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Article

The Double-Layer Clustering Based on K-Line Pattern Recognition Based on Similarity Matching

by
Xinglong Li
1,
Qingyang Liu
2,*,
Yanrong Hu
1,* and
Hongjiu Liu
1,*
1
College of Mathematics and Computer Science, Zhejiang A & F University, Hangzhou 311300, China
2
Institute of Informatics, Georg-August-Universität Göttingen, 37073 Göttingen, Germany
*
Authors to whom correspondence should be addressed.
Information 2024, 15(12), 821; https://doi.org/10.3390/info15120821
Submission received: 22 October 2024 / Revised: 20 November 2024 / Accepted: 2 December 2024 / Published: 23 December 2024
Browse Figures
Figure 1
<p>K-line legend showing (<b>a</b>) an increase with red or white K-line, (<b>b</b>) a decrease with green or black K-line, and (<b>c</b>) market stability with a Doji K-line [<a href="#B30-information-15-00821" class="html-bibr">30</a>].</p> "> Figure 2
<p>Ineffective candlestick pattern rate for different numbers of clusters.</p> ">
Versions Notes

Abstract

:
Candlestick charts provide a visual representation of price trends and market sentiment, enabling investors to identify key trends, support, and resistance levels, thus improving the success rate of stock trading. The research presented in this paper aims to overcome the limitations of traditional candlestick pattern analysis, which is constrained by fixed pattern definitions, quantity limitations, and subjectivity in pattern recognition, thus improving its effectiveness in dynamic market environments. To address this, a two-layer clustering method based on a candlestick sequence simlarity matching model is proposed for identifying valid candlestick patterns and constructing a pattern library. First, the candlestick sequence similarity matching model is used to address the pattern matching issue; then, a two-layer clustering method based on the K-means algorithm is designed to identify valid candlestick patterns. Finally, a valid candlestick pattern library is built, and the predictive ability and profitability of some patterns in the library are evaluated. In this study, ten stocks from different industries and of various sizes listed on the Shanghai Stock Exchange were selected, using nearly 1000 days of their data as the test set. The predictive ability of some patterns in the library was evaluated using out-of-sample data from the same period. This selection method ensures the diversity of the dataset. The experimental results show that the proposed method can effectively distinguish between bullish and bearish patterns, breaking through the limitations of traditional candlestick pattern classification methods that rely on predefined patterns. By clearly distinguishing these two patterns, it provides clear buy and sell signals for investors, significantly improving the reliability and profitability of trading strategies.

1. Introduction

Since the Dow theory was first introduced in the late 19th century, technical analysis has been favored by market participants for its intuitiveness and practicality. It encompasses various methods such as chart analysis, pattern recognition, and seasonal and cyclical analysis. These techniques aim to predict future market trends by studying historical prices and trading volume data. However, in modern financial theory, Fama’s weak-form efficient market hypothesis [1] asserts that market prices fully reflect all past price information. Therefore, in a weak-form efficient market, technical analysis is considered ineffective in providing predictive insights into future prices. Furthermore, traditional capital asset pricing models (CAPMs) [2,3,4] are based on the assumption of market efficiency, advocating a linear relationship between an asset’s systematic risk and its expected return. This theory further reinforces the notion of random walks in market prices, denying the possibility of achieving abnormal returns by utilizing historical data [5]. Jönsson et al. investigated the predictive power of candlestick patterns in the Swedish stock market. The results indicated that candlestick patterns did not show significant predictive effectiveness in the Swedish market, suggesting that they may lack universality in certain market environments [6]. Stasiak et al. explored the limitations of using candlestick charts in high-frequency markets, pointing out that over-reliance on candlestick charts could lead to erroneous economic research conclusions. The authors emphasized that high-frequency data and more complex market factors should be considered to avoid errors from relying solely on pattern analysis [7].
However, recent studies suggest that markets may not be completely efficient, and candlestick analysis is not ineffective in all situations. In the short term, investors can profit using technical analysis tools, such as candlestick patterns [8,9,10,11,12,13].
One relevant branch of technical analysis involves recognizing chart patterns from Japanese candlestick charts [14]. Discretionary traders often use candlestick patterns to predict the direction of future stock prices. To benefit from the integration of specific domain knowledge in data-driven methods, there is growing interest in combining pattern recognition techniques applied to candlestick charts with machine learning models used for stock-related data [15,16,17,18]. However, existing hybrid solutions have two main drawbacks: (1) machine learning models often generate too many trade signals, leading to a relatively high false alarm rate [19]; (2) models trained on hybrid candlestick patterns and stock price-related features may suffer from the curse of dimensionality [20]. To overcome these issues, the steps of pattern recognition and machine learning can be decoupled to generate profitable trading signals [8]. By including machine learning-based suggestions in the candidate list through pattern recognition, the number of generated trading signals is limited to a reduced subset of more reliable, double-checked recommendations.
Therefore, identifying effective candlestick patterns plays a crucial role in optimizing trading strategies and promoting the application of machine learning models in stock prediction research. Currently, many scholars have proposed different methods for classifying candlestick patterns, which can be categorized into supervised and unsupervised classification. In supervised classification, rule-based (RB) methods are widely applied [8,21]. Fuzzy logic reasoning has also been used for the classification of candlestick patterns [22,23,24,25,26,27,28].
Unsupervised classification typically uses clustering methods for candlestick patterns, including agglomerative hierarchical clustering with Euclidean distance metrics [29], nearest-neighbor clustering algorithms based on candlestick sequence similarity matching models [30], and content-based image retrieval (CBIR) techniques [31]. Clustering algorithms can automatically uncover hidden patterns or categories from large datasets, thus helping users simplify data and discover the underlying structure of the data.
Although the results of these systems have been proven valuable, previous methods in supervised classification required traders and researchers to manually define which candlestick chart patterns were important. This meant that they needed to understand and identify these patterns beforehand, a process that was both time-consuming and subjective. Additionally, the predefined pattern rules were typically derived from historical data and may not adapt to current market changes. If market conditions change significantly, these rules may become invalid or no longer applicable. This paper proposes an unsupervised learning method that can identify important candlestick chart patterns without any prior knowledge or manual definition. The method analyzes large amounts of historical data to uncover hidden patterns that can predict stock price movements. Because it does not rely on human experience or predefined rules, this approach is both reliable and flexible, making it suitable for developing more robust trading systems. The output of this method can also create an effective pattern library, with each pattern containing substantial historical data, which can be used alongside trading systems or strategies.
This study optimizes the process of candlestick pattern recognition through a two-layer clustering method, improving both accuracy and efficiency. Unlike traditional candlestick pattern recognition methods, the two-layer clustering approach automatically identifies and classifies valid candlestick patterns by analyzing the similarity of stock data, overcoming the limitations of fixed patterns and manual intervention. The research also advances the automation and intelligence of financial data analysis. By combining similarity matching with clustering methods, this study introduces a new data-driven tool for financial market prediction. This method can automatically uncover hidden patterns from large datasets, reducing manual intervention and thereby improving both the efficiency and accuracy of data analysis. Furthermore, this study provides more reliable support for investment decisions. By identifying effective candlestick patterns and building a pattern library, this study offers a more scientific basis for generating trading signals, optimizing trading strategies, and enhancing their reliability, thus helping investors make more precise decisions in dynamic markets.
To achieve effective stock prediction, this paper includes the following sections: a comparison of the recent and relevant research literature (Section 2); an introduction to the proposed method (Section 3); and a presentation of the experimental results (Section 4).

2. Review of the Literature

2.1. The Origin of Candlestick Charts and Their Application in Market Analysis

The origin of candlestick charts (also known as K-line charts) dates back to 18th century Japan, where they were invented by the rice merchant Munehisa Homma. By observing rice price fluctuations and recording price changes, he gradually developed the candlestick chart. Candlestick charts display price fluctuations and market sentiment through the shape and color of the body and wicks. Investor sentiment can alter expected profit growth and the required rate of return, thus influencing stock prices [32]. Nison provided a detailed description of the structure and history of candlestick charts and explained their applications, which contributed to the global popularity of candlestick charts [33].
The core assumption of candlestick pattern analysis is that the emotions and behaviors of market participants repeat, creating specific price fluctuation patterns. By identifying historical candlestick patterns, the underlying market trends can be revealed. Early studies showed that candlestick patterns could effectively predict stock price movements, especially in short-term trading strategies [14]. Lu et al. explored the profitability of candlestick chart trading strategies and proposed analyzing the predictability and profitability of candlestick shapes from a new perspective. Their research used more complex statistical methods to explore whether different candlestick patterns could effectively predict market trends [9]. Later studies discussed the influence of trend definitions and position strategies on the profitability of candlestick chart strategies, analyzing how various strategies affect trading results in practice. These studies demonstrated that combining trend definitions with position strategies could significantly improve the profitability of candlestick trading strategies, especially in highly volatile markets, where timely trend identification and appropriate position strategies can effectively reduce risks and increase returns [10]. Heinz et al. conducted a statistical analysis of the bullish and bearish markets engulfing candlestick patterns on the S&P 500 index, examining their market forecasting ability. Their study found that these patterns exhibit some degree of trend predictive power, particularly during periods of high market volatility [11].

2.2. Supervised Classification

With the development of technology, more algorithms have been proposed to automatically identify candlestick patterns, improving prediction accuracy [8]. Currently, many researchers have introduced different methods for classifying candlestick patterns. In supervised classification, rule-based (RB) methods have been widely applied. RB methods directly identify candlestick patterns using explicit rules. Lu et al. classified two-day candlestick patterns using 1 × 4 vectors and systematically studied candlestick shapes, then evaluated their profitability on three European stocks [21]. Cagliero et al. separated pattern recognition from the machine learning steps, using candlestick patterns to filter data, and combining technical characteristics with expert confidence to generate more reliable trading suggestions [8].
Fuzzy logic reasoning has also been widely used in candlestick pattern classification. Etschberger et al. described the size, relationships, and colors of candlestick charts using fuzzy logic [22]. Leon et al. introduced a fuzzy logic-based candlestick pattern recognition system, which compares different patterns by calculating Hamming distance and identifies candlestick patterns with specific size, relationships, colors, and trends [23]. Roy et al. used fuzzy reasoning mechanisms to predict future trends based on the “Hammer” pattern classification method [24]. Vásquez et al. employed fuzzy classification to identify candlestick patterns in real data sequences and designed trading strategies based on the extracted patterns [25]. Chen et al. identified fuzzy candlestick patterns from large amounts of financial transaction data in a prototype system and stored investment strategies in a knowledge base [26]. Arévalo et al. proposed and validated a trading rule based on flag pattern recognition, which improved profitability and reduced trading risk [27]. Cervelló-Royo et al. proposed risk-adjusted profit trading rules based on technical analysis and newly defined flag patterns, clarifying buy and sell timing, target profits, and maximum acceptable losses [28].

2.3. Unsupervised Classification

Clustering methods have also been widely used for the unsupervised classification of candlestick patterns. Martiny et al. employed a hierarchical agglomerative clustering method with Euclidean distance metrics to automatically discover important candlestick patterns from the price data’s time series, integrating the current trend [29]. Tao et al. proposed a nearest-neighbor clustering algorithm based on a candlestick sequence similarity matching model to test the profitability of patterns and mine these patterns from time series data [30]. Additionally, image retrieval methods have been used to search for similar historical candlestick charts represented by image features. Quan et al. applied content-based image retrieval (CBIR) techniques, utilizing low-level image features of candlestick charts, such as wavelet textures and Canny edges, to search for similar historical candlestick charts. Based on these charts’ “future” trends, they predicted stock prices for query charts [31].

2.4. Machine Learning Models

In recent studies, the combination of candlestick patterns and modern machine learning techniques has been widely applied to stock market timing prediction. Jasemi et al. proposed a model combining candlestick analysis with neural networks, which effectively predicts market up and down trends, demonstrating the effectiveness of candlestick patterns in capturing market trends [15]. Marszałek et al. introduced an ordered fuzzy candlestick model, using fuzzy logic to handle uncertainty in market data, thereby improving the accuracy of stock market predictions [16]. Additionally, Ahmadi et al. developed an efficient hybrid candlestick analysis model by combining support vector machines with heuristic algorithms, such as genetic algorithms and imperialist competitive algorithms, further optimizing stock market timing predictions [17]. Bustos et al. conducted a systematic review of the application of candlestick patterns in stock market predictions, emphasizing the potential of combining candlestick patterns with other technical analysis tools to improve market prediction accuracy [19]. Mahmoodi et al. proposed a method combining support vector machine (SVM) and particle swarm optimization (PSO) for the classification analysis of candlestick patterns. By optimizing the parameters of SVM, the study improved the classification accuracy of candlestick charts, thereby enhancing the accuracy of stock market predictions [18]. Cohen et al. explored the application of optimized candlestick pattern analysis in Bitcoin trading systems, proposing a machine learning-based approach to improve prediction accuracy. The results showed that the optimized model significantly enhanced decision-making in Bitcoin trading [12].
An increasing number of studies show that combining machine learning with K-line pattern techniques or trading strategies can significantly improve the accuracy of stock price trend predictions. As a result, efficiently identifying valid K-line patterns has become a key research direction in stock market analysis. Although current research can classify K-line patterns, most methods rely on domain experts to define valid patterns, which may involve subjectivity or even misinterpretation of the patterns. The systems developed by Martiny et al. and Tao et al. reduce the reliance on expert knowledge, but the former does not consider the impact of the weight of wicks and bodies on the model’s accuracy, while the latter, although considering these factors, cannot automatically classify valid K-line patterns. To address these issues, this paper proposes a two-layer clustering method based on a K-line sequence similarity matching model, which has the following advantages: (1) Automated Pattern Recognition: The model can automatically extract K-line shape features from historical data without predefining pattern rules, effectively avoiding the influence of human factors and subjective bias; (2) Improved Market Adaptability: Traditional methods struggle to cope with market environmental changes, whereas this model can dynamically identify new K-line patterns through unsupervised learning, improving adaptability to different market conditions; (3) Enhanced Model Robustness: The two-layer clustering structure optimizes pattern recognition from both global and local levels, more effectively distinguishing noise from key patterns, thus enhancing the model’s robustness and resistance to interference; (4) Support for Decision-Making: The model’s output pattern library can be integrated with trading systems to provide specific trading signals and strategies, improving the scientific and effective nature of trading decisions; (5) Compatibility with Machine Learning Models: The pattern library generated by the model can further enhance the intelligence of the prediction system. When combined with advanced models such as deep learning, it can optimize trading signal generation and risk control strategies, reduce data dimensions, and improve the overall decision-support capability of the system.

3. Material and Method

3.1. Data Acquisition

The dataset used in this paper comes from East Money Information, selecting 10 stocks from various industries with different total market capitalizations on the Shanghai Stock Exchange. The data covers 1000 days of post-adjustment K-line data from 11 November 2019 to 20 December 2023 and is used as the training set. Additionally, Shanxi Fenjiu’s 1000 days of post-adjustment K-line data during the same period was used for out-of-sample testing of selected patterns. Each data point includes four indicators: the opening price, closing price, highest price, and lowest price, resulting in a total of 11,000 data points, with the selected stocks listed in Table 1.
Firstly, this time period encompasses both the pre- and post-outbreak stages of the COVID-19 pandemic, providing a rich data context for analyzing the pandemic’s impact on the financial market. During this period, global financial markets experienced extreme volatility and uncertainty. The economic shock triggered by the pandemic caused fluctuations in stock prices across various industries. By selecting stocks from different industries with various total market capitalizations, this dataset provides a comprehensive reflection of overall market trends. Furthermore, the 10 selected stocks include companies from both top- and middle-ranking industries, ensuring diversity in the dataset and allowing the model to learn more general and representative patterns. Given the background of the pandemic, this dataset is helpful in deeply analyzing stock performance under special market conditions, aiding in the development of a trading system that remains robust even under high uncertainty.
The relevant parameter settings for the K-line sequence similarity matching algorithm are as follows: ω S = 0.8, ω P = 0.2, ω B d = 0.6, ω U S = 0.2, ω L S = 0.2, ω S p t = ω R p t = 1, and the random seed is set to 42.

3.2. K-Line Sequence Similarity Matching

A K-line consists of the opening price, closing price, highest price, and lowest price. Each K-line includes the following parts: The body, which is the main portion of the K-line, represents the price fluctuation range between the opening and closing prices. The shape and color of the body provide important information about market trends. The opening price (O) is the first trading price of the day, while the closing price (C) is the last trading price of the day. The color of the body typically indicates whether the price has increased or decreased. In the Chinese stock market, red or white indicates that the closing price is higher than the opening price (i.e., an increase), as shown in Figure 1a, while green or black indicates that the closing price is lower than the opening price (i.e., a decrease), as shown in Figure 1b. In contrast, this color scheme is reversed in Western stock markets. If the opening price is equal to the closing price, the K-line is called a doji, which signifies market stability, as shown in Figure 1c.
The upper shadow is a thin line above the body, representing the price fluctuation between the highest price during the period and the top of the body (either the opening or closing price). The highest price (high price, H) is the highest trading price during the period, and the length of the upper shadow extends from the top of the body to the highest price. The lower shadow is a thin line below the body, representing the price fluctuation between the lowest price and the bottom of the body (either the opening or closing price). The lowest price (low price, L) is the lowest trading price during the period, and the length of the lower shadow extends from the bottom of the body to the lowest price.
The similarity of K-line sequences affects the model’s performance and is divided into two main aspects: (1) Shape similarity: This involves comparing the opening price, closing price, highest price, and lowest price of corresponding K-lines in two sequences to measure their consistency in shape; (2) Position similarity: This evaluates the similarity in the relative positions of corresponding K-lines within the sequences. Therefore, this paper proposes both a shape similarity matching model and a position similarity matching model, which are integrated to build a comprehensive K-line sequence similarity matching model. Suppose there are two K-line sequences, K S i and K S j , that need to be compared, and let the similarity between them be denoted as Sim i, j. The specific introduction to the similarity matching model between K S i and K S j is as follows: K S i represents i sets of K-line sequence, which means K S i = { D t i |t ∈ N , 1≤t≤ | K S i | }, | K S i | ( | K S i | ∈ N ) represents items of K S i . D t i represents the K-line of K S i of t-th days. Each D t i represents K-line data, which is defined as a four-element array: D t i = { O t i , C t i , H t i , L t i }. O t i , C t i , H t i , L t i represent opening price, closing price, highest price, and lowest price of K S i at day t.

3.2.1. Candlestick Pattern Similarity

First, based on the structural features of the K-line, the K-line shape is divided into three parts: upper shadow shape, lower shadow shape, and body shape. Then, similarity measurement methods are defined for each of these three shapes. Finally, the similarity of these three shapes is weighted and summed to obtain the overall shape similarity of the K-line. D t i and D t j represent the K S i and K S j of K-line day t separately. The shape similarity measurement model between them is as follows:
(1) The upper shadow of D t i is U S i [t], which formula is shown below:
U S i [ t ] = H t i − m a x ( O t i , C t i ) C ( t − 1 ) i ∗ 0.1
where C t − 1 i *0.1 is primarily for normalization. The purpose of normalization is to standardize the K-line shapes of different stocks and time periods, allowing them to be comparable across different price levels.
The upper shadow similarity of D t i and D t j is S i m U S i , j t , which formula is shown below:
Sim us ( i , j ) = 0 , U S i [ t ] ∗ U S j [ t ] = 0 , U S i [ t ] ≠ U S j [ t ] M i n ( U S i [ t ] , U S j [ t ] ) M a x ( U S i [ t ] , U S j [ t ] ) , U S i [ t ] ∗ U S j [ t ] > 0 1 , U S i [ t ] = U S j [ t ] = 0
(2) The lower shadow length of D t i is L S i t , which formula is shown below:
L S i [ t ] = m i n ( O t i , C t i ) − L t i C ( t − 1 ) i ∗ 0.1
The lower shadow similarity of D t i and D t j is S i m L S i , j t , which formula is shown below:
S i m L S ( i , j ) = 0 , L S i [ t ] ∗ L S j [ t ] = 0 , L S i [ t ] ≠ L S j [ t ] M i n ( L S i [ t ] , L S j [ t ] ) M a x ( L S i [ t ] , L S j [ t ] ) , L S i [ t ] ∗ L S j [ t ] > 0 1 , L S i [ t ] = L S j [ t ] = 0
(3) The body length of is [t], which formula is shown below:
B i [ t ] = C t i − O t i C ( t − 1 ) i ∗ 0.1
The body similarity of D t i and D t j is S i m B d i , j t , which formula is shown below:
S i m B d ( i , j ) = 0 , B i [ t ] ∗ B j [ t ] < 0 0 , B i [ t ] ∗ B j [ t ] = 0 , B i [ t ] ≠ B j [ t ] 1 , B i [ t ] = B j [ t ] = 0 M i n ( B i [ t ] , B j [ t ] ) M a x ( B i [ t ] , B j [ t ] ) , B i [ t ] ∗ B j [ t ] > 0
(4) The pattern similarity of D t i and D t j is S i m S p i , j t , which formula is shown below:
S i m S p i , j ( t ) = ω US ∗ S i m US i , j ( t ) + ω B d ∗ S i m Bd i , j ( t ) + ω LS ∗ S i m LS i , j ( t ) ω US + ω B d + ω LS = 1 ω US ≥ 0 , ω B d ≥ 0 , ω LS ≥ 0
where ω U S , ω B d , ω L S represent the weight of S i m U S i , j t , S i m U S i , j t , S i m B d i , j t , S i m L S i , j t . Generally, in K-line technical analysis, the importance of the body is equal to that of the shadows. Therefore, under normal circumstances, the weights of these parameters can be set as follows: ω B d = 0.6 and ω U S = ω L S = 0.2 [30].
(5) The pattern similarity of K S i and K S j is S S i m i , j , which formula is shown below:
S S i m i , j = ω S p t ∗ ∑ t = 1 n S i m S p i , j t
where n = | K S i |, ∑ t = 1 n ω S p t = 1 , and ω S p t represents the weight of S i m S p i , j t . Generally, the weight of each candlestick in the K-line sequence is the same [30].

3.2.2. K-Line Position Similarity

When calculating the similarity of K-line sequences, both shape and spatial position similarity must be considered. To address the issue of position similarity matching, this paper introduces the concept of a coordinate system. Specifically, the order of the K-lines is used as the horizontal axis, while the daily closing price change relative to the previous day’s closing price is used as the vertical axis. The y-coordinate of the first candlestick in the sequence is set to 1; therefore, the x-coordinate of D t i (t = 1) is 1, and the y-coordinate is 1; the x-coordinate of D t i is t, and the y-coordinate is C t i − C t − 1 i /( C t − 1 i * 0.1 ). The K-line sequence position similarity measurement model based on K-line coordinates is shown as follows:
(1) ( x t i , y t i ) represents the axis of D t i , which formula is shown below:
x t i = t , y t i = 1 , t = 1 C t i − C ( t − 1 ) i C ( t − 1 ) i ∗ 0.1 , t > 1
The positional similarity of D t i and D t j is S i m R P i , j t , which formula is shown below:
S i m R P ( i , j ) ( t ) = 0 , y t i ∗ y t j = 0 , y t i ≠ y t j 0 , y t i ∗ y t j < 0 1 , y t i = y t j = 0 M i n ( y t i , y t j ) M a x ( y t i , y t j ) , y t i ∗ y t j > 0
(2) The positional similarity of K S i and K S j is P S i m i , j , which formula is shown below:
P S i m ( i , j ) = ∑ t = 1 n S i m R P ( i , j ) ( t ) ∗ ω R P t
where n = | K S i |, ∑ t = 1 n ω R P t = 1, and ω R P t represents weight of S i m R P i , j t . Generally, each candlestick in the K-line sequence has the same weight [30].

3.2.3. K-Line Sequence Similarity

Based on the shape similarity and position similarity of the K-line sequences, the overall similarity of the entire K-line sequence can be obtained. Therefore, the similarity matching model for K S i and K S j is shown below:
S i m ( i , j ) = ω S ∗ S S i m ( i , j ) + ω P ∗ P S i m ( i , j )
where ω S represents the weight of the K-line sequence’s shape similarity, and ω P represents the weight of the position similarity. Generally, the shape similarity is considered more important than the position similarity, so the recommended weight settings are as follows: ω S = 0.8 and ω P = 0.2 [30].

3.3. Double-Layer Clustering of K-Line Sequences

The distinguishing pattern can accurately predict the direction for the next day, but if the prediction is extended further into the future, its reliability decreases significantly [29]. Therefore, this paper investigates the probability of price increase or decrease for the short-term closing price after the pattern appears. The similarity matching model based on K-line sequences uses the K-means algorithm to cluster K-line patterns. The K-means algorithm requires the number of clusters to be predefined, but the number of effective K-line patterns is not clearly defined. Hence, a two-layer clustering method is used to determine the exact number of effective K-line patterns.

3.3.1. First-Layer Clustering

The first layer of clustering for K-line patterns aims to obtain a complete set of initial valid patterns. To ensure these initial valid K-line patterns can effectively predict the price direction for the next day, their prediction probability (P_R/P_D) must be greater than 60%. If the prediction probability is below 60%, the clustering results may be influenced by randomness, indicating that the clustered patterns might lack sufficient representativeness or stability. For example, in a stock market prediction model using clustering algorithms to classify stock K-line patterns, if the prediction probability (P_R/P_D) is 55%, it means the model has low confidence in predicting this pattern, suggesting that the classification result might not be stable or could be the result of random fluctuations. This low probability indicates that the model may struggle to distinguish between valid patterns and noise data, potentially affecting its real-world application. To ensure the reliability and practical value of the clustering results, setting a higher prediction probability threshold helps avoid incorporating low-confidence patterns into the model, thus improving the accuracy and effectiveness of the clustering results.
Additionally, the number of pattern members within each cluster must exceed a specific value, x, since rare valid patterns have no value in practical applications. Due to the high volatility and complexity of financial market data, a fixed value may not be suitable for all datasets. The chosen x value may vary depending on the scale, characteristics, and market conditions of the data. Therefore, to ensure the model adapts to different datasets and demonstrates good robustness, we have not set a fixed threshold for x.
We start with two clusters and gradually increase the number of clusters until any cluster in the current clustering fails to meet the prediction probability requirement due to insufficient members, at which point we stop the first-layer clustering and tally all the initial valid K-line patterns obtained from the first to the last clustering. Through these steps, we can determine the final number of clusters in the first layer.

3.3.2. Second-Layer Clustering

The goal of the second layer of clustering is to identify redundant and invalid patterns within the initial valid K-line patterns. Redundant patterns are similar K-line patterns that consistently predict the same direction for the next day’s stock closing price, while invalid patterns are those clustered together but fail to consistently predict the stock closing price direction. Based on the principles of the K-means algorithm, when the number of clusters is adjusted, the algorithm recalculates the cluster centers. Therefore, each new clustering could reveal redundant patterns or uncover new ones. Relying solely on the patterns obtained from the final clustering might overlook many hidden patterns. To ensure a comprehensive and accurate set of target patterns, we re-cluster the cluster centers of all initial valid K-line patterns from the first layer of clustering. Starting with two clusters, we gradually increase the number of clusters until the proportion of invalid K-line patterns reaches a predefined threshold, at which point the clustering stops. By eliminating redundant and invalid patterns, we can obtain the final set of valid K-line patterns.

3.4. Pattern Library Creation

The final effective K-line patterns will be compiled into a pattern library, which includes the price data and predictive capability information of the patterns. Each pattern will contain at least thirty different instances for direct use by traders or trading systems. A sufficient number of instances ensures that trading strategies perform well under different market conditions, thereby enhancing the robustness of the trading strategies and improving the flexibility of the trading systems.

3.5. Pattern Profitability Analysis

This paper uses cumulative return to calculate the return of K-line patterns. The specific trading strategy is as follows: (1) Buy stocks at the opening price on the first day after the pattern appears, which is the initial asset value. (2) Hold for a period of time and then sell. This period is the holding period, denoted as f. Since K-line technical analysis is mainly used for short-term prediction, we set the holding period as 1 ≤ f ≤ 5. (3) Sell the stock at the closing price on the f-th day after the pattern appears. This price is the final asset value. (4) Calculate the return of the K-line pattern holding for f days based on the initial asset price and final asset value, denoted as E f . If E f > 0, the return is positive; if E f < 0, the return is negative. The formula for calculating E f   is shown in Equation (13).
E f = I n i t i a l   V a l u e − F i n a l   V a l u e / I n i t i a l   V a l u e

4. Results and Discussion

4.1. Cluster Analysis

Based on the K-line sequence similarity matching model defined earlier, the first-layer clustering was performed on 10,000 stock data points in the training dataset. The stopping condition for clustering was set to 144 clusters, resulting in a total of 832 initial effective K-line pattern clusters, as detailed in Table 2.
To filter out redundant duplicate patterns and remove invalid patterns, we conducted a second-layer clustering analysis on the cluster centers of the 832 initial effective K-line pattern clusters. In each class, the group with the best predictive ability (the highest of P R / P D ) was selected as the final effective K-line pattern group. As shown in Figure 2, as the number of clusters gradually increased to 110, the rate of invalid K-line patterns rapidly decreased; when the number of clusters increased from 110 to 170, the rate of decline in invalid K-line patterns slowed; and after exceeding 170 clusters, the rate of invalid K-line patterns stabilized. Since similar K-line patterns with the same predictive ability are regarded as the same pattern, having too many clusters may lead to the same K-line pattern being split into multiple clusters, increasing the difficulty of identifying effective patterns. Therefore, a higher number of clusters does not necessarily yield more effective results. Based on this principle, we determined 170 as the final number of clusters. After screening and removing 14 invalid patterns, the number of final effective K-line patterns in the library was reduced to 156. The rate of invalid K-line patterns corresponding to different cluster counts is shown in Figure 2, and detailed information about the effective K-line pattern library can be found in Table 3.
In the effective K-line pattern library, each pattern contains price data for at least 30 K-line sequences and the price data for the next day following the occurrence of the pattern. For the evaluation of the pattern’s predictive ability, if P R ≥ 0.6, the pattern is considered a bullish pattern; if P D ≥ 0.6, it is considered a bearish pattern. Among the 156 effective patterns in the library, there are 44 bullish patterns and 112 bearish patterns.

4.2. Patterns Validation

In this study, we validated four randomly selected bullish patterns and four bearish patterns from the library using the stock data of Shanxi Fenjiu during the same period. First, we employed a sliding window technique to divide the 1000 days of data for this stock, resulting in a validation set of 998 three-day K-line patterns. Next, we clustered the selected K-line patterns with the validation set data, using the same number of clusters as that of the first-layer clustering for the respective patterns. Finally, we counted the occurrences of the stock price rise or fall for the next day after the selected patterns appeared, along with other patterns in the same group. Examples of the selected K-line patterns are shown in Table 4 and Table 5.
Bullish pattern 1: This K-line pattern is a common three consecutive bullish candlestick formation. The three consecutive bullish candlesticks consist of three continuous rising bullish candles, where the body of each bullish candle is longer than the previous one. Additionally, the opening price of each bullish candle is usually higher than the closing price of the preceding candle, typically indicating positive market sentiment and the potential for further upward movement in the future.
Bullish pattern 2: This K-line pattern features a first candlestick that is a bearish candle, with the closing price slightly lower than the opening price, followed by two consecutive bullish candles, each with an opening price higher than the previous day’s closing price. This formation typically indicates a shift in market sentiment from negative to positive, suggesting that prices may rise in the future.
Bullish pattern 3: This K-line pattern consists of a long bearish candle as the first candlestick, followed by a smaller bearish candle as the second, and a bullish candle as the third, with its closing price higher than the previous day’s closing price. This formation typically suggests that the market may rebound and rise.
Bullish pattern 4: This K-line pattern consists of three consecutive bearish candles, with each candle’s closing price lower than that of the previous one. However, the entity of the bearish candle on the last day is smaller than that of the previous two days. This formation typically suggests that the selling pressure in the market is gradually weakening, and a rebound or upward movement may be imminent.
Bearish pattern 1: This K-line pattern consists of three candles: the first is a bullish candle, the second is a shorter candle (usually a doji or a small bearish candle), and the third is a long bearish candle, with each day’s closing price lower than the previous day. This formation indicates that the market may continue to move downward.
Bearish pattern 2: This K-line pattern consists of three candles: the first is a long bullish candle, the second is a shorter doji or small bullish candle, and the third is a long bearish candle. This formation indicates market hesitation and suggests that a downward reversal may be imminent.
Bearish pattern 3: This K-line pattern consists of the first two candles being short bullish candles or dojis, followed by a third long bearish candle. This formation suggests that a downward reversal may be imminent.
Bearish pattern 4: This K-line pattern consists of three increasingly shorter bullish candles, indicating that market optimism has peaked, which suggests that a downward reversal may be imminent.
The verification results are shown in Table 6. In the concurrent data of Shanxi Fenjiu stocks, the actual performance of the patterns is as follows: Bullish Pattern 1 appeared thirteen times, with the closing price rising the next day on twelve occasions; Bullish Pattern 2 appeared seventeen times, with the closing price rising the next day on eleven occasions; Bullish Pattern 3 appeared fourteen times, with the closing price rising the next day on eight occasions; Bullish Pattern 4 appeared eight times, with the closing price rising the next day on five occasions. Bearish Pattern 1 appeared eighteen times, with the closing price falling the next day on eleven occasions; Bearish Pattern 2 appeared thirteen times, with the closing price falling the next day on ten occasions; Bearish Pattern 3 appeared ten times, with the closing price falling the next day on seven occasions; Bearish Pattern 4 appeared eleven times, with the closing price falling the next day on seven occasions. The verification results indicate that the actual performance of each K-line pattern in the concurrent data of Shanxi Fenjiu stocks is generally consistent with expectations. Both bullish and bearish patterns demonstrate high accuracy in predicting price movements the following day. Specifically, bullish patterns have a high probability of an increase the next day, while bearish patterns correspond to a high probability of a decline.

4.3. Analysis of Pattern Profitability

The profitability of the patterns is shown in Table 7. When a bullish pattern appears, we buy the stock at the opening price the next day and sell it at the closing price after holding it for f days, with all stocks realizing positive returns. Conversely, when a bearish pattern appears, the same operation is performed, but the returns on the stocks during the holding period are negative.
Although only a subset of patterns was verified in this study, their actual performance in the concurrent data of Shanxi Fenjiu stock closely aligns with the expected results. This indicates that the method proposed in this paper is highly applicable and reliable in predicting short-term stock price movements. Through pattern selection and clustering, the retained valid patterns can accurately determine the short-term direction of stock price changes, providing strong support for subsequent market applications. The pattern profitability analysis further confirms that the proposed model effectively distinguishes between bullish and bearish patterns, offering clear buy and sell signals for investors and significantly enhancing the reliability and profitability of trading strategies.

5. Conclusions

In previous studies, candlestick charts have often been used for predicting stock prices or market trends, typically relying on experts’ deep understanding and knowledge of specific candlestick patterns. However, the unsupervised pattern detection method used in this paper allows for the construction of an independent and complete pattern knowledge base, enabling the development of an adaptive system for predicting the next day’s price movements. This method can automatically identify potential important patterns from training data and can re-match patterns when the stock market changes, providing flexibility to adapt to the complex variations in different stocks.
This research has significant theoretical implications. First, it enriches the theoretical framework in the field of technical analysis of candlestick patterns by proposing a dual-layer clustering model based on candlestick sequence similarity matching, overcoming the limitations of traditional pattern definitions that rely on domain experts’ subjective understanding. Secondly, the study provides a new perspective on combining candlestick patterns with machine learning techniques, deepening the understanding of financial market price behavior and pushing technical analysis toward a data-driven, intelligent direction. Additionally, our findings validate the potential application of unsupervised learning in financial time series analysis, providing theoretical support for exploring automated pattern recognition in other market domains. Finally, the proposed model is highly versatile, offering a reference for future financial technology research and expanding the boundaries of candlestick pattern recognition methods.
The research also holds important practical significance. By constructing an automated candlestick pattern recognition and prediction system, companies can efficiently identify patterns with potential investment value without the need for extensive domain expert involvement. This technology can be applied in quantitative trading platforms, assisting in the formulation of dynamic trading strategies and improving the scientific accuracy of trading decisions. Moreover, businesses can leverage the reliable buy and sell signals provided by the model to optimize investment portfolios and reduce market risks. Especially in volatile market environments, this method can capture market trends in a timely manner, enhance capital efficiency, and improve overall profitability. By integrating the results of this research into existing financial analysis and trading systems, companies can gain a competitive edge in the capital markets, achieving breakthroughs in both technology and business.
The results indicate that the proposed candlestick pattern recognition system shows certain advantages in terms of effectiveness and potential, though some limitations still exist. For example: (1) Only a subset of patterns from the library was randomly selected for predictive ability and profitability analysis, without covering all patterns comprehensively; (2) Validation was only carried out on a single stock out-of-sample, lacking extensive verification across multiple stocks; (3) Insufficient consideration of weights for body and shadow in patterns like the doji could have impacted the model’s accuracy. Future research can expand and deepen in the following areas: (1) Broadening the validation scope to test more stocks and verify the effectiveness of other patterns in the pattern library; (2) Investigating how different weight combinations affect model performance to optimize it further; (3) Combining machine learning methods with candlestick pattern recognition, utilizing technologies such as deep learning or reinforcement learning to improve pattern recognition accuracy and the model’s adaptability, better responding to changes in various market conditions.

Author Contributions

Conceptualization, X.L.; Data curation, X.L.; Formal analysis, X.L.; Funding acquisition, H.L.; Investigation, X.L.; Methodology, X.L.; Project administration, X.L.; Resources, X.L.; Software, X.L.; Supervision, X.L.; Validation, X.L.; Visualization, X.L.; Writing—original draft, X.L.; Writing—review and editing, X.L., Q.L., Y.H. and H.L. All authors have read and agreed to the published version of the manuscript.

Funding

The work was supported by the Humanity and Social Science Foundation of Ministry of Education of China (No. 18YJA630037, 21YJA630054). Zhejiang Province Soft Science Research Program Project (No. 2024C350470).

Data Availability Statement

The data in this paper are available from the website netease (https://finance.sina.com.cn/).

Conflicts of Interest

Xinglong Li, Qingyang Liu, Yanrong Hu and Hongjiu Liu declare that there is no conflicts of interests regarding the publication of our paper “The Double-Layer clustering k-line pattern recognition based on similarity matching”.

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Information 15 00821 g001
Figure 1. K-line legend showing (a) an increase with red or white K-line, (b) a decrease with green or black K-line, and (c) market stability with a Doji K-line [30].
Figure 1. K-line legend showing (a) an increase with red or white K-line, (b) a decrease with green or black K-line, and (c) market stability with a Doji K-line [30].
Information 15 00821 g001
Information 15 00821 g002
Figure 2. Ineffective candlestick pattern rate for different numbers of clusters.
Figure 2. Ineffective candlestick pattern rate for different numbers of clusters.
Information 15 00821 g002
Table 1. The selected stocks.
Table 1. The selected stocks.
Stock CodeStock NameIndustryMarket Size/USD
sh601012Longi Green EnergyPhotovoltaic Equipment20.85 billion
sh600519Kweichow MoutaiLiquor Industry271.64 billion
sh601127SeresAutomotive 29.87 billion
sh601888China Duty Free GroupTourism and Hotels21.02 billion
sh600630Longtou SharesTextiles and Apparel0.62 billion
sh600036China Merchants BankBanking130.64 billion
sh600571XinyadaInternet Services0.92 billion
sh601318Ping An InsuranceInsurance142.6 billion
sh600900China Yangtze PowerElectric Power Industry91.81 billion
sh603178Shenglong SharesAutomotive Parts0.73 billion
sh600809Shanxi FenjiuLiquor Industry37.26 billion
Table 2. Initial effective K-line pattern cluster.
Table 2. Initial effective K-line pattern cluster.
Pattern IDFirst-Layer Cluster Count (Effective Pattern Label)Occurrence Count P R P D
032–281030.39 0.61
132–29550.36 0.60
237–13670.36 0.63
340–5780.37 0.62
441–39570.37 0.61
543–2840.61 0.37
……………
828144–11350.34 0.63
829144–65330.33 0.67
830144–107310.65 0.35
831144–113300.27 0.73
Table 3. Effective K-line pattern library.
Table 3. Effective K-line pattern library.
Pattern IDFirst-Layer Cluster Count (Effective Pattern Label)Occurrence Count P R P D Price
049–35760.36 0.63 …
152–46410.63 0.37 …
253–44550.33 0.67 …
355–5470.62 0.36 …
456–34440.32 0.68 …
556–44620.36 0.63 …
………………
152141–71330.64 0.33 …
153142–122310.68 0.32 …
154144–11330.33 0.67 …
155144–113310.65 0.35 …
Table 4. Selection of patterns shape.
Table 4. Selection of patterns shape.
1234
Bullish patternInformation 15 00821 i001Information 15 00821 i002Information 15 00821 i003Information 15 00821 i004
Bearish patternInformation 15 00821 i005Information 15 00821 i006Information 15 00821 i007Information 15 00821 i008
Table 5. Selection of patterns.
Table 5. Selection of patterns.
Pattern NamePattern LabelOccurrence Count P R P D
Bullish pattern 1106–56310.650.35
Bullish pattern 292–32350.690.31
Bullish pattern 3115–9350.770.23
Bullish pattern 4107–66310.650.35
Bearish pattern 182–58310.290.71
Bearish pattern 2102–41340.29 0.71
Bearish pattern 378–3320.28 0.69
Bearish pattern 4109–90330.330.64
Table 6. Validation results of bullish/bearish patterns.
Table 6. Validation results of bullish/bearish patterns.
Pattern NameOccurrence CountNumber of Next-Day Increases/Number of OccurrencesNumber of Next-Day Decreases/Number of Occurrences
Bullish pattern 1130.920.08
Bullish pattern 2170.650.35
Bullish pattern 3140.570.43
Bullish pattern 480.6250.375
Bearish pattern 1180.390.61
Bearish pattern 2130.230.77
Bearish pattern 3100.300.70
Bearish pattern 4110.360.64
Table 7. Profitability analysis of bullish/bearish patterns.
Table 7. Profitability analysis of bullish/bearish patterns.
fBullish Pattern 1Bullish Pattern 2Bullish Pattern 3Bullish Pattern 4Bearish Pattern 1Bearish Pattern 2Bearish Pattern 3Bearish Pattern 4
11.0%1.3%1.2%1.8%−1.3%−2.1%−1.9%−1.5%
21.6%1.1%1.7%1.6%−1.2%−1.8%−1.7%−1.6%
31.9%0.9%1.6%1.7%−1.5%−1.8%−1.6%−1.3%
43.8%1.4%1.4%2.4%−1.9%−1.7%−1.3%−1.2%
55.1%1.1%1.0%4.3%−1.2%−2.2%−1.5%−1.8%
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Li, X.; Liu, Q.; Hu, Y.; Liu, H. The Double-Layer Clustering Based on K-Line Pattern Recognition Based on Similarity Matching. Information 2024, 15, 821. https://doi.org/10.3390/info15120821

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Li X, Liu Q, Hu Y, Liu H. The Double-Layer Clustering Based on K-Line Pattern Recognition Based on Similarity Matching. Information. 2024; 15(12):821. https://doi.org/10.3390/info15120821

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Li, Xinglong, Qingyang Liu, Yanrong Hu, and Hongjiu Liu. 2024. "The Double-Layer Clustering Based on K-Line Pattern Recognition Based on Similarity Matching" Information 15, no. 12: 821. https://doi.org/10.3390/info15120821

APA Style

Li, X., Liu, Q., Hu, Y., & Liu, H. (2024). The Double-Layer Clustering Based on K-Line Pattern Recognition Based on Similarity Matching. Information, 15(12), 821. https://doi.org/10.3390/info15120821

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