Define following. 1) Learning vector quantisation ii) Adaptive pattern classification

Learning Vector Quantisation (LVQ)

Definition:

Learning Vector Quantisation (LVQ) is a supervised learning algorithm used for classification tasks. It is a type of competitive learning neural network that relies on the concept of prototypes, which are representative vectors for each class. LVQ is designed to improve the accuracy of vector quantization by leveraging labeled training data.

Key Concepts:

1. Prototypes:

   • Prototypes are representative vectors for each class in the dataset.
   • Each prototype is associated with a specific class label.

2. Training:

   • LVQ adjusts the positions of the prototypes to better represent the classes.
   • During training, input vectors are compared to the prototypes, and the closest prototype (the winner) is updated.

Algorithm Steps:

1. Initialization:

   • Initialize a set of prototypes, each with a random position and associated class label.

2. Input Presentation:

   • Present an input vector to the network.

3. Find the Winning Prototype:

   • Compute the distance between the input vector and each prototype.
   • Select the prototype with the smallest distance as the winning prototype.

4. Prototype Update:

   • If the winning prototype has the same class label as the input vector: [ \mathbf{w}_i(t+1) = \mathbf{w}_i(t) + \eta(t) (\mathbf{x} - \mathbf{w}_i(t)) ]
   • If the winning prototype has a different class label: [ \mathbf{w}_i(t+1) = \mathbf{w}_i(t) - \eta(t) (\mathbf{x} - \mathbf{w}_i(t)) ]
   • Here, (\mathbf{w}_i) is the weight vector of the winning prototype, (\mathbf{x}) is the input vector, and (\eta(t)) is the learning rate.

5. Repeat:

   • Repeat the process for all input vectors over multiple iterations.

Adaptive Pattern Classification

Definition:

Adaptive Pattern Classification refers to the process of classifying input patterns using adaptive learning techniques that allow the model to update its parameters based on new data. It encompasses methods that enable the system to learn and adapt to new patterns dynamically without forgetting previously learned patterns.

Key Concepts:

1. Adaptivity:

   • The system can adjust its parameters or structure in response to new data.
   • Ensures the model remains accurate over time, even as new patterns are encountered.

2. Incremental Learning:

   • The model learns from new data incrementally, updating its knowledge without requiring retraining from scratch.

3. Stability-Plasticity Dilemma:

   • A balance between stability (retaining learned information) and plasticity (learning new information) is essential for effective adaptive pattern classification.

Techniques:

1. Adaptive Resonance Theory (ART):

   • ART networks address the stability-plasticity dilemma by using a vigilance parameter to control the degree of match required for learning new patterns.
   • They are capable of learning new patterns while preserving previously learned information.

2. Self-Organizing Maps (SOM):

   • SOMs can be adapted to incorporate new data, adjusting the positions of neurons in the map to reflect new input patterns.

3. Incremental Learning Algorithms:

   • Algorithms that allow models to update their parameters based on new data without retraining from scratch.
   • Examples include online learning methods and algorithms designed for continual learning.

Applications:

1. Real-Time Systems:

   • Adaptive pattern classification is crucial in systems that operate in real-time and require continuous learning, such as speech recognition systems and adaptive control systems.

2. Dynamic Environments:

   • Used in environments where the data distribution changes over time, such as financial markets, weather prediction, and autonomous driving.

3. Personalized Systems:

   • Systems that require personalization based on user behavior, such as recommendation systems and personalized health monitoring.

Conclusion

Learning Vector Quantization (LVQ) and Adaptive Pattern Classification are crucial concepts in the field of neural networks and machine learning. LVQ is a supervised learning algorithm that refines the positions of prototypes to improve classification accuracy. In contrast, adaptive pattern classification encompasses a broader range of techniques that allow models to dynamically learn and adapt to new data, maintaining a balance between stability and plasticity. These methods are essential for applications that require continuous learning and adaptation to changing environments.