Internal Knowledge Score (IKS) Analysis

• Internal Knowledge Score (IKS) is a quantitative measure that integrates learning session data, topic modeling, and decay dynamics to assess internalized knowledge.
• The methodology logs session duration, topic proportions, and elapsed time to compute weighted and normalized scores for granular knowledge points.
• IKS provides actionable insights for academic and professional development by objectively comparing expertise, identifying learning gaps, and informing training strategies.

An Internal Knowledge Score (IKS) quantifies the degree, structure, and dynamics of knowledge internalized within an individual reader, learner, or model, as formulated in quantitative, modular, or layer-structured frameworks. IKS arises as a solution to the challenge of evaluating knowledge without formal exams, and in contexts where understanding the depth, specificity, and decay of "internalized" information—be it human, crowd, or parametric—is crucial. The concept is formally developed in the context of knowledge modeling, where textual learning experiences are algorithmically processed and scored to yield interpretable, dynamic indices reflecting mastery across granular knowledge points.

1. Mathematical Framework for Internal Knowledge Score

IKS in knowledge modeling is rooted in a formal, accumulation-based approach that leverages learning histories and topical analyses. Each learning session $j$ is recorded with duration $d_j$, and the proportion $\xi_{ij}$ of the session assigned to a knowledge point $k_i$ is determined via probabilistic topic modeling (typically LDA or similar):

$F_{k_i} = \sum_j (d_j \times \xi_{ij} \times b_j)$

where $b_j$ models cognitive retention over time according to a forgetting curve:

$b = \frac{k}{(\log t)^c + k}$

with $t$ the elapsed time since learning, and $k$, $c$ empirical constants (e.g., $k=1.84$, $c=1.25$). The share $\xi_{ij}$ is determined by topic distribution and word association for each session, ensuring sessions contribute proportionately to their specific knowledge point.

$$\phi_{ij} = \frac{\pi_j \times p(t_i | \theta_j)}{\sum_{j=1}^K \sum_{i=1}^M (\pi_j \times p(t_i | \theta_j))}$$

The familiarity $F_{k_i}$ aggregates the time-weighted, topic-allocated, and memory-corrected learning impacts for a knowledge point, and can be normalized to produce an interpretable and comparable IKS.

2. Learning Session Recording and Knowledge Structuring

The operationalization of IKS relies on rigorous logging of learning sessions:

• Learning sequence ID: unique identifier for session ordering
• Stop time: precise session end timestamp
• Duration: measured in seconds
• Knowledge point proportion: computed via topic model analysis

Short sessions (below a fixed threshold) are filtered to ensure data reliability. These events are stored hierarchically in a personal knowledge tree, where leaves represent explicit knowledge points (e.g., "Bayes' Rule" or "Expectation-Maximization Algorithm"). For each node, aggregated session data supports dynamic adjustment based on memory retention (i.e., decay) and continuous learning.

This design enables the system to track not only the static accumulation of facts but also the dynamic erosion and reinforcement of knowledge over time.

3. Topic Model Algorithms and Knowledge Allocation

Textual content from each session is subjected to probabilistic topic modeling, which extracts latent topics and identifies the share of each knowledge point in the context of the session. Typically:

• The document (e.g., PDF pages actively read) is processed as input to the topic model.
• The top $m$ terms for each topic are selected to represent candidate knowledge points.
• The conditional topic-term probabilities ($\pi_j$ and $p(t_i | \theta_j)$) yield the session's allocation vector.

The intermediate share $\xi_{ij}$ is then fed into familiarity and decay formulae, tightly coupling session engagement, content relevance, and forgetting dynamics.

Advanced implementations handle multi-word concepts ("inverse document frequency") as merged tokens to prevent dilution across topics.

4. Score Aggregation, Normalization, and Interpretation

Individual familiarity measures are summed across all sessions associated with each knowledge point. A raw IKS is computed as the time-, relevance-, and retention-adjusted sum for each leaf node in the knowledge tree. Normalization may be performed:

• Relative to group averages (for peer comparison)
• Relative to period averages (for temporal trends in learning concentration)

Such normalization transforms raw IKS values into metrics that can be used to compare expertise, concentration, or deficiency between individuals, time slices, or professional cohorts. Table 2 in the referenced work exemplifies this with explicit session breakdowns, supporting traceability.

5. System Implementation and Workflow

A preliminary validating system is described:

• PDF Reader Plug-in: Monitors document open/close, app switch, and user inactivity events to detect session boundaries
• Page-level Text Extraction: Processes only directly engaged pages to minimize noise
• External Topic Modeling Toolkit: (e.g., MeTA) parses textual data for topic allocation
• Knowledge Tree Database: Stores user sessions, topic allocations, and computed scores

Algorithm 1 in the source paper discriminates session boundaries based on window activation, page switching, and inactivity thresholds. Data is stored in a personalized hierarchy, ready for real-time update and retrieval of IKS values.

6. Practical Implications in Academic and Organizational Contexts

The IKS methodology supports several use cases:

Application	Process	Benefit
Common Topic Identification	Compare IKS metrics between profiles	Efficient collaboration pairing
Lecture Selection	Assess attendee readiness/mismatch	Targeted educational engagement
Research Concentration	Analyze IKS over recent periods	Strategic self-assessment/development
Referee Selection	Match paper topics to candidate IKS	Objective, expertise-aligned review
Professional Development	Monitor domain-specific IKS over time	Quantitative HR/training decisions

By making knowledge quantifiable and traceable at the individual level, the IKS enables data-driven self-diagnosis and benchmarking, supports automated expertise matching, and informs institutional training strategies.

7. Limitations, Extensions, and Research Directions

The methodology assumes that all learning experiences are logged and accurately analyzed, which may suffer from incomplete coverage or noisy topic models. Forgetting curve parameters are fixed and may require personalization. The system is primarily designed for text-based learning; adaptation for multimodal or experiential learning remains open.

Future research may extend topic modeling sophistication, automate multi-session aggregation, and enrich the knowledge tree schema to capture complex interdependencies. Personalized forgetting curves and integration with active learning analytics represent promising directions.

Summary

The Internal Knowledge Score (IKS) as defined in knowledge modeling frameworks is a time-, context-, and memory-weighted quantitative measure of an individual's mastery of explicit knowledge points. It emerges from the robust integration of learning-session logging, probabilistic topic modeling, and mathematical decay dynamics, yielding a real-time, comparable metric for expertise evaluation, concentration analysis, and strategic self-development in academic and professional environments. The systematic nature of IKS enables transparent, granular, and actionable insight into the structure and dynamics of human or organizational knowledge.