_{m}-I_{m}\right\| \div \left\| I_{0}-I_{1}\right\|
,0)$ where $I_{m}$ is the midpoint of $I_{0}$ and $I_{1}$.
Eq. (12) is the overall compatibility calculation formula:
Eq. (12) combines the above four compatibility edge binding rules to obtain overall compatibility
$C_{e}(P,Q)$. At this point, $C_{e}(P,Q)\in [0,1]$.