Orthogonal Factor-Based Biclustering Algorithm (BCBOF) for High-Dimensional Data and Its Application in Stock Trend Prediction

TL;DR

BCBOF introduces an orthogonal-factor–based biclustering approach to address high-dimensionality challenges in clustering, reducing data to an orthogonal subspace via $X = A F + \varepsilon$, rotating with Varimax, then clustering columns and rows with hierarchical methods and DBSCAN to form biclusters. The learned patterns are translated into fuzzy rules for stock-trend prediction, with PSO tuning a trading threshold and risk-management rules (time delays, loss caps) guiding buy/sell signals. Empirical results show BCBOF outperforms several biclustering baselines on multiple metrics (e.g., $MSR$, $VAR$, $MAR$, $SMSR$, $RI$) and that the SSOBC trading strategy yields higher returns than rivals across a 10-stock Shanghai/Shenzhen test. The work delivers an interpretable, high-dimensional biclustering framework with practical financial impact and outlines future integration with deep learning for enhanced pattern learning.

Abstract

Biclustering is an effective technique in data mining and pattern recognition. Biclustering algorithms based on traditional clustering face two fundamental limitations when processing high-dimensional data: (1) The distance concentration phenomenon in high-dimensional spaces leads to data sparsity, rendering similarity measures ineffective; (2) Mainstream linear dimensionality reduction methods disrupt critical local structural patterns. To apply biclustering to high-dimensional datasets, we propose an orthogonal factor-based biclustering algorithm (BCBOF). First, we constructed orthogonal factors in the vector space of the high-dimensional dataset. Then, we performed clustering using the coordinates of the original data in the orthogonal subspace as clustering targets. Finally, we obtained biclustering results of the original dataset. Since dimensionality reduction was applied before clustering, the proposed algorithm effectively mitigated the data sparsity problem caused by high dimensionality. Additionally, we applied this biclustering algorithm to stock technical indicator combinations and stock price trend prediction. Biclustering results were transformed into fuzzy rules, and we incorporated profit-preserving and stop-loss rules into the rule set, ultimately forming a fuzzy inference system for stock price trend predictions and trading signals. To evaluate the performance of BCBOF, we compared it with existing biclustering methods using multiple evaluation metrics. The results showed that our algorithm outperformed other biclustering techniques. To validate the effectiveness of the fuzzy inference system, we conducted virtual trading experiments using historical data from 10 A-share stocks. The experimental results showed that the generated trading strategies yielded higher returns for investors.

Figures (8)

• Figure 1: The algorithm proposed in this paper comprises two phases: the training phase and the system application phase. During the training phase, we utilize the BCBOF algorithm in conjunction with a fuzzy inference system to generate fuzzy rules and employ the PSO algorithm to obtain the trading threshold $T_h$. Subsequently, we apply this system to fuzzify new data, ascertain whether it conforms to the established fuzzy rules, and derive a defuzzified value $\bar{y}$. We apply $\bar{y}$ to the proposed trading strategy to generate trading signals.
• Figure 2: For each bicluster, we use the average value of each column as an input variable for the fuzzy inference system, applying fuzzification to construct the antecedent. The trend level corresponding to each bicluster is also fuzzified to build the consequent. We combine the antecedent and the consequent into an IF-THEN fuzzy rule. Technical trading patterns are composed of biclusters and their corresponding trend levels. Each technical trading pattern can generate an IF-THEN fuzzy rule.
• Figure 3: The BM-FM algorithm predicted three trades for the SZ000790 stock. The buying points primarily occurred within a downward channel that was characterized by lower prices. while the selling price was higher than the buying price, it was not notably high relative to the overall trend.
• Figure 4: The SSOBC algorithm predicted four trades for the SZ000790 stock. The price differences between the buying and selling points were large. Adhering to Trading Rule 1, which stipulated that the buying point price must be lower than the historical average, the algorithm acquired the buying points in the downward channel.
• Figure 5: The BM-FM algorithm predicted three trades for the SH600007 stock. The buying point was basically the lowest point within a given period of time. However, the price differences between the buying point and the selling point were very small.

Theorems & Definitions (1)

• Definition 1