assignment_75.ipynb

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    "Q1. What is the role of feature selection in anomaly detection?"
   ]
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    "Ans: Feature selection plays a crucial role in anomaly detection by influencing the effectiveness, efficiency, and interpretability of anomaly detection models. Here's how feature selection contributes to anomaly detection:\n",
    "\n",
    "1. **Dimensionality Reduction**: Anomaly detection often deals with high-dimensional data, where the number of features can be very large. Feature selection helps reduce the dimensionality of the data by selecting a subset of the most relevant features. By focusing on the most informative features, dimensionality reduction techniques such as feature selection can improve the efficiency of anomaly detection algorithms and mitigate the curse of dimensionality.\n",
    "\n",
    "2. **Noise Reduction**: Not all features in a dataset may be relevant for anomaly detection. Some features may contain noise or irrelevant information that could distract the model and degrade its performance. Feature selection helps filter out noisy features, thereby improving the signal-to-noise ratio and enhancing the detection of meaningful anomalies.\n",
    "\n",
    "3. **Improved Performance**: By focusing on the most informative features, feature selection can lead to more accurate anomaly detection models. Selecting relevant features reduces the complexity of the model and helps it focus on the most discriminative aspects of the data, leading to better detection of anomalies.\n",
    "\n",
    "4. **Computational Efficiency**: Anomaly detection algorithms often involve complex computations, especially when dealing with high-dimensional data. Feature selection reduces the computational burden by reducing the number of features that need to be processed and analyzed. This can lead to faster model training and inference times.\n",
    "\n",
    "5. **Interpretability**: Feature selection can improve the interpretability of anomaly detection models by focusing on a subset of features that are more easily understandable and interpretable by humans. Selecting a smaller set of relevant features can help users understand the factors contributing to the detection of anomalies and make more informed decisions based on the model's output.\n",
    "\n",
    "6. **Generalization**: Feature selection can improve the generalization ability of anomaly detection models by reducing overfitting. By selecting only the most relevant features, feature selection helps prevent the model from memorizing noise or irrelevant patterns in the training data, leading to more robust and generalizable models.\n",
    "\n",
    "Overall, feature selection is essential in anomaly detection for improving model performance, reducing computational complexity, enhancing interpretability, and promoting generalization. It helps tailor the model to focus on the most relevant aspects of the data, leading to more effective anomaly detection in various application domains."
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   "source": [
    "Q2. What are some common evaluation metrics for anomaly detection algorithms and how are they\n",
    "computed?"
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    "Ans: Several evaluation metrics are commonly used to assess the performance of anomaly detection algorithms. These metrics provide insights into the algorithm's ability to correctly identify anomalies and distinguish them from normal instances. Some common evaluation metrics for anomaly detection algorithms include:\n",
    "\n",
    "1. **True Positive Rate (TPR) or Recall**:\n",
    "   - TPR measures the proportion of actual anomalies that are correctly identified by the algorithm. It is calculated as the number of true positive predictions (correctly identified anomalies) divided by the total number of actual anomalies.\n",
    "   - $ TPR = \\frac{\\text{True Positives}}{\\text{True Positives} + \\text{False Negatives}} $\n",
    "\n",
    "2. **False Positive Rate (FPR)**:\n",
    "   - FPR measures the proportion of normal instances that are incorrectly classified as anomalies by the algorithm. It is calculated as the number of false positive predictions (normal instances incorrectly identified as anomalies) divided by the total number of actual normal instances.\n",
    "   - $ FPR = \\frac{\\text{False Positives}}{\\text{False Positives} + \\text{True Negatives}} $\n",
    "\n",
    "3. **Precision**:\n",
    "   - Precision measures the proportion of true positive predictions among all positive predictions made by the algorithm. It is calculated as the number of true positive predictions divided by the total number of positive predictions (true positives plus false positives).\n",
    "   - $ Precision = \\frac{\\text{True Positives}}{\\text{True Positives} + \\text{False Positives}} $\n",
    "\n",
    "4. **F1 Score**:\n",
    "   - The F1 score is the harmonic mean of precision and recall. It provides a balanced measure of the algorithm's performance by considering both false positives and false negatives. A higher F1 score indicates better overall performance.\n",
    "   - $ F1 \\text{ Score} = 2 \\times \\frac{\\text{Precision} \\times \\text{Recall}}{\\text{Precision} + \\text{Recall}} $\n",
    "\n",
    "5. **Area Under the Receiver Operating Characteristic Curve (AUC-ROC)**:\n",
    "   - AUC-ROC measures the performance of the algorithm across different threshold settings. It plots the true positive rate (TPR) against the false positive rate (FPR) at various threshold values and calculates the area under the curve. A higher AUC-ROC indicates better discrimination between anomalies and normal instances.\n",
    "\n",
    "6. **Area Under the Precision-Recall Curve (AUC-PR)**:\n",
    "   - AUC-PR measures the trade-off between precision and recall at various threshold settings. It plots precision against recall and calculates the area under the curve. A higher AUC-PR indicates better overall performance, particularly in cases of imbalanced datasets.\n",
    "\n",
    "These evaluation metrics provide quantitative measures of an anomaly detection algorithm's performance, helping assess its effectiveness in identifying anomalies and distinguishing them from normal instances. Depending on the specific requirements and characteristics of the dataset, different metrics may be more appropriate for evaluating the performance of anomaly detection algorithms."
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   "source": [
    "Q3. What is DBSCAN and how does it work for clustering?"
   ]
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    "Ans: DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is a popular density-based clustering algorithm used in machine learning and data mining. Unlike traditional centroid-based clustering algorithms like k-means, DBSCAN does not require the user to specify the number of clusters beforehand. Instead, it automatically identifies clusters based on the density of data points in the feature space.\n",
    "\n",
    "Here's how DBSCAN works for clustering:\n",
    "\n",
    "1. **Core Points and Density Reachability**:\n",
    "   - DBSCAN defines two key parameters: epsilon (ε) and MinPts.\n",
    "   - ε is the maximum radius around a data point within which other points are considered neighbors.\n",
    "   - MinPts is the minimum number of points required within ε to consider a point a core point.\n",
    "   - A core point is a point that has at least MinPts points (including itself) within its ε-neighborhood.\n",
    "   - A point is considered density-reachable from another core point if there is a path of core points leading from one to the other, such that each consecutive core point is within ε distance of the previous one.\n",
    "\n",
    "2. **Cluster Formation**:\n",
    "   - DBSCAN iterates through each data point in the dataset.\n",
    "   - For each point, it checks whether the point is a core point. If it is, DBSCAN expands a new cluster starting from that core point.\n",
    "   - It does this by recursively adding all points that are density-reachable from the core point to the same cluster.\n",
    "   - If a point is not a core point and is not density-reachable from any core point, it is labeled as noise and not assigned to any cluster.\n",
    "\n",
    "3. **Cluster Identification**:\n",
    "   - As DBSCAN iterates through the data points, clusters are formed and expanded until all points have been processed.\n",
    "   - The algorithm may create several clusters of varying shapes and sizes, depending on the density and distribution of the data.\n",
    "   - Some points may be labeled as noise if they do not meet the criteria for being core points or density-reachable from core points.\n",
    "\n",
    "4. **Parameter Tuning**:\n",
    "   - Tuning the parameters ε and MinPts is crucial for the performance of DBSCAN.\n",
    "   - Choosing appropriate values for these parameters depends on the characteristics of the dataset, such as the density and distribution of the data points.\n",
    "   - If ε is too small, clusters may be fragmented, and many points may be labeled as noise. If ε is too large, clusters may merge, and the algorithm may fail to capture the underlying structure of the data.\n",
    "\n",
    "DBSCAN is particularly effective for identifying clusters of arbitrary shape and handling noise in the dataset. It does not assume that clusters are spherical or that they have a specific number of points. However, it may struggle with datasets of varying densities or datasets with high-dimensional feature spaces, as the definition of distance becomes less intuitive in higher dimensions."
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   "source": [
    "Q4. How does the epsilon parameter affect the performance of DBSCAN in detecting anomalies?"
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    "Ans: In DBSCAN (Density-Based Spatial Clustering of Applications with Noise), the epsilon (ε) parameter determines the radius within which points are considered neighbors. This parameter plays a crucial role in the performance of DBSCAN in detecting anomalies. Here's how the epsilon parameter affects DBSCAN's performance:\n",
    "\n",
    "1. **Size of Neighborhoods**:\n",
    "   - A smaller value of ε results in smaller neighborhoods around each point, meaning that only nearby points are considered neighbors. This can lead to the detection of finer details in the data and more localized clusters.\n",
    "   - Conversely, a larger value of ε results in larger neighborhoods, allowing points that are farther apart to be considered neighbors. This can lead to the merging of clusters and the creation of larger, more generalized clusters.\n",
    "\n",
    "2. **Density of Clusters**:\n",
    "   - In DBSCAN, clusters are formed based on the density of points within neighborhoods. A smaller ε parameter leads to denser clusters, as more points are required to be close to each other to form a cluster.\n",
    "   - On the other hand, a larger ε parameter leads to sparser clusters, as fewer points are required to form a cluster due to the larger neighborhood size.\n",
    "\n",
    "3. **Effect on Anomaly Detection**:\n",
    "   - In anomaly detection, anomalies are often characterized by being isolated or lying in regions of low density. A smaller ε parameter can help in identifying such anomalies by focusing on local neighborhoods and detecting isolated points or points with few neighbors.\n",
    "   - Conversely, a larger ε parameter may not be as effective in detecting anomalies, as it may lead to the formation of larger, denser clusters that obscure the presence of anomalies.\n",
    "\n",
    "4. **Tuning for Anomaly Detection**:\n",
    "   - The ε parameter needs to be carefully tuned for anomaly detection tasks to balance between capturing the underlying structure of the data and identifying anomalies.\n",
    "   - A smaller ε parameter may be more suitable for detecting anomalies in dense regions of the data or for capturing fine-grained details, while a larger ε parameter may be more suitable for detecting anomalies in sparser regions or for capturing more global patterns.\n",
    "\n",
    "In summary, the epsilon parameter in DBSCAN affects the size of neighborhoods, the density of clusters, and ultimately the algorithm's ability to detect anomalies. Tuning this parameter appropriately is essential for achieving optimal performance in anomaly detection tasks."
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   "source": [
    "Q5. What are the differences between the core, border, and noise points in DBSCAN, and how do they relate\n",
    "to anomaly detection?"
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    "Ans: In DBSCAN (Density-Based Spatial Clustering of Applications with Noise), points are categorized into three types: core points, border points, and noise points. These categories are based on the density of points within the neighborhood defined by the epsilon (ε) parameter. Understanding these point types is essential for anomaly detection:\n",
    "\n",
    "1. **Core Points**:\n",
    "   - Core points are data points that have at least MinPts (a user-defined parameter) points, including themselves, within their ε-neighborhood.\n",
    "   - Core points are typically located in the dense regions of the dataset and are crucial for forming clusters.\n",
    "   - They serve as central points around which clusters are expanded during the clustering process.\n",
    "\n",
    "2. **Border Points**:\n",
    "   - Border points are data points that do not meet the criteria to be considered core points themselves but are within the ε-neighborhood of at least one core point.\n",
    "   - Border points lie on the periphery of clusters and are adjacent to core points.\n",
    "   - They may be part of a cluster but are not central to it and may have fewer neighboring points than core points.\n",
    "\n",
    "3. **Noise Points**:\n",
    "   - Noise points (also known as outliers) are data points that do not meet the criteria to be considered core points and are not within the ε-neighborhood of any core point.\n",
    "   - Noise points do not belong to any cluster and are considered as outliers or anomalies.\n",
    "   - They are typically located in regions of low density or far from any cluster.\n",
    "\n",
    "Relation to Anomaly Detection:\n",
    "\n",
    "- **Core Points**: Core points are unlikely to be anomalies themselves, as they are located in dense regions where most of the data points are concentrated. However, if a core point is surrounded by a significant number of noise points, it might be indicative of a local anomaly or an unusual cluster.\n",
    "  \n",
    "- **Border Points**: Border points are also less likely to be anomalies, as they are adjacent to core points and usually part of clusters. However, border points near the boundary of clusters may have characteristics similar to anomalies, especially if they are sparsely surrounded by other points.\n",
    "\n",
    "- **Noise Points**: Noise points are often considered anomalies or outliers in anomaly detection tasks. They represent data points that do not conform to the expected patterns or structures defined by clusters. Detecting noise points is a key aspect of anomaly detection with DBSCAN, as they may represent interesting patterns, anomalies, or errors in the data.\n",
    "\n",
    "In summary, understanding the differences between core, border, and noise points in DBSCAN is essential for anomaly detection. Noise points, in particular, play a significant role in identifying anomalies, while core and border points provide context for understanding the structure of the data and the formation of clusters."
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   "source": [
    "Q6. How does DBSCAN detect anomalies and what are the key parameters involved in the process?"
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    "Ans: DBSCAN (Density-Based Spatial Clustering of Applications with Noise) can be used for anomaly detection by identifying points that are labeled as noise or outliers. Here's how DBSCAN detects anomalies and the key parameters involved in the process:\n",
    "\n",
    "1. **Density-Based Approach**:\n",
    "   - DBSCAN detects anomalies based on the density of points in the dataset. Anomalies are typically points that are located in regions of low density or are isolated from dense clusters.\n",
    "   - The algorithm identifies clusters as dense regions of points connected by density-reachable core points.\n",
    "   - Points that are not part of any cluster and do not meet the criteria to be considered core points are labeled as noise or outliers.\n",
    "\n",
    "2. **Key Parameters**:\n",
    "\n",
    "   a. **Epsilon (ε)**: Epsilon defines the radius within which points are considered neighbors. It determines the size of the neighborhood used to calculate the density of points.\n",
    "   \n",
    "   b. **MinPts**: MinPts is the minimum number of points required within the ε-neighborhood of a point to consider it a core point. It controls the minimum density required for a region to be considered a cluster.\n",
    "   \n",
    "   c. **Distance Metric**: The choice of distance metric (e.g., Euclidean distance, Manhattan distance) affects how distance is measured between points, influencing the definition of neighborhoods and density.\n",
    "\n",
    "3. **Detection Process**:\n",
    "   \n",
    "   a. **Cluster Formation**: DBSCAN first identifies core points, which are points with at least MinPts neighbors within their ε-neighborhood. It then expands clusters by connecting core points that are density-reachable from each other.\n",
    "   \n",
    "   b. **Noise Detection**: Points that are not part of any cluster and do not meet the criteria to be considered core points are labeled as noise or outliers.\n",
    "   \n",
    "   c. **Anomaly Identification**: Noise points identified by DBSCAN are typically considered anomalies or outliers. These points are often located in regions of low density or are isolated from dense clusters, making them distinct from the majority of the data points.\n",
    "\n",
    "4. **Parameter Tuning**:\n",
    "   \n",
    "   - Tuning the ε and MinPts parameters is crucial for anomaly detection with DBSCAN. \n",
    "   - Smaller values of ε and larger values of MinPts may lead to the detection of finer-grained anomalies, while larger values of ε and smaller values of MinPts may result in the detection of more global anomalies.\n",
    "   \n",
    "   - Choosing appropriate parameter values depends on the characteristics of the dataset, such as the density and distribution of the data points, as well as the specific requirements of the anomaly detection task.\n",
    "\n",
    "In summary, DBSCAN detects anomalies by identifying points that are labeled as noise or outliers based on their density and proximity to other points. The key parameters involved in the process include ε, MinPts, and the distance metric, which influence how clusters and anomalies are identified in the data. Proper parameter tuning is essential for effectively using DBSCAN for anomaly detection."
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   "source": [
    "Q7. What is the make_circles package in scikit-learn used for?"
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    "Ans: The `make_circles` function in scikit-learn is used to generate synthetic datasets consisting of concentric circles. It is primarily used for testing and illustrating clustering and classification algorithms, particularly those designed to handle non-linearly separable data. \n",
    "\n",
    "Here's a brief overview of the `make_circles` package:\n",
    "\n",
    "1. **Generating Synthetic Data**:\n",
    "   - The `make_circles` function generates a dataset with two features (attributes) and two classes.\n",
    "   - The data points are distributed in such a way that they form concentric circles.\n",
    "\n",
    "2. **Parameters**:\n",
    "   - The function takes several parameters to control the characteristics of the generated dataset, such as the number of samples, noise level, and random state.\n",
    "   - The key parameters include:\n",
    "     - `n_samples`: The total number of data points to generate.\n",
    "     - `noise`: The standard deviation of the Gaussian noise added to the data.\n",
    "     - `factor`: The factor controlling the relative size of the inner circle to the outer circle.\n",
    "\n",
    "3. **Usage**:\n",
    "   - The `make_circles` function is often used as a toy dataset for testing and visualizing clustering and classification algorithms.\n",
    "   - It helps demonstrate how algorithms perform on non-linearly separable data and evaluate their ability to capture complex patterns.\n",
    "   - Additionally, it serves as a benchmark for comparing the performance of different algorithms on similar datasets.\n",
    "\n",
    "Here's an example of how to use `make_circles` to generate a synthetic dataset:\n"
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_circles\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Generate a dataset with 100 samples, noise level of 0.1, and random state of 42\n",
    "X, y = make_circles(n_samples=100, noise=0.1, random_state=42)\n",
    "\n",
    "# Plot the generated dataset\n",
    "plt.scatter(X[y == 0][:, 0], X[y == 0][:, 1], label='Class 0', marker='o')\n",
    "plt.scatter(X[y == 1][:, 0], X[y == 1][:, 1], label='Class 1', marker='s')\n",
    "plt.xlabel('Feature 1')\n",
    "plt.ylabel('Feature 2')\n",
    "plt.title('Synthetic Dataset: Concentric Circles')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "848032df-b06c-43de-99e0-00965224d6a3",
   "metadata": {},
   "source": [
    "Q8. What are local outliers and global outliers, and how do they differ from each other?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "121a7191-fb43-4a55-acb5-aa220914a733",
   "metadata": {},
   "source": [
    "Ans: Local outliers and global outliers are concepts used in outlier detection to describe different types of anomalous data points within a dataset. They differ primarily in terms of their relationship to their local neighborhoods versus the dataset as a whole.\n",
    "\n",
    "1. **Local Outliers**:\n",
    "   - Local outliers, also known as contextual outliers or conditional outliers, are data points that are unusual or anomalous within their local neighborhoods.\n",
    "   - These outliers may not be considered anomalies when viewed in the context of the entire dataset, but they exhibit abnormal behavior relative to their immediate surroundings.\n",
    "   - Local outliers are often identified by comparing a data point's characteristics to those of its nearest neighbors, typically using density-based or distance-based methods.\n",
    "   - Examples of local outliers include points that have significantly different attributes compared to their nearest neighbors, points located in regions of low local density, or points that violate local patterns or structures.\n",
    "\n",
    "2. **Global Outliers**:\n",
    "   - Global outliers, also known as unconditional outliers or global anomalies, are data points that are anomalous when compared to the entire dataset.\n",
    "   - These outliers exhibit abnormal behavior when considered in the context of the entire dataset, rather than just their local neighborhoods.\n",
    "   - Global outliers are typically identified by comparing a data point's characteristics to the overall distribution of the dataset, without considering local neighborhoods.\n",
    "   - Examples of global outliers include points that have extreme values or are located far from the bulk of the data distribution, points that are inconsistent with the general trends or patterns in the dataset, or points that represent rare events or occurrences.\n",
    "\n",
    "In summary, the main differences between local outliers and global outliers lie in their relationship to their local neighborhoods versus the dataset as a whole. Local outliers are anomalies relative to their local surroundings, while global outliers are anomalies when considered in the context of the entire dataset. Both types of outliers are important to consider in outlier detection tasks, as they may provide valuable insights into different aspects of the data distribution and underlying processes."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f66c4d30-665d-43ec-a2f1-9abad1c7fd4a",
   "metadata": {},
   "source": [
    "Q9. How can local outliers be detected using the Local Outlier Factor (LOF) algorithm?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41ed16d4-c9b1-47da-a0aa-7157ce2a6a12",
   "metadata": {},
   "source": [
    "Ans: The Local Outlier Factor (LOF) algorithm is a popular method for detecting local outliers in a dataset. It measures the local deviation of a data point with respect to its neighbors, allowing for the identification of points that are outliers within their local neighborhoods. Here's how the LOF algorithm detects local outliers:\n",
    "\n",
    "1. **Compute Reachability Distance**:\n",
    "   - For each data point $ p $, compute its reachability distance with respect to its $ k $ nearest neighbors. The reachability distance of point $ p $ with respect to a neighbor $ q $ is defined as the maximum of the distance between $ p $ and $ q $, and the k-distance of $ q $. Formally, the reachability distance $ \\text{reach-dist}_k(p, q) $ is calculated as:\n",
    "   $ \\text{reach-dist}_k(p, q) = \\max(\\text{dist}(p, q), \\text{k-distance}(q)) $\n",
    "   - Here, $ \\text{dist}(p, q) $ represents the distance between points $ p $ and $ q $, and $ \\text{k-distance}(q) $ is the distance to the $ k -th$ nearest neighbor of $ q $.\n",
    "\n",
    "2. **Compute Local Reachability Density**:\n",
    "   - For each data point $ p $, compute its local reachability density (LRD) based on the reachability distances of its $ k $ nearest neighbors. The LRD of point $ p $ is the inverse of the average reachability distance of its neighbors. Formally, the LRD of $ p $, denoted as $ \\text{LRD}_k(p) $, is calculated as:\n",
    "   $ \\text{LRD}_k(p) = \\left( \\frac{\\sum_{q \\in N_k(p)} \\text{reach-dist}_k(p, q)}{|N_k(p)|} \\right)^{-1} $\n",
    "   - Here, $ N_k(p) $ represents the set of $ k $ nearest neighbors of point $ p $.\n",
    "\n",
    "3. **Compute Local Outlier Factor (LOF)**:\n",
    "   - For each data point $ p $, compute its local outlier factor (LOF) based on the local reachability densities of its neighbors. The LOF of point $ p $ measures how much more or less dense its local neighborhood is compared to the local neighborhoods of its neighbors. Formally, the LOF of $ p $, denoted as $ \\text{LOF}_k(p) $, is calculated as the ratio of the average LRD of its neighbors to its own LRD:\n",
    "   $ \\text{LOF}_k(p) = \\frac{\\sum_{q \\in N_k(p)} \\text{LRD}_k(q)}{|N_k(p)| \\times \\text{LRD}_k(p)} $\n",
    "   - An anomaly score is then assigned to each data point based on its LOF value. Higher LOF values indicate that the data point is more likely to be an outlier or anomaly.\n",
    "\n",
    "By computing the LOF for each data point, the LOF algorithm identifies local outliers that exhibit significantly different density patterns compared to their neighbors. These local outliers represent points that are anomalous within their local neighborhoods, making the LOF algorithm effective for detecting anomalies in high-dimensional datasets with complex density distributions."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a54cd3cc-863b-447d-84a3-67d19d2a262f",
   "metadata": {},
   "source": [
    "Q10. How can global outliers be detected using the Isolation Forest algorithm?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4bd6810-7b10-4d71-becc-95ff20a231a1",
   "metadata": {},
   "source": [
    "Ans: The Isolation Forest algorithm is a popular method for detecting global outliers, also known as isolation-based outlier detection. It works by isolating anomalies that are relatively rare and different from the majority of the data points. Here's how the Isolation Forest algorithm detects global outliers:\n",
    "\n",
    "1. **Isolation Tree Construction**:\n",
    "   - The Isolation Forest algorithm constructs a collection of isolation trees, which are binary trees used to isolate anomalies.\n",
    "   - Each isolation tree is built recursively by randomly selecting a feature and then randomly selecting a split value within the range of that feature.\n",
    "   - The process is repeated until all data points are isolated into individual leaf nodes, forming a tree structure.\n",
    "\n",
    "2. **Path Length Calculation**:\n",
    "   - The anomaly score of a data point is calculated based on the average path length of the data point in all isolation trees.\n",
    "   - During the construction of each isolation tree, the path length from the root node to the leaf node containing the data point is recorded.\n",
    "   - The average path length of the data point across all isolation trees is then computed.\n",
    "\n",
    "3. **Anomaly Score Calculation**:\n",
    "   - The anomaly score of a data point is inversely proportional to its average path length across all isolation trees.\n",
    "   - Data points with shorter average path lengths are considered to be anomalies, as they require fewer splits to isolate and are thus less likely to be part of the normal data distribution.\n",
    "   - Anomaly scores are typically normalized to the range [0, 1], where a higher score indicates a higher likelihood of being an outlier.\n",
    "\n",
    "4. **Thresholding**:\n",
    "   - An optional step involves setting a threshold on the anomaly scores to classify data points as outliers.\n",
    "   - Data points with anomaly scores above the threshold are considered global outliers, while those below the threshold are considered normal.\n",
    "\n",
    "5. **Detection of Global Outliers**:\n",
    "   - Global outliers are detected based on their anomalous behavior relative to the majority of the data points.\n",
    "   - These outliers exhibit patterns or characteristics that are different from the normal data distribution and are relatively rare in the dataset.\n",
    "\n",
    "By leveraging the isolation tree structure and the average path length of data points, the Isolation Forest algorithm efficiently identifies global outliers in high-dimensional datasets with complex distributions. It is particularly effective for detecting outliers that are distinct from the majority of the data points and do not conform to the expected patterns or structures."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb551c79-28d1-45aa-b1f3-3b2062fb24ce",
   "metadata": {},
   "source": [
    "Q11. What are some real-world applications where local outlier detection is more appropriate than global\n",
    "outlier detection, and vice versa?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8839bfd9-483f-4cf0-ac53-5ba05c84bbce",
   "metadata": {},
   "source": [
    "Ans: Local outlier detection and global outlier detection each have their strengths and are suitable for different real-world applications depending on the characteristics of the data and the specific requirements of the task. Here are some examples of real-world applications where each approach may be more appropriate:\n",
    "\n",
    "**Local Outlier Detection:**\n",
    "\n",
    "1. **Network Intrusion Detection**:\n",
    "   - In network traffic analysis, local outlier detection can be used to identify unusual behavior within specific segments of a network.\n",
    "   - Anomalies such as port scanning, denial-of-service attacks, or unusual traffic patterns may be localized to specific hosts or subnetworks.\n",
    "\n",
    "2. **Manufacturing Quality Control**:\n",
    "   - In manufacturing processes, local outlier detection can be applied to detect anomalies in sensor readings or product characteristics within specific production lines or batches.\n",
    "   - Unusual variations or defects may occur locally in certain components or production stages, indicating potential quality issues.\n",
    "\n",
    "3. **Medical Anomaly Detection**:\n",
    "   - In healthcare, local outlier detection can be used to identify unusual patient conditions or symptoms within specific demographic groups or medical conditions.\n",
    "   - Anomalies such as rare diseases, adverse drug reactions, or abnormal test results may manifest locally in certain patient populations.\n",
    "\n",
    "**Global Outlier Detection:**\n",
    "\n",
    "1. **Financial Fraud Detection**:\n",
    "   - In banking and finance, global outlier detection can be applied to identify fraudulent transactions or activities that deviate from the overall patterns of legitimate transactions.\n",
    "   - Anomalies such as large-scale money laundering schemes or unauthorized account access may be global outliers affecting the entire financial system.\n",
    "\n",
    "2. **Environmental Monitoring**:\n",
    "   - In environmental science, global outlier detection can be used to detect anomalies in large-scale environmental phenomena such as climate patterns, air quality, or natural disasters.\n",
    "   - Anomalies such as extreme weather events, pollution spikes, or ecosystem disturbances may be considered global outliers affecting a wide geographic area.\n",
    "\n",
    "3. **Market Basket Analysis**:\n",
    "   - In retail and e-commerce, global outlier detection can be applied to identify unusual purchasing patterns or product associations across the entire customer base.\n",
    "   - Anomalies such as sudden shifts in consumer preferences, rare item combinations, or unexpected market trends may be detected as global outliers affecting overall sales patterns.\n",
    "\n",
    "In summary, the choice between local and global outlier detection depends on the specific context and characteristics of the data. Local outlier detection is more suitable for identifying anomalies within localized regions or subgroups, whereas global outlier detection is better suited for detecting anomalies that affect the entire dataset or system. Both approaches have valuable applications in various domains, and the selection of the appropriate method depends on the desired level of granularity and the scope of the analysis."
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