From 5542f6ba9d665838d273257859992efe958eca6a Mon Sep 17 00:00:00 2001 From: Revanth <109272714+revanth1718@users.noreply.github.com> Date: Tue, 4 Jun 2024 22:18:48 +0530 Subject: [PATCH 01/18] Added K-Means --- .../machine-learning/K-Means_Clustering.md | 84 +++++++++++++++++++ 1 file changed, 84 insertions(+) create mode 100644 contrib/machine-learning/K-Means_Clustering.md diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/K-Means_Clustering.md new file mode 100644 index 0000000..f90e290 --- /dev/null +++ b/contrib/machine-learning/K-Means_Clustering.md @@ -0,0 +1,84 @@ +# K-Means Clustering +Unsupervised Learning Algorithm for Grouping Similar Data. +## Introduction +K-means clustering is a fundamental unsupervised machine learning algorithm that excels at grouping similar data points together. It's a popular choice due to its simplicity and efficiency in uncovering hidden patterns within unlabeled datasets. +## Unsupervised Learning +Unlike supervised learning algorithms that rely on labeled data for training, unsupervised algorithms, like K-means, operate solely on input data (without predefined categories). Their objective is to discover inherent structures or groupings within the data. +## The K-Means Objective +Organize similar data points into clusters to unveil underlying patterns. The main objective is to minimize total intra-cluster variance or the squared function. + +![enter image description here](https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcQnDTFfxrrAttYMwwjZV0RAA8J8rmUxgrnWc2gU_ArEqrxEMlHm) +## Clusters and Centroids +A cluster represents a collection of data points that share similar characteristics. K-means identifies a pre-determined number (k) of clusters within the dataset. Each cluster is represented by a centroid, which acts as its central point (imaginary or real). +## Minimizing In-Cluster Variation +The K-means algorithm strategically assigns each data point to a cluster such that the total variation within each cluster (measured by the sum of squared distances between points and their centroid) is minimized. In simpler terms, K-means strives to create clusters where data points are close to their respective centroids. +## The Meaning Behind "K-Means" +The "means" in K-means refers to the averaging process used to compute the centroid, essentially finding the center of each cluster. +## K-Means Algorithm in Action +![enter image description here](https://d3i71xaburhd42.cloudfront.net/2f49631bb3103a61fbc3045dd035c3d8f2175887/11-Figure2-1.png) +The K-means algorithm follows an iterative approach to optimize cluster formation: + +1. **Initial Centroid Placement:** The process begins with randomly selecting k centroids to serve as initial reference points for each cluster. +2. **Data Point Assignment:** Each data point is assigned to the closest centroid, effectively creating a preliminary clustering. +3. **Centroid Repositioning:** Once data points are assigned, the centroids are recalculated by averaging the positions of the points within their respective clusters. These new centroids represent the refined centers of the clusters. +4. **Iteration Until Convergence:** Steps 2 and 3 are repeated iteratively until a stopping criterion is met. This criterion can be either: + - **Centroid Stability:** No significant change occurs in the centroids' positions, indicating successful clustering. + - **Reaching Maximum Iterations:** A predefined number of iterations is completed. + ## Code + Following is a simple implementation of K-Means. + + + # Generate and Visualize Sample Data + # import the necessary Libraries + + import numpy as np + import matplotlib.pyplot as plt + + # Create data points for cluster 1 and cluster 2 + X = -2 * np.random.rand(100, 2) + X1 = 1 + 2 * np.random.rand(50, 2) + + # Combine data points from both clusters + X[50:100, :] = X1 + + # Plot data points and display the plot + plt.scatter(X[:, 0], X[:, 1], s=50, c='b') + plt.show() + + # K-Means Model Creation and Training + from sklearn.cluster import KMeans + + # Create KMeans object with 2 clusters + kmeans = KMeans(n_clusters=2) + kmeans.fit(X) # Train the model on the data + + # Visualize Data Points with Centroids + centroids = kmeans.cluster_centers_ # Get centroids (cluster centers) + + plt.scatter(X[:, 0], X[:, 1], s=50, c='b') # Plot data points again + plt.scatter(centroids[0, 0], centroids[0, 1], s=200, c='g', marker='s') # Plot centroid 1 + plt.scatter(centroids[1, 0], centroids[1, 1], s=200, c='r', marker='s') # Plot centroid 2 + plt.show() # Display the plot with centroids + + # Predict Cluster Label for New Data Point + new_data = np.array([-3.0, -3.0]) + new_data_reshaped = new_data.reshape(1, -1) + predicted_cluster = kmeans.predict(new_data_reshaped) + print("Predicted cluster for new data:", predicted_cluster) + + ### Output: + Before Implementing K-Means Clustering : +![Before Implementing K-Means Clustering](https://miro.medium.com/v2/resize:fit:640/format:webp/1*jnyQxmEj7rFhazeMH7KXVg.png) + + + After Implementing K-Means Clustering:![enter image description here](https://miro.medium.com/v2/resize:fit:640/format:webp/1*H3L3EH3Jh6kWFmbec0ewKA.png) +## Conclusion +**K-Means** can be applied to data that has a smaller number of dimensions, is numeric, and is continuous or can be used to find groups that have not been explicitly labeled in the data. As an example, it can be used for Document Classification, Delivery Store Optimization, or Customer Segmentation. + + + + + + + + From 7259dc7047a0576721b852fc4aeb08ddf5bd8b84 Mon Sep 17 00:00:00 2001 From: Revanth <109272714+revanth1718@users.noreply.github.com> Date: Tue, 4 Jun 2024 22:24:02 +0530 Subject: [PATCH 02/18] Update K-Means_Clustering.md --- contrib/machine-learning/K-Means_Clustering.md | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/K-Means_Clustering.md index f90e290..ab5fba9 100644 --- a/contrib/machine-learning/K-Means_Clustering.md +++ b/contrib/machine-learning/K-Means_Clustering.md @@ -67,11 +67,12 @@ The K-means algorithm follows an iterative approach to optimize cluster formatio print("Predicted cluster for new data:", predicted_cluster) ### Output: - Before Implementing K-Means Clustering : + Before Implementing K-Means Clustering ![Before Implementing K-Means Clustering](https://miro.medium.com/v2/resize:fit:640/format:webp/1*jnyQxmEj7rFhazeMH7KXVg.png) - After Implementing K-Means Clustering:![enter image description here](https://miro.medium.com/v2/resize:fit:640/format:webp/1*H3L3EH3Jh6kWFmbec0ewKA.png) + After Implementing K-Means Clustering + ![enter image description here](https://miro.medium.com/v2/resize:fit:640/format:webp/1*H3L3EH3Jh6kWFmbec0ewKA.png) ## Conclusion **K-Means** can be applied to data that has a smaller number of dimensions, is numeric, and is continuous or can be used to find groups that have not been explicitly labeled in the data. As an example, it can be used for Document Classification, Delivery Store Optimization, or Customer Segmentation. From e9eb68ab3832ec651264b967de709ee8ae41af5f Mon Sep 17 00:00:00 2001 From: Revanth <109272714+revanth1718@users.noreply.github.com> Date: Tue, 4 Jun 2024 23:28:27 +0530 Subject: [PATCH 03/18] Update K-Means_Clustering.md --- contrib/machine-learning/K-Means_Clustering.md | 11 +++++------ 1 file changed, 5 insertions(+), 6 deletions(-) diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/K-Means_Clustering.md index ab5fba9..c6aee6a 100644 --- a/contrib/machine-learning/K-Means_Clustering.md +++ b/contrib/machine-learning/K-Means_Clustering.md @@ -15,7 +15,6 @@ The K-means algorithm strategically assigns each data point to a cluster such th ## The Meaning Behind "K-Means" The "means" in K-means refers to the averaging process used to compute the centroid, essentially finding the center of each cluster. ## K-Means Algorithm in Action -![enter image description here](https://d3i71xaburhd42.cloudfront.net/2f49631bb3103a61fbc3045dd035c3d8f2175887/11-Figure2-1.png) The K-means algorithm follows an iterative approach to optimize cluster formation: 1. **Initial Centroid Placement:** The process begins with randomly selecting k centroids to serve as initial reference points for each cluster. @@ -66,13 +65,13 @@ The K-means algorithm follows an iterative approach to optimize cluster formatio predicted_cluster = kmeans.predict(new_data_reshaped) print("Predicted cluster for new data:", predicted_cluster) - ### Output: - Before Implementing K-Means Clustering -![Before Implementing K-Means Clustering](https://miro.medium.com/v2/resize:fit:640/format:webp/1*jnyQxmEj7rFhazeMH7KXVg.png) + ### Output: +![Before Implementing K-Means Clustering](data:image/png;base64,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) - After Implementing K-Means Clustering - ![enter image description here](https://miro.medium.com/v2/resize:fit:640/format:webp/1*H3L3EH3Jh6kWFmbec0ewKA.png) + + ![After Implementing K-Means Clustering](data:image/png;base64,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+ Predicted cluster for new data: [0] ## Conclusion **K-Means** can be applied to data that has a smaller number of dimensions, is numeric, and is continuous or can be used to find groups that have not been explicitly labeled in the data. As an example, it can be used for Document Classification, Delivery Store Optimization, or Customer Segmentation. 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z!s>5(N}+(ZYo14FzRtNg^TU^uiyqHBaGpQV4i=4`3*N;iYFt-VS!I<~R#|10RaRLg arT+(~s&-lbfZ;O$0000 Date: Tue, 4 Jun 2024 23:41:27 +0530 Subject: [PATCH 05/18] Update K-Means_Clustering.md --- contrib/machine-learning/K-Means_Clustering.md | 11 ++++++----- 1 file changed, 6 insertions(+), 5 deletions(-) diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/K-Means_Clustering.md index c6aee6a..82a5c83 100644 --- a/contrib/machine-learning/K-Means_Clustering.md +++ b/contrib/machine-learning/K-Means_Clustering.md @@ -7,7 +7,7 @@ Unlike supervised learning algorithms that rely on labeled data for training, un ## The K-Means Objective Organize similar data points into clusters to unveil underlying patterns. The main objective is to minimize total intra-cluster variance or the squared function. -![enter image description here](https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcQnDTFfxrrAttYMwwjZV0RAA8J8rmUxgrnWc2gU_ArEqrxEMlHm) +![image](assets/Knm.png) ## Clusters and Centroids A cluster represents a collection of data points that share similar characteristics. K-means identifies a pre-determined number (k) of clusters within the dataset. Each cluster is represented by a centroid, which acts as its central point (imaginary or real). ## Minimizing In-Cluster Variation @@ -15,6 +15,7 @@ The K-means algorithm strategically assigns each data point to a cluster such th ## The Meaning Behind "K-Means" The "means" in K-means refers to the averaging process used to compute the centroid, essentially finding the center of each cluster. ## K-Means Algorithm in Action +![image](assets/Km_.png) The K-means algorithm follows an iterative approach to optimize cluster formation: 1. **Initial Centroid Placement:** The process begins with randomly selecting k centroids to serve as initial reference points for each cluster. @@ -66,11 +67,11 @@ The K-means algorithm follows an iterative approach to optimize cluster formatio print("Predicted cluster for new data:", predicted_cluster) ### Output: -![Before Implementing K-Means Clustering](data:image/png;base64,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) + Before Implementing K-Means Clustering +![Before Implementing K-Means Clustering](assets/Km_2.png) - - - ![After Implementing K-Means Clustering](data:image/png;base64,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) + After Implementing K-Means Clustering + ![After Implementing K-Means Clustering](assets/Km_3.png) Predicted cluster for new data: [0] ## Conclusion **K-Means** can be applied to data that has a smaller number of dimensions, is numeric, and is continuous or can be used to find groups that have not been explicitly labeled in the data. As an example, it can be used for Document Classification, Delivery Store Optimization, or Customer Segmentation. From d65dce72e10873a2554cbc37b00fab868fdfb0d5 Mon Sep 17 00:00:00 2001 From: Revanth <109272714+revanth1718@users.noreply.github.com> Date: Tue, 4 Jun 2024 23:46:20 +0530 Subject: [PATCH 06/18] update k-means --- contrib/machine-learning/K-Means_Clustering.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/K-Means_Clustering.md index 82a5c83..bf72ffd 100644 --- a/contrib/machine-learning/K-Means_Clustering.md +++ b/contrib/machine-learning/K-Means_Clustering.md @@ -7,7 +7,7 @@ Unlike supervised learning algorithms that rely on labeled data for training, un ## The K-Means Objective Organize similar data points into clusters to unveil underlying patterns. The main objective is to minimize total intra-cluster variance or the squared function. -![image](assets/Knm.png) +![image](assets\knm.png) ## Clusters and Centroids A cluster represents a collection of data points that share similar characteristics. K-means identifies a pre-determined number (k) of clusters within the dataset. Each cluster is represented by a centroid, which acts as its central point (imaginary or real). ## Minimizing In-Cluster Variation @@ -15,7 +15,7 @@ The K-means algorithm strategically assigns each data point to a cluster such th ## The Meaning Behind "K-Means" The "means" in K-means refers to the averaging process used to compute the centroid, essentially finding the center of each cluster. ## K-Means Algorithm in Action -![image](assets/Km_.png) +![image](assets\km_.png) The K-means algorithm follows an iterative approach to optimize cluster formation: 1. **Initial Centroid Placement:** The process begins with randomly selecting k centroids to serve as initial reference points for each cluster. @@ -68,10 +68,10 @@ The K-means algorithm follows an iterative approach to optimize cluster formatio ### Output: Before Implementing K-Means Clustering -![Before Implementing K-Means Clustering](assets/Km_2.png) +![Before Implementing K-Means Clustering](assets\km_2.png) After Implementing K-Means Clustering - ![After Implementing K-Means Clustering](assets/Km_3.png) + ![After Implementing K-Means Clustering](assets\km_3.png) Predicted cluster for new data: [0] ## Conclusion **K-Means** can be applied to data that has a smaller number of dimensions, is numeric, and is continuous or can be used to find groups that have not been explicitly labeled in the data. As an example, it can be used for Document Classification, Delivery Store Optimization, or Customer Segmentation. From 7bc7b0621eb59fa6e85c076885d1e18d2f103847 Mon Sep 17 00:00:00 2001 From: Revanth <109272714+revanth1718@users.noreply.github.com> Date: Wed, 5 Jun 2024 11:26:57 +0530 Subject: [PATCH 07/18] Update K-Means_Clustering.md --- contrib/machine-learning/K-Means_Clustering.md | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/K-Means_Clustering.md index bf72ffd..859636b 100644 --- a/contrib/machine-learning/K-Means_Clustering.md +++ b/contrib/machine-learning/K-Means_Clustering.md @@ -7,7 +7,7 @@ Unlike supervised learning algorithms that rely on labeled data for training, un ## The K-Means Objective Organize similar data points into clusters to unveil underlying patterns. The main objective is to minimize total intra-cluster variance or the squared function. -![image](assets\knm.png) +![image](assets/knm.png) ## Clusters and Centroids A cluster represents a collection of data points that share similar characteristics. K-means identifies a pre-determined number (k) of clusters within the dataset. Each cluster is represented by a centroid, which acts as its central point (imaginary or real). ## Minimizing In-Cluster Variation @@ -15,7 +15,7 @@ The K-means algorithm strategically assigns each data point to a cluster such th ## The Meaning Behind "K-Means" The "means" in K-means refers to the averaging process used to compute the centroid, essentially finding the center of each cluster. ## K-Means Algorithm in Action -![image](assets\km_.png) +![image](assets/km_.png) The K-means algorithm follows an iterative approach to optimize cluster formation: 1. **Initial Centroid Placement:** The process begins with randomly selecting k centroids to serve as initial reference points for each cluster. @@ -68,10 +68,11 @@ The K-means algorithm follows an iterative approach to optimize cluster formatio ### Output: Before Implementing K-Means Clustering -![Before Implementing K-Means Clustering](assets\km_2.png) +![Before Implementing K-Means Clustering](assets/km_2.png) After Implementing K-Means Clustering - ![After Implementing K-Means Clustering](assets\km_3.png) + ![After Implementing K-Means Clustering](assets/km_3.png) + Predicted cluster for new data: [0] ## Conclusion **K-Means** can be applied to data that has a smaller number of dimensions, is numeric, and is continuous or can be used to find groups that have not been explicitly labeled in the data. As an example, it can be used for Document Classification, Delivery Store Optimization, or Customer Segmentation. From 92571f619700a05019853aff0230015fe4b85a2d Mon Sep 17 00:00:00 2001 From: saiumasankar Date: Wed, 5 Jun 2024 11:29:23 +0530 Subject: [PATCH 08/18] update dynamic programming Added LIS problem and Tabulation code of LCS and 0-1 Knapsack --- contrib/ds-algorithms/dynamic-programming.md | 124 ++++++++++++++++++- 1 file changed, 121 insertions(+), 3 deletions(-) diff --git a/contrib/ds-algorithms/dynamic-programming.md b/contrib/ds-algorithms/dynamic-programming.md index 43149f8..54c6fcb 100644 --- a/contrib/ds-algorithms/dynamic-programming.md +++ b/contrib/ds-algorithms/dynamic-programming.md @@ -84,8 +84,32 @@ Y = "GXTXAYB" print("Length of Longest Common Subsequence:", longest_common_subsequence(X, Y, len(X), len(Y))) ``` +## Longest Common Subsequence Code in Python (Bottom-Up Approach) + +```python + +def longestCommonSubsequence(X, Y, m, n): + L = [[None]*(n+1) for i in range(m+1)] + for i in range(m+1): + for j in range(n+1): + if i == 0 or j == 0: + L[i][j] = 0 + elif X[i-1] == Y[j-1]: + L[i][j] = L[i-1][j-1]+1 + else: + L[i][j] = max(L[i-1][j], L[i][j-1]) + return L[m][n] + + +S1 = "AGGTAB" +S2 = "GXTXAYB" +m = len(S1) +n = len(S2) +print("Length of LCS is", longestCommonSubsequence(S1, S2, m, n)) +``` + ## Complexity Analysis -- **Time Complexity**: O(m * n) for the top-down approach, where m and n are the lengths of the input sequences +- **Time Complexity**: O(m * n) for both approaches, where m and n are the lengths of the input sequences - **Space Complexity**: O(m * n) for the memoization table
@@ -122,11 +146,105 @@ capacity = 50 n = len(weights) print("Maximum value that can be obtained:", knapsack(weights, values, capacity, n)) ``` +## 0-1 Knapsack Problem Code in Python (Bottom-up Approach) +```python +def knapSack(capacity, weights, values, n): + K = [[0 for x in range(capacity + 1)] for x in range(n + 1)] + for i in range(n + 1): + for w in range(capacity + 1): + if i == 0 or w == 0: + K[i][w] = 0 + elif weights[i-1] <= w: + K[i][w] = max(values[i-1] + + K[i-1][w-weights[i-1]], + K[i-1][w]) + else: + K[i][w] = K[i-1][w] + + return K[n][capacity] + +values = [60, 100, 120] +weights = [10, 20, 30] +capacity = 50 +n = len(weights) +print(knapSack(capacity, weights, values, n)) +``` ## Complexity Analysis -- **Time Complexity**: O(n * W) for the top-down approach, where n is the number of items and W is the capacity of the knapsack +- **Time Complexity**: O(n * W) for both approaches, where n is the number of items and W is the capacity of the knapsack - **Space Complexity**: O(n * W) for the memoization table

-
\ No newline at end of file +
+ +# 4. Longest Increasing Subsequence + +The Longest Increasing Subsequence (LIS) is a task is to find the longest subsequence that is strictly increasing, meaning each element in the subsequence is greater than the one before it. This subsequence must maintain the order of elements as they appear in the original sequence but does not need to be contiguous. The goal is to identify the subsequence with the maximum possible length. + +**Algorithm Overview:** +- **Base cases:** If the sequence is empty, the LIS length is 0. +- **Memoization:** Store the results of previously computed subproblems to avoid redundant computations. +- **Recurrence relation:** Compute the LIS length by comparing characters of the sequences and making decisions based on their values. + +## Longest Increasing Subsequence Code in Python (Top-Down Approach using Memoization) + +```python + +import sys + +def f(idx, prev_idx, n, a, dp): + if (idx == n): + return 0 + + if (dp[idx][prev_idx + 1] != -1): + return dp[idx][prev_idx + 1] + + notTake = 0 + f(idx + 1, prev_idx, n, a, dp) + take = -sys.maxsize - 1 + if (prev_idx == -1 or a[idx] > a[prev_idx]): + take = 1 + f(idx + 1, idx, n, a, dp) + + dp[idx][prev_idx + 1] = max(take, notTake) + return dp[idx][prev_idx + 1] + +def longestSubsequence(n, a): + + dp = [[-1 for i in range(n + 1)]for j in range(n + 1)] + return f(0, -1, n, a, dp) + +a = [3, 10, 2, 1, 20] +n = len(a) + +print("Length of lis is", longestSubsequence(n, a)) + +``` + +## Longest Increasing Subsequence Code in Python (Bottom-Up Approach) + +```python +def lis(arr): + n = len(arr) + lis = [1]*n + + for i in range(1, n): + for j in range(0, i): + if arr[i] > arr[j] and lis[i] < lis[j] + 1: + lis[i] = lis[j]+1 + + maximum = 0 + for i in range(n): + maximum = max(maximum, lis[i]) + + return maximum + +arr = [10, 22, 9, 33, 21, 50, 41, 60] +print("Length of lis is", lis(arr)) +``` +## Complexity Analysis +- **Time Complexity**: O(n * n) for both approaches, where n is the length of the array. +- **Space Complexity**: O(n * n) for the memoization table in Top-Down Approach, O(n) in Bottom-Up Approach. + +
+
+
From f742fddff366a0eff24520c8ee292b81d2188d45 Mon Sep 17 00:00:00 2001 From: saiumasankar Date: Wed, 5 Jun 2024 17:28:33 +0530 Subject: [PATCH 09/18] Adding the BeautifulSoup web scrapping --- contrib/web-scrapping/beautifulsoup.md | 206 +++++++++++++++++++++++++ contrib/web-scrapping/index.md | 1 + 2 files changed, 207 insertions(+) create mode 100644 contrib/web-scrapping/beautifulsoup.md diff --git a/contrib/web-scrapping/beautifulsoup.md b/contrib/web-scrapping/beautifulsoup.md new file mode 100644 index 0000000..372b8f2 --- /dev/null +++ b/contrib/web-scrapping/beautifulsoup.md @@ -0,0 +1,206 @@ +# Beautiful Soup Library in Python + +## Table of Contents +1. Introduction +2. Prerequisites +3. Setting Up Environment +4. Beautiful Soup Objects +5. Tag object +6. Children, Parents and Siblings +7. Filter: Findall method +8. Web Scraping the Contents of a Web Page + +## 1. Introduction +Beautiful Soup is a Python library used for web scraping purposes to extract data from HTML and XML files. It creates a parse tree for parsed pages that can be used to extract data easily. + +## 2. Prerequisites +- Understanding of HTTP Requests and Responses. +- Understanding of HTTP methods (GET method). +- Basic Knowledge on HTML. +- Python installed on your machine (version 3.6 or higher). +- pip (Python package installer) installed. + +## 3. Setting Up Environment +1.**Install latest version of Python:** Go to Python.org and Download the latest version of Python. + +2.**Install a IDE:** Install any IDE of your choice to code. VS code is preferred. +>Note: You can use Google Colab without installing Python and IDE. + +3.**Install Beautiful Soup:** +```python +!pip install bs4 +``` + +## 4. Beautiful Soup Objects +Beautiful Soup is a Python library for pulling data out of HTML and XML files. This can be done by presenting the HTML as a set of objects. + +Take the below HTML page as input +``` + + + +Page Title + + +

Title

+

This is the main context of the page

+ + +``` + +lets store the HTML code in a variable +``` +html= " + + + Page Title + + +

Title

+

This is the main context of the page

+ + " +``` + +To parse the HTML document, pass the variable to the `BeautifulSoup` Constructor. +``` +soup = BeautifulSoup(html,'html.parser') +``` +Beautiful Soup transforms a complex HTML document into a complex tree of Python objects. + +## 5. Tags + +The Tag object corresponds to an HTML tag in the original document. + +``` +tag_obj = soup.title +print("tag object:", tag_obj) +print("tag object type:",type(tag_obj)) +``` +``` +Result: +tag object: Page Title + +tag object type: +``` + +## 6. Children, Parent and Siblings + +We can access the child of the tag or navigate down. + +``` +tag_obj = soup.h3 +child = tag_obj.b +print(child) +parent = child.parent +print(parent) +sib = tag_obj.next_sibling +print(sib); +``` +``` +Result: + Title +

Title

+

This is the main context of the page

+``` + +> We need to mention the child to which we want to navigate. It is because there can be more than one child to a tag but only one parent and next sibling. + +**Navigable String:** A string corresponds to a bit of text or content within a tag. Beautiful Soup uses the NavigableString class to contain this text. + +``` +tagstr = child.string +print(tagstr) +``` +``` +Result: +Title +``` + +## 7. Filter + +Filters allow you to find complex patterns, the simplest filter is a string. + +Consider the following HTML code: + +``` + + + + + + Sample Table + + +

Sample Table

+ + + + + + + + + + + + + + + + + + + + + + + + + +
NameAgeCity
John Doe28New York
Jane Smith34Los Angeles
Emily Jones23Chicago
+ + + +``` +Store the above code in a variable. +``` +table = " + + + + + Sample Table +.............. + +table_bs = BeautifulSoup(table, 'html.parser') +" +``` +**Find All:** The find_all() method looks through a tag’s descendants and retrieves all descendants that match your filters. It places all the objects in a list. We can access by indexing. + +## 8. Web Scraping the Contents of a Web Page + +1. Get the URL of the webpage we need to scrape. + +2. Get the HTML content by using `get` method in HTTP request. + +3. Pass the HTML content to the BeautifulSoup Constructor to prepare an object. + +4. Access the HTML elements using Tag name. + +Below is the code to extract the img tags in a wikipedia page. + +``` +import requests +!pip install bs4 +from bs4 import BeautifulSoup + +url = "https://en.wikipedia.org/wiki/Encyclopedia" +data = requests.get(url).text +soup = BeautifulSoup(data,"html.parser") + +for link in soup.find_all('a'): + print(link) + print(link.get('src')) +``` +We can retrieve any data in the webpage by access through the tags. diff --git a/contrib/web-scrapping/index.md b/contrib/web-scrapping/index.md index 276014e..29f558a 100644 --- a/contrib/web-scrapping/index.md +++ b/contrib/web-scrapping/index.md @@ -2,3 +2,4 @@ - [Section title](filename.md) - [Introduction to Flask](flask.md) +- [Web Scrapping Using Beautiful Soup](beautifulsoup.md) From b2643ad26d31b8e70e3bb41842745bb9f3129716 Mon Sep 17 00:00:00 2001 From: saiumasankar Date: Sat, 8 Jun 2024 15:03:43 +0530 Subject: [PATCH 10/18] deleting unnecessary --- contrib/web-scrapping/beautifulsoup.md | 206 ------------------------- contrib/web-scrapping/index.md | 1 - 2 files changed, 207 deletions(-) delete mode 100644 contrib/web-scrapping/beautifulsoup.md diff --git a/contrib/web-scrapping/beautifulsoup.md b/contrib/web-scrapping/beautifulsoup.md deleted file mode 100644 index 372b8f2..0000000 --- a/contrib/web-scrapping/beautifulsoup.md +++ /dev/null @@ -1,206 +0,0 @@ -# Beautiful Soup Library in Python - -## Table of Contents -1. Introduction -2. Prerequisites -3. Setting Up Environment -4. Beautiful Soup Objects -5. Tag object -6. Children, Parents and Siblings -7. Filter: Findall method -8. Web Scraping the Contents of a Web Page - -## 1. Introduction -Beautiful Soup is a Python library used for web scraping purposes to extract data from HTML and XML files. It creates a parse tree for parsed pages that can be used to extract data easily. - -## 2. Prerequisites -- Understanding of HTTP Requests and Responses. -- Understanding of HTTP methods (GET method). -- Basic Knowledge on HTML. -- Python installed on your machine (version 3.6 or higher). -- pip (Python package installer) installed. - -## 3. Setting Up Environment -1.**Install latest version of Python:** Go to Python.org and Download the latest version of Python. - -2.**Install a IDE:** Install any IDE of your choice to code. VS code is preferred. ->Note: You can use Google Colab without installing Python and IDE. - -3.**Install Beautiful Soup:** -```python -!pip install bs4 -``` - -## 4. Beautiful Soup Objects -Beautiful Soup is a Python library for pulling data out of HTML and XML files. This can be done by presenting the HTML as a set of objects. - -Take the below HTML page as input -``` - - - -Page Title - - -

Title

-

This is the main context of the page

- - -``` - -lets store the HTML code in a variable -``` -html= " - - - Page Title - - -

Title

-

This is the main context of the page

- - " -``` - -To parse the HTML document, pass the variable to the `BeautifulSoup` Constructor. -``` -soup = BeautifulSoup(html,'html.parser') -``` -Beautiful Soup transforms a complex HTML document into a complex tree of Python objects. - -## 5. Tags - -The Tag object corresponds to an HTML tag in the original document. - -``` -tag_obj = soup.title -print("tag object:", tag_obj) -print("tag object type:",type(tag_obj)) -``` -``` -Result: -tag object: Page Title - -tag object type: -``` - -## 6. Children, Parent and Siblings - -We can access the child of the tag or navigate down. - -``` -tag_obj = soup.h3 -child = tag_obj.b -print(child) -parent = child.parent -print(parent) -sib = tag_obj.next_sibling -print(sib); -``` -``` -Result: - Title -

Title

-

This is the main context of the page

-``` - -> We need to mention the child to which we want to navigate. It is because there can be more than one child to a tag but only one parent and next sibling. - -**Navigable String:** A string corresponds to a bit of text or content within a tag. Beautiful Soup uses the NavigableString class to contain this text. - -``` -tagstr = child.string -print(tagstr) -``` -``` -Result: -Title -``` - -## 7. Filter - -Filters allow you to find complex patterns, the simplest filter is a string. - -Consider the following HTML code: - -``` - - - - - - Sample Table - - -

Sample Table

- - - - - - - - - - - - - - - - - - - - - - - - - -
NameAgeCity
John Doe28New York
Jane Smith34Los Angeles
Emily Jones23Chicago
- - - -``` -Store the above code in a variable. -``` -table = " - - - - - Sample Table -.............. - -table_bs = BeautifulSoup(table, 'html.parser') -" -``` -**Find All:** The find_all() method looks through a tag’s descendants and retrieves all descendants that match your filters. It places all the objects in a list. We can access by indexing. - -## 8. Web Scraping the Contents of a Web Page - -1. Get the URL of the webpage we need to scrape. - -2. Get the HTML content by using `get` method in HTTP request. - -3. Pass the HTML content to the BeautifulSoup Constructor to prepare an object. - -4. Access the HTML elements using Tag name. - -Below is the code to extract the img tags in a wikipedia page. - -``` -import requests -!pip install bs4 -from bs4 import BeautifulSoup - -url = "https://en.wikipedia.org/wiki/Encyclopedia" -data = requests.get(url).text -soup = BeautifulSoup(data,"html.parser") - -for link in soup.find_all('a'): - print(link) - print(link.get('src')) -``` -We can retrieve any data in the webpage by access through the tags. diff --git a/contrib/web-scrapping/index.md b/contrib/web-scrapping/index.md index 29f558a..276014e 100644 --- a/contrib/web-scrapping/index.md +++ b/contrib/web-scrapping/index.md @@ -2,4 +2,3 @@ - [Section title](filename.md) - [Introduction to Flask](flask.md) -- [Web Scrapping Using Beautiful Soup](beautifulsoup.md) From c2c84a09d21445382fc535a99d2745d8a8be0a29 Mon Sep 17 00:00:00 2001 From: Kosuri Indu Date: Sat, 8 Jun 2024 19:10:46 +0530 Subject: [PATCH 11/18] Added Splay Trees in DSA section --- contrib/ds-algorithms/index.md | 3 +- contrib/ds-algorithms/splay-trees.md | 162 +++++++++++++++++++++++++++ 2 files changed, 164 insertions(+), 1 deletion(-) create mode 100644 contrib/ds-algorithms/splay-trees.md diff --git a/contrib/ds-algorithms/index.md b/contrib/ds-algorithms/index.md index 9c05b15..e099f97 100644 --- a/contrib/ds-algorithms/index.md +++ b/contrib/ds-algorithms/index.md @@ -15,4 +15,5 @@ - [Trie](trie.md) - [Two Pointer Technique](two-pointer-technique.md) - [Hashing through Linear Probing](hashing-linear-probing.md) -- [Hashing through Chaining](hashing-chaining.md) \ No newline at end of file +- [Hashing through Chaining](hashing-chaining.md) +- [Splay Trees](splay-trees.md) \ No newline at end of file diff --git a/contrib/ds-algorithms/splay-trees.md b/contrib/ds-algorithms/splay-trees.md new file mode 100644 index 0000000..ee900ed --- /dev/null +++ b/contrib/ds-algorithms/splay-trees.md @@ -0,0 +1,162 @@ +# Splay Tree + +In Data Structures and Algorithms, a **Splay Tree** is a self-adjusting binary search tree with the additional property that recently accessed elements are quick to access again. It performs basic operations such as insertion, search, and deletion in O(log n) amortized time. This is achieved by a process called **splaying**, where the accessed node is moved to the root through a series of tree rotations. + +## Points to be Remembered + +- **Splaying**: Moving the accessed node to the root using rotations. +- **Rotations**: Tree rotations (left and right) are used to balance the tree during splaying. +- **Self-adjusting**: The tree adjusts itself with each access, keeping frequently accessed nodes near the root. + +## Real Life Examples of Splay Trees + +- **Cache Implementation**: Frequently accessed data is kept near the top of the tree, making repeated accesses faster. +- **Networking**: Routing tables in network switches can use splay trees to prioritize frequently accessed routes. + +## Applications of Splay Trees + +Splay trees are used in various applications in Computer Science: + +- **Cache Implementations** +- **Garbage Collection Algorithms** +- **Data Compression Algorithms (e.g., LZ78)** + +Understanding these applications is essential for Software Development. + +## Operations in Splay Tree + +Key operations include: + +- **INSERT**: Insert a new element into the splay tree. +- **SEARCH**: Find the position of an element in the splay tree. +- **DELETE**: Remove an element from the splay tree. + +## Implementing Splay Tree in Python + +```python +class SplayTreeNode: + def __init__(self, key): + self.key = key + self.left = None + self.right = None + +class SplayTree: + def __init__(self): + self.root = None + + def insert(self, key): + self.root = self.splay_insert(self.root, key) + + def search(self, key): + self.root = self.splay_search(self.root, key) + return self.root + + def splay(self, root, key): + if not root or root.key == key: + return root + + if root.key > key: + if not root.left: + return root + if root.left.key > key: + root.left.left = self.splay(root.left.left, key) + root = self.rotateRight(root) + elif root.left.key < key: + root.left.right = self.splay(root.left.right, key) + if root.left.right: + root.left = self.rotateLeft(root.left) + return root if not root.left else self.rotateRight(root) + + else: + if not root.right: + return root + if root.right.key > key: + root.right.left = self.splay(root.right.left, key) + if root.right.left: + root.right = self.rotateRight(root.right) + elif root.right.key < key: + root.right.right = self.splay(root.right.right, key) + root = self.rotateLeft(root) + return root if not root.right else self.rotateLeft(root) + + def splay_insert(self, root, key): + if not root: + return SplayTreeNode(key) + + root = self.splay(root, key) + + if root.key == key: + return root + + new_node = SplayTreeNode(key) + + if root.key > key: + new_node.right = root + new_node.left = root.left + root.left = None + else: + new_node.left = root + new_node.right = root.right + root.right = None + + return new_node + + def splay_search(self, root, key): + return self.splay(root, key) + + def rotateRight(self, node): + temp = node.left + node.left = temp.right + temp.right = node + return temp + + def rotateLeft(self, node): + temp = node.right + node.right = temp.left + temp.left = node + return temp + + def preOrder(self, root): + if root: + print(root.key, end=' ') + self.preOrder(root.left) + self.preOrder(root.right) + +#Example usage: +splay_tree = SplayTree() +splay_tree.insert(50) +splay_tree.insert(30) +splay_tree.insert(20) +splay_tree.insert(40) +splay_tree.insert(70) +splay_tree.insert(60) +splay_tree.insert(80) + +print("Preorder traversal of the Splay tree is:") +splay_tree.preOrder(splay_tree.root) + +splay_tree.search(60) + +print("\nSplay tree after search operation for key 60:") +splay_tree.preOrder(splay_tree.root) +``` + +## Output + +```markdown +Preorder traversal of the Splay tree is: +50 30 20 40 70 60 80 + +Splay tree after search operation for key 60: +60 50 30 20 40 70 80 +``` + +## Complexity Analysis + +The worst-case time complexities of the main operations in a Splay Tree are as follows: + +- **Insertion**: (O(n)). In the worst case, insertion may take linear time if the tree is highly unbalanced. +- **Search**: (O(n)). In the worst case, searching for a node may take linear time if the tree is highly unbalanced. +- **Deletion**: (O(n)). In the worst case, deleting a node may take linear time if the tree is highly unbalanced. + +While these operations can take linear time in the worst case, the splay operation ensures that the tree remains balanced over a sequence of operations, leading to better average-case performance. \ No newline at end of file From 65e2aa42f851628e8aa1f5916236edc15aeae99b Mon Sep 17 00:00:00 2001 From: Kosuri Indu Date: Sun, 9 Jun 2024 09:33:07 +0530 Subject: [PATCH 12/18] Added AVL Trees in DSA section --- contrib/ds-algorithms/avl-trees.md | 185 +++++++++++++++++++++++++++++ contrib/ds-algorithms/index.md | 3 +- 2 files changed, 187 insertions(+), 1 deletion(-) create mode 100644 contrib/ds-algorithms/avl-trees.md diff --git a/contrib/ds-algorithms/avl-trees.md b/contrib/ds-algorithms/avl-trees.md new file mode 100644 index 0000000..b87e82c --- /dev/null +++ b/contrib/ds-algorithms/avl-trees.md @@ -0,0 +1,185 @@ +# AVL Tree + +In Data Structures and Algorithms, an **AVL Tree** is a self-balancing binary search tree (BST) where the difference between heights of left and right subtrees cannot be more than one for all nodes. It ensures that the tree remains balanced, providing efficient search, insertion, and deletion operations. + +## Points to be Remembered + +- **Balance Factor**: The difference in heights between the left and right subtrees of a node. It should be -1, 0, or +1 for all nodes in an AVL tree. +- **Rotations**: Tree rotations (left, right, left-right, right-left) are used to maintain the balance factor within the allowed range. + +## Real Life Examples of AVL Trees + +- **Databases**: AVL trees can be used to maintain large indexes for database tables, ensuring quick data retrieval. +- **File Systems**: Some file systems use AVL trees to keep track of free and used memory blocks. + +## Applications of AVL Trees + +AVL trees are used in various applications in Computer Science: + +- **Database Indexing** +- **Memory Allocation** +- **Network Routing Algorithms** + +Understanding these applications is essential for Software Development. + +## Operations in AVL Tree + +Key operations include: + +- **INSERT**: Insert a new element into the AVL tree. +- **SEARCH**: Find the position of an element in the AVL tree. +- **DELETE**: Remove an element from the AVL tree. + +## Implementing AVL Tree in Python + +```python +class AVLTreeNode: + def __init__(self, key): + self.key = key + self.left = None + self.right = None + self.height = 1 + +class AVLTree: + def insert(self, root, key): + if not root: + return AVLTreeNode(key) + + if key < root.key: + root.left = self.insert(root.left, key) + else: + root.right = self.insert(root.right, key) + + root.height = 1 + max(self.getHeight(root.left), self.getHeight(root.right)) + balance = self.getBalance(root) + + if balance > 1 and key < root.left.key: + return self.rotateRight(root) + if balance < -1 and key > root.right.key: + return self.rotateLeft(root) + if balance > 1 and key > root.left.key: + root.left = self.rotateLeft(root.left) + return self.rotateRight(root) + if balance < -1 and key < root.right.key: + root.right = self.rotateRight(root.right) + return self.rotateLeft(root) + + return root + + def search(self, root, key): + if not root or root.key == key: + return root + + if key < root.key: + return self.search(root.left, key) + + return self.search(root.right, key) + + def delete(self, root, key): + if not root: + return root + + if key < root.key: + root.left = self.delete(root.left, key) + elif key > root.key: + root.right = self.delete(root.right, key) + else: + if root.left is None: + temp = root.right + root = None + return temp + elif root.right is None: + temp = root.left + root = None + return temp + + temp = self.getMinValueNode(root.right) + root.key = temp.key + root.right = self.delete(root.right, temp.key) + + if root is None: + return root + + root.height = 1 + max(self.getHeight(root.left), self.getHeight(root.right)) + balance = self.getBalance(root) + + if balance > 1 and self.getBalance(root.left) >= 0: + return self.rotateRight(root) + if balance < -1 and self.getBalance(root.right) <= 0: + return self.rotateLeft(root) + if balance > 1 and self.getBalance(root.left) < 0: + root.left = self.rotateLeft(root.left) + return self.rotateRight(root) + if balance < -1 and self.getBalance(root.right) > 0: + root.right = self.rotateRight(root.right) + return self.rotateLeft(root) + + return root + + def rotateLeft(self, z): + y = z.right + T2 = y.left + y.left = z + z.right = T2 + z.height = 1 + max(self.getHeight(z.left), self.getHeight(z.right)) + y.height = 1 + max(self.getHeight(y.left), self.getHeight(y.right)) + return y + + def rotateRight(self, z): + y = z.left + T3 = y.right + y.right = z + z.left = T3 + z.height = 1 + max(self.getHeight(z.left), self.getHeight(z.right)) + y.height = 1 + max(self.getHeight(y.left), self.getHeight(y.right)) + return y + + def getHeight(self, root): + if not root: + return 0 + return root.height + + def getBalance(self, root): + if not root: + return 0 + return self.getHeight(root.left) - self.getHeight(root.right) + + def getMinValueNode(self, root): + if root is None or root.left is None: + return root + return self.getMinValueNode(root.left) + + def preOrder(self, root): + if not root: + return + print(root.key, end=' ') + self.preOrder(root.left) + self.preOrder(root.right) + +#Example usage +avl_tree = AVLTree() +root = None + +root = avl_tree.insert(root, 10) +root = avl_tree.insert(root, 20) +root = avl_tree.insert(root, 30) +root = avl_tree.insert(root, 40) +root = avl_tree.insert(root, 50) +root = avl_tree.insert(root, 25) + +print("Preorder traversal of the AVL tree is:") +avl_tree.preOrder(root) +``` + +## Output + +```markdown +Preorder traversal of the AVL tree is: +30 20 10 25 40 50 +``` + +## Complexity Analysis + +- **Insertion**: O(logn). Inserting a node involves traversing the height of the tree, which is logarithmic due to the balancing property. +- **Search**: O(logn). Searching for a node involves traversing the height of the tree. +- **Deletion**: O(log⁡n). Deleting a node involves traversing and potentially rebalancing the tree, maintaining the logarithmic height. \ No newline at end of file diff --git a/contrib/ds-algorithms/index.md b/contrib/ds-algorithms/index.md index 9c05b15..d3dbe73 100644 --- a/contrib/ds-algorithms/index.md +++ b/contrib/ds-algorithms/index.md @@ -15,4 +15,5 @@ - [Trie](trie.md) - [Two Pointer Technique](two-pointer-technique.md) - [Hashing through Linear Probing](hashing-linear-probing.md) -- [Hashing through Chaining](hashing-chaining.md) \ No newline at end of file +- [Hashing through Chaining](hashing-chaining.md) +- [AVL Trees](avl-trees.md) \ No newline at end of file From aefb52e5b3e6a81e55dce1a22f4870b3ef0e2c69 Mon Sep 17 00:00:00 2001 From: Revanth <109272714+revanth1718@users.noreply.github.com> Date: Sun, 9 Jun 2024 11:48:46 +0530 Subject: [PATCH 13/18] Update K-Means_Clustering.md --- contrib/machine-learning/K-Means_Clustering.md | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/K-Means_Clustering.md index 859636b..83fbd80 100644 --- a/contrib/machine-learning/K-Means_Clustering.md +++ b/contrib/machine-learning/K-Means_Clustering.md @@ -76,6 +76,10 @@ The K-means algorithm follows an iterative approach to optimize cluster formatio Predicted cluster for new data: [0] ## Conclusion **K-Means** can be applied to data that has a smaller number of dimensions, is numeric, and is continuous or can be used to find groups that have not been explicitly labeled in the data. As an example, it can be used for Document Classification, Delivery Store Optimization, or Customer Segmentation. +## Reference +[[Survey of Machine Learning and Data Mining Techniques used in Multimedia System](https://www.researchgate.net/publication/333457161_Survey_of_Machine_Learning_and_Data_Mining_Techniques_used_in_Multimedia_System?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ)] + +[[A Clustering Approach for Outliers Detection in a Big Point-of-Sales Database](https://www.researchgate.net/publication/339267868_A_Clustering_Approach_for_Outliers_Detection_in_a_Big_Point-of-Sales_Database?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ)] From bb38f8fb5a9418a359635dcbec275e77e364c6fa Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Wed, 12 Jun 2024 21:57:30 +0530 Subject: [PATCH 14/18] Update K-Means_Clustering.md --- .../machine-learning/K-Means_Clustering.md | 96 ++++++++++--------- 1 file changed, 53 insertions(+), 43 deletions(-) diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/K-Means_Clustering.md index 83fbd80..ee615c3 100644 --- a/contrib/machine-learning/K-Means_Clustering.md +++ b/contrib/machine-learning/K-Means_Clustering.md @@ -1,19 +1,25 @@ # K-Means Clustering Unsupervised Learning Algorithm for Grouping Similar Data. + ## Introduction K-means clustering is a fundamental unsupervised machine learning algorithm that excels at grouping similar data points together. It's a popular choice due to its simplicity and efficiency in uncovering hidden patterns within unlabeled datasets. + ## Unsupervised Learning Unlike supervised learning algorithms that rely on labeled data for training, unsupervised algorithms, like K-means, operate solely on input data (without predefined categories). Their objective is to discover inherent structures or groupings within the data. + ## The K-Means Objective Organize similar data points into clusters to unveil underlying patterns. The main objective is to minimize total intra-cluster variance or the squared function. ![image](assets/knm.png) ## Clusters and Centroids A cluster represents a collection of data points that share similar characteristics. K-means identifies a pre-determined number (k) of clusters within the dataset. Each cluster is represented by a centroid, which acts as its central point (imaginary or real). + ## Minimizing In-Cluster Variation The K-means algorithm strategically assigns each data point to a cluster such that the total variation within each cluster (measured by the sum of squared distances between points and their centroid) is minimized. In simpler terms, K-means strives to create clusters where data points are close to their respective centroids. + ## The Meaning Behind "K-Means" The "means" in K-means refers to the averaging process used to compute the centroid, essentially finding the center of each cluster. + ## K-Means Algorithm in Action ![image](assets/km_.png) The K-means algorithm follows an iterative approach to optimize cluster formation: @@ -24,62 +30,66 @@ The K-means algorithm follows an iterative approach to optimize cluster formatio 4. **Iteration Until Convergence:** Steps 2 and 3 are repeated iteratively until a stopping criterion is met. This criterion can be either: - **Centroid Stability:** No significant change occurs in the centroids' positions, indicating successful clustering. - **Reaching Maximum Iterations:** A predefined number of iterations is completed. - ## Code - Following is a simple implementation of K-Means. + +## Code +Following is a simple implementation of K-Means. - - # Generate and Visualize Sample Data - # import the necessary Libraries - - import numpy as np - import matplotlib.pyplot as plt +```python +# Generate and Visualize Sample Data +# import the necessary Libraries - # Create data points for cluster 1 and cluster 2 - X = -2 * np.random.rand(100, 2) - X1 = 1 + 2 * np.random.rand(50, 2) - - # Combine data points from both clusters - X[50:100, :] = X1 - - # Plot data points and display the plot - plt.scatter(X[:, 0], X[:, 1], s=50, c='b') - plt.show() +import numpy as np +import matplotlib.pyplot as plt - # K-Means Model Creation and Training - from sklearn.cluster import KMeans - - # Create KMeans object with 2 clusters - kmeans = KMeans(n_clusters=2) - kmeans.fit(X) # Train the model on the data +# Create data points for cluster 1 and cluster 2 +X = -2 * np.random.rand(100, 2) +X1 = 1 + 2 * np.random.rand(50, 2) - # Visualize Data Points with Centroids - centroids = kmeans.cluster_centers_ # Get centroids (cluster centers) +# Combine data points from both clusters +X[50:100, :] = X1 + +# Plot data points and display the plot +plt.scatter(X[:, 0], X[:, 1], s=50, c='b') +plt.show() - plt.scatter(X[:, 0], X[:, 1], s=50, c='b') # Plot data points again - plt.scatter(centroids[0, 0], centroids[0, 1], s=200, c='g', marker='s') # Plot centroid 1 - plt.scatter(centroids[1, 0], centroids[1, 1], s=200, c='r', marker='s') # Plot centroid 2 - plt.show() # Display the plot with centroids +# K-Means Model Creation and Training +from sklearn.cluster import KMeans - # Predict Cluster Label for New Data Point - new_data = np.array([-3.0, -3.0]) - new_data_reshaped = new_data.reshape(1, -1) - predicted_cluster = kmeans.predict(new_data_reshaped) - print("Predicted cluster for new data:", predicted_cluster) +# Create KMeans object with 2 clusters +kmeans = KMeans(n_clusters=2) +kmeans.fit(X) # Train the model on the data - ### Output: - Before Implementing K-Means Clustering +# Visualize Data Points with Centroids +centroids = kmeans.cluster_centers_ # Get centroids (cluster centers) + +plt.scatter(X[:, 0], X[:, 1], s=50, c='b') # Plot data points again +plt.scatter(centroids[0, 0], centroids[0, 1], s=200, c='g', marker='s') # Plot centroid 1 +plt.scatter(centroids[1, 0], centroids[1, 1], s=200, c='r', marker='s') # Plot centroid 2 +plt.show() # Display the plot with centroids + +# Predict Cluster Label for New Data Point +new_data = np.array([-3.0, -3.0]) +new_data_reshaped = new_data.reshape(1, -1) +predicted_cluster = kmeans.predict(new_data_reshaped) +print("Predicted cluster for new data:", predicted_cluster) +``` + +### Output: +Before Implementing K-Means Clustering ![Before Implementing K-Means Clustering](assets/km_2.png) - After Implementing K-Means Clustering - ![After Implementing K-Means Clustering](assets/km_3.png) +After Implementing K-Means Clustering +![After Implementing K-Means Clustering](assets/km_3.png) + +Predicted cluster for new data: `[0]` - Predicted cluster for new data: [0] ## Conclusion **K-Means** can be applied to data that has a smaller number of dimensions, is numeric, and is continuous or can be used to find groups that have not been explicitly labeled in the data. As an example, it can be used for Document Classification, Delivery Store Optimization, or Customer Segmentation. -## Reference -[[Survey of Machine Learning and Data Mining Techniques used in Multimedia System](https://www.researchgate.net/publication/333457161_Survey_of_Machine_Learning_and_Data_Mining_Techniques_used_in_Multimedia_System?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ)] -[[A Clustering Approach for Outliers Detection in a Big Point-of-Sales Database](https://www.researchgate.net/publication/339267868_A_Clustering_Approach_for_Outliers_Detection_in_a_Big_Point-of-Sales_Database?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ)] +## References + +- [Survey of Machine Learning and Data Mining Techniques used in Multimedia System](https://www.researchgate.net/publication/333457161_Survey_of_Machine_Learning_and_Data_Mining_Techniques_used_in_Multimedia_System?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ) +- [A Clustering Approach for Outliers Detection in a Big Point-of-Sales Database](https://www.researchgate.net/publication/339267868_A_Clustering_Approach_for_Outliers_Detection_in_a_Big_Point-of-Sales_Database?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ) From cf01273be27a0d9f82c45a41e505fde46360b749 Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Wed, 12 Jun 2024 21:58:13 +0530 Subject: [PATCH 15/18] Update and rename K-Means_Clustering.md to kmeans.md --- contrib/machine-learning/{K-Means_Clustering.md => kmeans.md} | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename contrib/machine-learning/{K-Means_Clustering.md => kmeans.md} (100%) diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/kmeans.md similarity index 100% rename from contrib/machine-learning/K-Means_Clustering.md rename to contrib/machine-learning/kmeans.md From 8f0e9808356ae8a02937d490f8952f3de28a42e4 Mon Sep 17 00:00:00 2001 From: Revanth <109272714+revanth1718@users.noreply.github.com> Date: Wed, 12 Jun 2024 22:16:20 +0530 Subject: [PATCH 16/18] Update index.md --- contrib/machine-learning/index.md | 1 + 1 file changed, 1 insertion(+) diff --git a/contrib/machine-learning/index.md b/contrib/machine-learning/index.md index b6945cd..6227561 100644 --- a/contrib/machine-learning/index.md +++ b/contrib/machine-learning/index.md @@ -16,3 +16,4 @@ - [Types_of_Cost_Functions](cost-functions.md) - [Clustering](clustering.md) - [Grid Search](grid-search.md) +- [K-Means](kmeans.md) From 51011db02b624db7723f246984e3a2d9644c5d57 Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Thu, 13 Jun 2024 00:38:06 +0530 Subject: [PATCH 17/18] Update kmeans.md --- contrib/machine-learning/kmeans.md | 8 -------- 1 file changed, 8 deletions(-) diff --git a/contrib/machine-learning/kmeans.md b/contrib/machine-learning/kmeans.md index ee615c3..52db92e 100644 --- a/contrib/machine-learning/kmeans.md +++ b/contrib/machine-learning/kmeans.md @@ -90,11 +90,3 @@ Predicted cluster for new data: `[0]` - [Survey of Machine Learning and Data Mining Techniques used in Multimedia System](https://www.researchgate.net/publication/333457161_Survey_of_Machine_Learning_and_Data_Mining_Techniques_used_in_Multimedia_System?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ) - [A Clustering Approach for Outliers Detection in a Big Point-of-Sales Database](https://www.researchgate.net/publication/339267868_A_Clustering_Approach_for_Outliers_Detection_in_a_Big_Point-of-Sales_Database?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ) - - - - - - - - From 41e41d804d105358a512e7a6aaa0feb1e3db4522 Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Thu, 13 Jun 2024 01:33:30 +0530 Subject: [PATCH 18/18] Update dynamic-programming.md --- contrib/ds-algorithms/dynamic-programming.md | 20 +++----------------- 1 file changed, 3 insertions(+), 17 deletions(-) diff --git a/contrib/ds-algorithms/dynamic-programming.md b/contrib/ds-algorithms/dynamic-programming.md index 54c6fcb..0f16d5c 100644 --- a/contrib/ds-algorithms/dynamic-programming.md +++ b/contrib/ds-algorithms/dynamic-programming.md @@ -51,10 +51,6 @@ print(f"The {n}th Fibonacci number is: {fibonacci(n)}.") - **Time Complexity**: O(n) for both approaches - **Space Complexity**: O(n) for the top-down approach (due to memoization), O(1) for the bottom-up approach -
-
-
- # 2. Longest Common Subsequence The longest common subsequence (LCS) problem is to find the longest subsequence common to two sequences. A subsequence is a sequence that appears in the same relative order but not necessarily contiguous. @@ -112,10 +108,6 @@ print("Length of LCS is", longestCommonSubsequence(S1, S2, m, n)) - **Time Complexity**: O(m * n) for both approaches, where m and n are the lengths of the input sequences - **Space Complexity**: O(m * n) for the memoization table -
-
-
- # 3. 0-1 Knapsack Problem The 0-1 knapsack problem is a classic optimization problem where the goal is to maximize the total value of items selected while keeping the total weight within a specified limit. @@ -146,6 +138,7 @@ capacity = 50 n = len(weights) print("Maximum value that can be obtained:", knapsack(weights, values, capacity, n)) ``` + ## 0-1 Knapsack Problem Code in Python (Bottom-up Approach) ```python @@ -170,14 +163,11 @@ capacity = 50 n = len(weights) print(knapSack(capacity, weights, values, n)) ``` + ## Complexity Analysis - **Time Complexity**: O(n * W) for both approaches, where n is the number of items and W is the capacity of the knapsack - **Space Complexity**: O(n * W) for the memoization table -
-
-
- # 4. Longest Increasing Subsequence The Longest Increasing Subsequence (LIS) is a task is to find the longest subsequence that is strictly increasing, meaning each element in the subsequence is greater than the one before it. This subsequence must maintain the order of elements as they appear in the original sequence but does not need to be contiguous. The goal is to identify the subsequence with the maximum possible length. @@ -190,7 +180,6 @@ The Longest Increasing Subsequence (LIS) is a task is to find the longest subseq ## Longest Increasing Subsequence Code in Python (Top-Down Approach using Memoization) ```python - import sys def f(idx, prev_idx, n, a, dp): @@ -241,10 +230,7 @@ def lis(arr): arr = [10, 22, 9, 33, 21, 50, 41, 60] print("Length of lis is", lis(arr)) ``` + ## Complexity Analysis - **Time Complexity**: O(n * n) for both approaches, where n is the length of the array. - **Space Complexity**: O(n * n) for the memoization table in Top-Down Approach, O(n) in Bottom-Up Approach. - -
-
-

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