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Optimal node placement and number of nodes
D.GOPINATH AP/ECE
RAMCO INSTITUTE OF TECHNOLOGY,
RAJAPALAYAM
01/06/2025 2
Wearability
• Use of mobile sensor-based platforms for human action recognition is
an ever-growing area of research. Recent advances in this field allow
patients to wear several small sensors with embedded processors and
radios. Collectively, these sensors form a body sensor network (BSN).
• Although BSNs have the potential to enable many useful applications,
limited processing power, storage and energy make efficient use of
these systems crucial.
• Moreover, user comfort is a major issue, which can cause patients to
become frustrated and stop wearing the sensor nodes. The
interaction between the human body and these wearable nodes here
is defined as wearability.
01/06/2025 3
Wearability Issues
• Design for wearable BSNs focuses on specific and important issues for
developing wearable computing systems that take into account the
physical shape of the sensors and their active relationship with the
human form.
• Design for wearability requires unobtrusive sensor node placement
on the human body based on application-specific criteria. Criteria for
placement can vary with the needs of functionality and convenience.
• Functionality criteria constrains node placement to regions where
relevant data can be sensed. The number of nodes required to
capture all relevant data can vary based on the quality of information
sensed at individual locations.
01/06/2025 4
Wearability Issues
Convenience criteria include:
• (1) physical interference with movement,
• (2) difficulty in removing and placing nodes,
• (3) social and fashion concerns,
• (4) frequency and difficulty of maintenance (charging and cleaning)
• Batteries are the heaviest component in the system. By decreasing
power usage, the size and weight of each sensor node can decrease,
thus increasing patient comfort and device wearability.
01/06/2025 5
Wearability Issues
• This makes energy usage a primary constraint in designing BSNs,
limiting everything from data sensing rates and link bandwidth, to
node size and weight.
• Thus, one of the important goals in designing BSNs is to minimize
energy consumption while preserving an acceptable quality of
service.
• Energy consumption can be decreased by lower sampling frequency,
decreasing processing power, and simplifying signal processing.
Another effective technique is deactivating nodes that are
unnecessary for specific tasks.
01/06/2025 6
Action Coverage for Node Placement
• Action coverage aims to select the smallest number of sensor nodes
that can adequately distinguish among all expected activities.
• This selection can be altered dynamically to disperse power load,
route around a failed node, or cover a diverse set of activities.
• To address coverage problem in BSNs, a model of local knowledge
provided by individual sensor nodes is required.
• A compatibility graph is a powerful model that represents capability
of a sensor node in discriminating between movements.
01/06/2025 7
Compatibility Graph
• The amount of knowledge presented by each node determines the
node’s ability in action recognition. An example is shown in Figure a.
Figure a is an example of two feature spaces with associated
distributions drawn for four classes.
01/06/2025 8
Compatibility Graph
• The ellipses represent classification boundaries. In reality, the shapes
are not perfect ellipses.
• For example, each node in the test system may have five data streams
(x, y, z acceleration, and x, y angular velocity) and multiple features
per data stream, forming a high dimensional feature space per node.
• Regions where the ellipses overlap represent potential
misclassifications. Any point in the intersection of A and B or B and C
cannot be confidently assigned to either class.
01/06/2025 9
Compatibility Graph
• In Figure b, overlapping vs. well-separated classes is translated into a
conflict graph. The vertices represent classes, and the edges represent
ambiguities between the classes.
• Finally, Figure c, the so-called compatibility graph, is generated by
complementing the conflict graph of Figure b. If a compatibility graph
is not complete, then there exist some movements that the node
cannot correctly classify.
• A complete graph is equivalent to the capability of distinguishing
between every pair of classes.
01/06/2025 10
Compatibility Graph
• One of the most popular class separability measures in the field of
pattern recognition is the Bhattacharyya distance.
• This measure is related to the well-known Chernoff bound and
therefore has an explicit expression for a generalized Gaussian
distribution.
• The Transformed Divergence is another common empirical measure
of class separability, which is computationally simpler than the
Bhattacharyya distance.
01/06/2025 11
Compatibility Graph
• Both the Transformed Divergence and Bhattacharyya distance
measures are real values between 0 and 2, where 0 indicates
complete overlap between the signatures of two classes, and 2
indicates a complete separation between the two classes.
• Both measures are monotonically related to classification accuracies.
The larger the separability value, the better the final classification
result.
01/06/2025 12
Compatibility Graph
01/06/2025 13
Problem Definition
• Given a set of sensor nodes S={ s1, s2, . . . , sn} placed in a body
sensor network to detect a set of movements M={ 1, 2, . . . ,m}, the
action coverage problem can be formulated as follows.
• Definition 1. Two movements j1 and j2 are said to be compatible if
they have complete separability based on Bhattacharyya metric
indicated by (1).
• Definition 2. A compatibility graph is an undirected graph Gi=(V, Ei)
constructed for a sensor node si, where V is a set of vertices identical
to the set of movements M, and Ei is a set of undirected edges such
that edge (u, v)Ԑ Ei if movements u and v are compatible at node si.
01/06/2025 14
Problem Definition
• The action coverage problem is used to find a minimal set of nodes
that still encompasses full coverage within their capacity. The idea
behind action coverage is that a subset of sensor nodes is sufficient to
provide accurate detection of every target action. This subset is
referred to as complete set and is defined as follows.
01/06/2025 15
Integer Linear Programming (ILP Approach)
• In this section, an integer linear programming formulation for the
action coverage problem is presented. Since each node is represented
by a graph, this problem can be stated as follows.
01/06/2025 16
Integer Linear Programming (ILP Approach)
01/06/2025 17
Integer Linear Programming (ILP Approach)
• The variables xi= (1, 2, . . . , n) indicate whether graph Gi is selected to
form a complete graph.
• The inequality constraint (4) ensures that for each edge ej in the
complete graph, at least one of the compatibility graphs that contains
that edge is selected.
• The objective function (3) attempts to minimize the number of graphs
selected to form a complete graph.
• This is equivalent to minimizing the number of active nodes, which
suitably leads to energy reduction in the system.
01/06/2025 18
Greedy Approach
• The greedy approach selects the compatibility graphs as follows: at
each stage, it picks a compatibility graph Gi that covers the most
uncovered edges; next it picks the next graph that covers the most
remaining edges; this continues until all edges are covered. At the end
of the algorithm, graph G will be a complete graph.
01/06/2025 19
Dynamic Design Decision
• Static action coverage for a movement monitoring system finds the
minimum number of active nodes that cover all actions. However, the
model can be used for the dynamic deactivation of nodes.
• Once the action has occurred, each node classifies it individually. The
final classification involves some notion of collaboration between the
nodes in real-time.
• The dynamic sensor selection tends to find even smaller set of nodes
based on current classification results obtained by individual nodes.
01/06/2025 20
Dynamic Design Decision
• In this example, where the system consists of three sensor nodes with
compatibility graphs shown in Figure.
• This system monitors subjects for the five movements A, B, C, D, and
E. Sensor nodes I, II, and, III classify the movement as A, A, and E,
respectively.
01/06/2025 21
Dynamic Design Decision
• These classified movements are shown as shaded vertices. The
compatibility graph for node I indicates that the target movement
could be A or B as this node is not able to distinguish between A and
B.
• The graph for node II indicates that the movement could be A, D, or E;
and for node III, target movement could be one of E, D, or A.
• By intersecting these possibilities, global classification would result
movement A. However, not both nodes II and III are required to
determine this; one or the other is sufficient.
• Therefore, power can be potentially reduced by eliminating one of the
nodes before initiating communication.
01/06/2025 22
Dynamic Design Decision
• Hence, we propose the following approach: First, select a master
node. This is done by selecting the node whose target movement
vertex has the highest out degree.
• In this case, in the compatibility graph for node I, movement A has an
out-degree of three, for node II, movement B has an out-degree of
two; and for node III, movement D also has an out-degree of two.
Therefore, node I should be the master.
• Next, add the master node to the solution space. Then, apply the
action coverage problem from the master node’s point of view and
find the minimum number of nodes that will achieve full coverage of
the target movement.
01/06/2025 23
Dynamic Design Decision
• In this case, only the edge (A, B) is missing from the master node,
which can be covered by either of the remaining nodes. Finally, obtain
the set of possible classifications from each of the remaining nodes
(including the master), and intersect them to achieve final
classification.
• Assume the action coverage allows nodes I and II to be the active
nodes. The results issued are {A, B} and {B, E,D}, leaving B as the final
target movement.

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Sensor node and Optimal node placement in Body Area Network.pptx

  • 1. Optimal node placement and number of nodes D.GOPINATH AP/ECE RAMCO INSTITUTE OF TECHNOLOGY, RAJAPALAYAM
  • 2. 01/06/2025 2 Wearability • Use of mobile sensor-based platforms for human action recognition is an ever-growing area of research. Recent advances in this field allow patients to wear several small sensors with embedded processors and radios. Collectively, these sensors form a body sensor network (BSN). • Although BSNs have the potential to enable many useful applications, limited processing power, storage and energy make efficient use of these systems crucial. • Moreover, user comfort is a major issue, which can cause patients to become frustrated and stop wearing the sensor nodes. The interaction between the human body and these wearable nodes here is defined as wearability.
  • 3. 01/06/2025 3 Wearability Issues • Design for wearable BSNs focuses on specific and important issues for developing wearable computing systems that take into account the physical shape of the sensors and their active relationship with the human form. • Design for wearability requires unobtrusive sensor node placement on the human body based on application-specific criteria. Criteria for placement can vary with the needs of functionality and convenience. • Functionality criteria constrains node placement to regions where relevant data can be sensed. The number of nodes required to capture all relevant data can vary based on the quality of information sensed at individual locations.
  • 4. 01/06/2025 4 Wearability Issues Convenience criteria include: • (1) physical interference with movement, • (2) difficulty in removing and placing nodes, • (3) social and fashion concerns, • (4) frequency and difficulty of maintenance (charging and cleaning) • Batteries are the heaviest component in the system. By decreasing power usage, the size and weight of each sensor node can decrease, thus increasing patient comfort and device wearability.
  • 5. 01/06/2025 5 Wearability Issues • This makes energy usage a primary constraint in designing BSNs, limiting everything from data sensing rates and link bandwidth, to node size and weight. • Thus, one of the important goals in designing BSNs is to minimize energy consumption while preserving an acceptable quality of service. • Energy consumption can be decreased by lower sampling frequency, decreasing processing power, and simplifying signal processing. Another effective technique is deactivating nodes that are unnecessary for specific tasks.
  • 6. 01/06/2025 6 Action Coverage for Node Placement • Action coverage aims to select the smallest number of sensor nodes that can adequately distinguish among all expected activities. • This selection can be altered dynamically to disperse power load, route around a failed node, or cover a diverse set of activities. • To address coverage problem in BSNs, a model of local knowledge provided by individual sensor nodes is required. • A compatibility graph is a powerful model that represents capability of a sensor node in discriminating between movements.
  • 7. 01/06/2025 7 Compatibility Graph • The amount of knowledge presented by each node determines the node’s ability in action recognition. An example is shown in Figure a. Figure a is an example of two feature spaces with associated distributions drawn for four classes.
  • 8. 01/06/2025 8 Compatibility Graph • The ellipses represent classification boundaries. In reality, the shapes are not perfect ellipses. • For example, each node in the test system may have five data streams (x, y, z acceleration, and x, y angular velocity) and multiple features per data stream, forming a high dimensional feature space per node. • Regions where the ellipses overlap represent potential misclassifications. Any point in the intersection of A and B or B and C cannot be confidently assigned to either class.
  • 9. 01/06/2025 9 Compatibility Graph • In Figure b, overlapping vs. well-separated classes is translated into a conflict graph. The vertices represent classes, and the edges represent ambiguities between the classes. • Finally, Figure c, the so-called compatibility graph, is generated by complementing the conflict graph of Figure b. If a compatibility graph is not complete, then there exist some movements that the node cannot correctly classify. • A complete graph is equivalent to the capability of distinguishing between every pair of classes.
  • 10. 01/06/2025 10 Compatibility Graph • One of the most popular class separability measures in the field of pattern recognition is the Bhattacharyya distance. • This measure is related to the well-known Chernoff bound and therefore has an explicit expression for a generalized Gaussian distribution. • The Transformed Divergence is another common empirical measure of class separability, which is computationally simpler than the Bhattacharyya distance.
  • 11. 01/06/2025 11 Compatibility Graph • Both the Transformed Divergence and Bhattacharyya distance measures are real values between 0 and 2, where 0 indicates complete overlap between the signatures of two classes, and 2 indicates a complete separation between the two classes. • Both measures are monotonically related to classification accuracies. The larger the separability value, the better the final classification result.
  • 13. 01/06/2025 13 Problem Definition • Given a set of sensor nodes S={ s1, s2, . . . , sn} placed in a body sensor network to detect a set of movements M={ 1, 2, . . . ,m}, the action coverage problem can be formulated as follows. • Definition 1. Two movements j1 and j2 are said to be compatible if they have complete separability based on Bhattacharyya metric indicated by (1). • Definition 2. A compatibility graph is an undirected graph Gi=(V, Ei) constructed for a sensor node si, where V is a set of vertices identical to the set of movements M, and Ei is a set of undirected edges such that edge (u, v)Ԑ Ei if movements u and v are compatible at node si.
  • 14. 01/06/2025 14 Problem Definition • The action coverage problem is used to find a minimal set of nodes that still encompasses full coverage within their capacity. The idea behind action coverage is that a subset of sensor nodes is sufficient to provide accurate detection of every target action. This subset is referred to as complete set and is defined as follows.
  • 15. 01/06/2025 15 Integer Linear Programming (ILP Approach) • In this section, an integer linear programming formulation for the action coverage problem is presented. Since each node is represented by a graph, this problem can be stated as follows.
  • 16. 01/06/2025 16 Integer Linear Programming (ILP Approach)
  • 17. 01/06/2025 17 Integer Linear Programming (ILP Approach) • The variables xi= (1, 2, . . . , n) indicate whether graph Gi is selected to form a complete graph. • The inequality constraint (4) ensures that for each edge ej in the complete graph, at least one of the compatibility graphs that contains that edge is selected. • The objective function (3) attempts to minimize the number of graphs selected to form a complete graph. • This is equivalent to minimizing the number of active nodes, which suitably leads to energy reduction in the system.
  • 18. 01/06/2025 18 Greedy Approach • The greedy approach selects the compatibility graphs as follows: at each stage, it picks a compatibility graph Gi that covers the most uncovered edges; next it picks the next graph that covers the most remaining edges; this continues until all edges are covered. At the end of the algorithm, graph G will be a complete graph.
  • 19. 01/06/2025 19 Dynamic Design Decision • Static action coverage for a movement monitoring system finds the minimum number of active nodes that cover all actions. However, the model can be used for the dynamic deactivation of nodes. • Once the action has occurred, each node classifies it individually. The final classification involves some notion of collaboration between the nodes in real-time. • The dynamic sensor selection tends to find even smaller set of nodes based on current classification results obtained by individual nodes.
  • 20. 01/06/2025 20 Dynamic Design Decision • In this example, where the system consists of three sensor nodes with compatibility graphs shown in Figure. • This system monitors subjects for the five movements A, B, C, D, and E. Sensor nodes I, II, and, III classify the movement as A, A, and E, respectively.
  • 21. 01/06/2025 21 Dynamic Design Decision • These classified movements are shown as shaded vertices. The compatibility graph for node I indicates that the target movement could be A or B as this node is not able to distinguish between A and B. • The graph for node II indicates that the movement could be A, D, or E; and for node III, target movement could be one of E, D, or A. • By intersecting these possibilities, global classification would result movement A. However, not both nodes II and III are required to determine this; one or the other is sufficient. • Therefore, power can be potentially reduced by eliminating one of the nodes before initiating communication.
  • 22. 01/06/2025 22 Dynamic Design Decision • Hence, we propose the following approach: First, select a master node. This is done by selecting the node whose target movement vertex has the highest out degree. • In this case, in the compatibility graph for node I, movement A has an out-degree of three, for node II, movement B has an out-degree of two; and for node III, movement D also has an out-degree of two. Therefore, node I should be the master. • Next, add the master node to the solution space. Then, apply the action coverage problem from the master node’s point of view and find the minimum number of nodes that will achieve full coverage of the target movement.
  • 23. 01/06/2025 23 Dynamic Design Decision • In this case, only the edge (A, B) is missing from the master node, which can be covered by either of the remaining nodes. Finally, obtain the set of possible classifications from each of the remaining nodes (including the master), and intersect them to achieve final classification. • Assume the action coverage allows nodes I and II to be the active nodes. The results issued are {A, B} and {B, E,D}, leaving B as the final target movement.