Knn algorithm example in machine learning

Last UpdatedMarch 5, 2024

by

Some experts have written that k-nearest neighbours do the best about one Oct 23, 2020 · Step-1: Importing the required Packages. and regression algorithms. d) The output is the property value for the object. In machine learning, KNN is an algorithm that ranks data points based on the points that most closely resemble it. Step-by-Step Algorithm for KNN. Let’s break it down with a wine example examining two chemical components called rutin and myricetin. k-nearest neighbors (or k-NN for short) is a simple machine learning algorithm that categorizes an input by using its k nearest neighbors. SkalskiP · 7y ago · 113,738 views. For classification problems, it will find the k nearest Dec 14, 2023 · The K-Nearest Neighbors (KNN) algorithm is a supervised machine learning method employed to tackle classification and regression problems. The algorithm is trained on a set of labeled data points Jan 12, 2024 · A nearest neighbor algorithm analyzes all the data on every request. Nearest Neighbor implements rote learning. 2. More than 100 million people use GitHub to discover, fork, and contribute to over 420 million projects. for each test example z = (x’,y’) do 2. In other words, it makes its selection based Jun 11, 2020 · 1) KNN is a perfect first step for machine learning beginners as it is very easy to explain, simple to understand, and extremely powerful. [ ] Dec 2, 2023 · In this blog, we will learn about the differences between K-Nearest Neighbors (KNN) and Logistic Regression, two pivotal algorithms in machine learning, with the help of examples. In other words, similar things are near to each other. For example, suppose a k-NN algorithm was given an input of data points of specific men and women's weight and height, as plotted below. Image source. Apr 12, 2022 · K-nearest neighbors (KNN) is a type of supervised learning machine learning algorithm and is used for both regression and classification tasks. 5)/3 = 13. Lastly, because we do not make any assumption about the functional form of the kNN algorithm, a kNN model is also considered a nonparametric model. A real-life example of this would be if you needed to make predictions using machine learning on a data set of classified government information. The KNN algorithm is based on the idea that data points that are close to each other are more likely to be similar to each other. For example, if we have a dataset of tomatoes and bananas. Its mathematical foundation, which relies on distance metrics to measure the similarity between data points, provides a clear understanding of how the algorithm works. It uses test data to make an informed estimate of the classification of an unclassified point. Jan 8, 2017. This algorithm is a supervised learning algorithm, where the destination is known, but the path to the destination is not. psuedo code Implementation from Scratch. Aug 5, 2019 · So these points are 12. Feb 29, 2020 · Feb 29, 2020. It adopts a density-independent metric based on the distribution of K-nearest neighbors (KNNs) to distinguish between internal and boundary points. While it may be one of the most simple algorithms, it is also a very powerful one and is used in many real world applications. y’ = argmax 𝑣 𝒙 𝐼( = 𝑦𝑖) May 22, 2015 · KNN. KNN captures the idea of similarity May 29, 2024 · The KNN algorithm stands as an intuitive tool in the field of machine learning. 5, 14. A simple KNN example would be feeding the neural network or NN model a training dataset of cats and dogs and testing it on an input image. 5, 13. The article explores the fundamentals, workings, and implementation of the KNN algorithm. Jul 21, 2019 · K-Nearest Neighbors, or KNN for short, is one of the simplest machine learning algorithms and is used in a wide array of institutions. based on Similarity (Distance) calculation between instances. KNN stores all available cases and classifies new cases based on a similarity measure. KNN classifies the new data points based on the similarity measure of the earlier stored data points. K-nearest neighbor considers (data points) to predict the class or continuous value for a new data point, as the name suggests [13]. the most frequent label if using for the classification based problems, or. KNN is an algorithm considered both nonparametric and an example of lazy learning. This tutorial will cover the concept, workflow, and examples of the k-nearest neighbors (kNN) algorithm. Versatility: KNN can be applied to both classification and regression tasks. It is simple, intuitive, and effective for various applications, making it a popular choice among data scientists and machine learning practitioners. A fantastic application of this is the use of KNN in collaborative filtering algorithms for recommender systems. In other words, KNN captures the idea of similarity (sometimes called distance, proximity, or Feb 20, 2024 · The K Nearest Neighbor (KNN) algorithm is a cornerstone in the realm of supervised Machine Learning, renowned for its simplicity and effectiveness in tackling classification challenges. Nov 3, 2021 · Distance Weighted K nearest Neighbor Learning Algorithm Discrete Valued and Real-Valued Functions Dr. We will be working with an anonymous data set similar to the situation described above. In previous post Python Machine Learning Example (KNN), we used a movie catalog data which has the categories label encoded to 0s and 1s already. A flexible approach may also be used to fill in missing values and resample datasets. Oct 21, 2020 · Introduction to KNN Algorithm. Basically, the algorithm run 4 steps: Calculates all the distances between training data and test example. Nếu như con người có kiểu học “nước đến chân mới nhảy”, thì trong Machine Learning cũng có một thuật toán như vậy. No Training Period: Since KNN is an instance-based learning algorithm, it doesn’t require a training phase. Sort the data by distance and pick 'k' of them. It is extremely easy to implement in its most basic form but can perform fairly complex tasks. The main objective of the KNN algorithm is to predict the classification of a new sample point based on data points that are Aug 9, 2023 · The k-nearest neighbor algorithm is a supervised machine learning algorithm used to solve classification and regression problems. -nearest neighbors algorithm. Mahesh HuddarThe following concepts are discussed:_____ Jan 8, 2017 · Bài 6: K-nearest neighbors. It relies on the idea that similar data points tend to have similar labels or values. Feb 23, 2024 · Simple Implementation: KNN is easy to understand and implement, making it suitable for quick prototyping. using this distance we find k-nearest neighbors from the training examples. 6- The k-mean algorithm is different than K- nearest neighbor algorithm. The number of nearest neighbours to a new unknown variable that has to be predicted or classified is denoted by the symbol ‘K’. The k-nearest neighbors (KNN) algorithm is a simple, easy-to-implement supervised machine learning algorithm that can be used to solve both classification and regression problems. 17 likes • 24,091 views. 80. In this tutorial, I will be doing the following: Explain the KNN algorithm and how it works The K-nearest neighbor algorithm is a type of supervised learning technique that is used for classification and regression. It is a supervised machine learning algorithm. Aug 27, 2021 · K-Nearest Neighbors (KNN) is the simplest algorithm in machine learning with a lot of intuition to real words which actually make people… 22 min read · Mar 7, 2024 Theo Wolf Oct 26, 2021 · Introduction. KNN K-Nearest Neighbors (KNN) Simple, but a very powerful classification algorithm Classifies based on a similarity measure Non-parametric Lazy learning Does not “learn” until the test example is given Whenever we have a new data to classify, we find its K-nearest neighbors from the training data The K-Nearest Neighbors (KNN) algorithm is a popular machine learning technique used for classification and regression tasks. This algorithm is perhaps one of the Mar 26, 2024 · Conclusion. K-Nearest Neighbor (KNN) is a supervised Machine Learning algorithm that can solve classification and regression problems. the averages the label if using for regression Jun 27, 2021 · k-Nearest Neighbors (kNN) Machine Learning Algorithm. The model is Feb 2, 2021 · Introduction. KNN is one of the simplest forms of machine learning algorithms mostly used for classification. In this tutorial, you will learn to write your first K nearest neighbors machine learning algorithm in Python. algorithm {‘auto’, ‘ball_tree’, ‘kd_tree’, ‘brute’}, default=’auto’ Algorithm used to compute the nearest neighbors: ‘ball_tree’ will use BallTree ‘kd_tree’ will use KDTree Dec 29, 2023 · Dive into this K-Nearest Neighbors (KNN) a versatile algorithm to classify and predict with clarity. Cosine similarity is used as a metric in different machine learning algorithms like the KNN for determining the distance between the neighbors, in recommendation systems, it is used to recommend movies with the same similarities and for textual data, it is used to find the similarity of texts in the document. 4. Note k is hyper parameter and decision to take how many k’s will discuss in next heading. Sep 26, 2018 · For example, if k = 5, and 3 of points are ‘green’ and 2 are ‘red’, then the data point in question would be labeled ‘green’, since ‘green’ is the majority (as shown in the above graph). KNN has been used in machine learning in some computer vision tasks such as recognizing hand-written numbers. Intro. for classification. Nov 16, 2023 · The K-nearest Neighbors (KNN) algorithm is a type of supervised machine learning algorithm used for classification, regression as well as outlier detection. Then the algorithm searches for the 5 customers closest to Monica, i. Sep 21, 2019 · In this article, I will explain the basic concept of KNN algorithm and how to implement a machine learning model using KNN in Python. KNN’s adaptability to various domains, from healthcare to finance, underscores its relevance. Sort the distance and determine nearest neighbors based on the K-th minimum distance. K-nearest neighbors (KNN) is a type of supervised learning algorithm used for both regression and classification. Because it makes sense for beginners, it also makes a lot of sense when explaining it to anyone unfamiliar with machine learning. Oct 15, 2023 · Conclusion. 1. Feb 6, 2024 · Part 2: Finding Nearest Neighbors. K-mean is used for clustering and is a unsupervised learning algorithm whereas Knn is supervised leaning algorithm that works on classification problems. Next, let’s write a function to find the ‘k’ nearest neighbors of a query point within a dataset. Significance of k. The algorithm can be used to solve both classification and regression problem statements. To build our KNN model, our primary packages include scikit-learn for The KNN classification algorithm Let k be the number of nearest neighbors and D be the set of training examples. The boundary points generate enclosed cages to bind the connections of internal points. This algorithm’s ease of understanding and implementation, coupled with its robust performance, makes it indispensable for anyone venturing into the field of Iris data visualization and KNN classification. Instance-based learning is an important aspect of supervised machine learning. The value of k is a hyperparameter that needs to be. The “K” value refers to the number of nearest neighbor data points to include in the majority voting process. By understanding its principles, properly preparing data, and tuning hyperparameters, you can effectively leverage KNN for both classification and regression tasks. Mahesh HuddarInstance-based Learning: https://youtu. The K-Nearest Neighbours (KNN) algorithm is one of the simplest supervised machine learning algorithms that is used to solve both classification and regression problems. Whether using KNN for practical applications in healthcare, finance, or marketing Oct 6, 2020 · KNN can be used both for classification and regression problems under the category of Supervised Machine Learning Algorithms. c) If k = 1, then the object is simply assigned to the class of that single nearest neighbor. The k-nearest neighbors (kNN) algorithm is a simple non-parametric supervised ML algorithm that can be used to solve classification and regression tasks. It classifies the data point on how its neighbor is classified. K-nearest neighbors (kNN) is a supervised machine learning algorithm that can be used to solve both classification and regression tasks. May 25, 2024 · K-Nearest Neighbors (KNN) is a versatile and powerful algorithm in the machine learning toolkit. Another advantage of k-Nearest Neighbors algorithm is that it can be used for both Classification and Regression type of Problems. Sep 7, 2022 · K-nearest neighbor (KNN) is an algorithm that is used to classify a data point based on how its neighbors are classified. Image by author. It's based on a local average calculation. The k-Nearest-Neighbours (kNN) is a simple but effective method. The search needs to be able to handle an unknown amount of data and an unknown amount of users at any given second. View Answer. The smallest distance value will be ranked 1 and considered as nearest neighbor. Oct 18, 2019 · K is the number of nearby points that the model will look at when evaluating a new point. If you are unaware of the difference between these Sep 4, 2021 · The KNN Classification algorithm itself is quite simple and intuitive. Nov 9, 2023 · The abbreviation KNN stands for “K-Nearest Neighbour”. Let k be 5. K-Nearest Neighbors (KNN) is a powerful machine learning algorithm with a straightforward approach to classification and regression tasks. The modus operandi of this algorithm is that the training examples are being stored and when the test example is fed, the closest matches are being found. Specifically, the KNN algorithm works in the way: find a distance between a query and all examples (variables) of data, select the particular number of examples (say K) nearest to the query, then decide. When a data point is provided to the algorithm, with a given value of K, it searches for the K nearest neighbors to that data point. Understanding nearest neighbors Which of the following statements is not true about k-Nearest Neighbor classification? a) The output is a class membership. com To associate your repository with the k-nearest-neighbor topic, visit your repo's landing page and select "manage topics. The model functions by calculating distances of a selected number of examples, K, nearest to the predicting point. Scikit-learn is a machine learning library for Python. During the training phase, the KNN algorithm stores the entire training dataset as a reference. KNN is also known as an instance-based model or a lazy learner because it doesn’t construct an internal model. The goal is to understand the intricacies of KNN ’s instance-based learning and Logistic Regression ‘s probability modeling for binary and multinomial outcomes Oct 9, 2020 · An essential algorithm in a Machine Learning Practitioner’s toolkit has to be K Nearest Neighbours(or KNN, for short). For classification, this article examined the top six machine learning algorithms: Decision Tree, Random Forest, Naive Bayes, Support Vector Machines, K-Nearest Neighbors, and Gradient Boosting. 120. When making predictions, it calculates k. May 25, 2020 · KNN: K Nearest Neighbor is one of the fundamental algorithms in machine learning. Given the path to a . It is a lazy learning algorithm since it doesn't have a specialized training phase. kNN specifically requires labeled training data to classify new data points based on their similarity to existing data points with known Apr 22, 2019 · KNN is an algorithm that is considered both non-parametric and an example of lazy learning. Linear regression is a supervised machine learning technique used for predicting and forecasting values that fall within a continuous range, such as sales numbers or housing prices. It makes sense for beginners — intuitive, easy to understand, and you can even implement it without using dedicated packages. What do these two terms mean exactly? Non-parametric means that it makes no assumptions. e. Sep 10, 2018 · The k-nearest neighbors (KNN) algorithm is a simple, easy-to-implement supervised machine learning algorithm that can be used to solve both classification and regression problems. instagram. Feb 16, 2023 · KNN is one of the simplest forms of machine learning algorithms mostly used for classification. Load the Data: In the k-nearest neighbor’s algorithm, first, we calculate the distance between the new example and the training examples. May 22, 2015 • Download as PPTX, PDF •. You could, however, have chosen to look at the nearest 2 or 3 points. 8+13. In this tutorial, you'll learn all about the k-Nearest Neighbors (kNN) algorithm in Python, including how to implement kNN from scratch, kNN hyperparameter tuning, and improving kNN performance using bagging. Aug 8, 2004 · Abstract. " GitHub is where people build software. Machine learning models use a set of input values to predict output values. K-NN algorithm assumes the similarity between the new case/data and available cases and put the new case into the category that is most similar to the available categories. Gather the category of the nearest neighbors. K Nearest Neighbours (KNN) is a supervised machine learning algorithm that makes predictions based on the K K ‘ closest ‘ training data points to our point of interest, in data space. K-NN is a lazy learning algorithm that assigns May 23, 2023 · KNN stands for K-nearest neighbour, it’s one of the Supervised learning algorithm mostly used for classification of data on the basis how it’s neighbour are classified. KNN works by finding the K training examples that are closest in distance to a new data point, and assigning the most common class among those K examples as the prediction for the new data point. What is t May 20, 2024 · The K-Nearest Neighbors (KNN) algorithm is a fundamental machine learning technique used for classification and regression tasks. KNN is unique in that it does not explicitly map input variables to target variables during the learning process, making it even more Refer to the example entitled Nearest Neighbors Classification showing the impact of the weights parameter on the decision boundary. It’s a highly used, simple yet efficient example of a non-parametric, lazy learner classification algorithm. KNN is used to make predictions on the test data set based on the characteristics of the current training data points. Sep 4, 2016 · The document discusses the K-nearest neighbors (KNN) algorithm, a simple machine learning algorithm used for classification problems. But in our case, the dataset set contains the categorical values. The KNN algorithm assumes that similar things exist in close proximity. K Nearest Neighbours (KNN) falls under the supervised learning umbrella and is one of the core algorithms in machine learning. I see kNN as an algorithm that comes from real life. KNN is a non-parametric, lazy learning algorithm. Learn how it works by reading this guide with practical example of a k-nearest neighbors implementation. com contact me on Instagram at https://www. b) An object is classified by a plurality vote of its neighbors. May 3, 2024 · Learning K-Nearest Neighbors is a great way to introduce yourself to machine learning and classification in general. However, the kNN algorithm is still a common and very useful algorithm to use for a large variety of classification problems. 1. Linear regression. kNN is a lazy instance-based learning algorithm, an example of an eager instance-based learning algorithm would be the support vector machine, which will be covered later in this course. Classification, categorization, and everything in between will happen at the time of search (ie: just-in-time results). Jan 11, 2021 · Supervised learning implies that you are training a model using a labelled dataset. Evelyn Fix and Joseph Hodges developed this algorithm in 1951, which was subsequently expanded by Thomas Cover. Step 2 : Find K-Nearest Neighbors. #. We will see that in the code below. The major drawbacks with respect to kNN are (1) its low. In both cases, the input consists of the k closest training Here is step by step on how to compute K-nearest neighbors KNN algorithm: Determine parameter K = number of nearest neighbors. In statistics, the k-nearest neighbors algorithm ( k-NN) is a non-parametric supervised learning method first developed by Evelyn Fix and Joseph Hodges in 1951, [1] and later expanded by Thomas Cover. It is one of the oldest ML algorithms and is still widely used due to its simplicity. KNN tries to predict the correct class for the test data by Jul 7, 2022 · Cosine similarity is a measure of similarity between two data points in a plane. May 5, 2023 · The K-Nearest Neighbors (KNN) algorithm is a simple, easy-to-implement supervised machine learning algorithm that can be used to solve both classification and regression problems. In supervised learning, the algorithm learns from labeled training data, where each data point is associated with a known label or outcome. However, it's mainly used for classification problems. It is a way of solving tasks of approximating real or discrete-valued target functions. West Virginia University. k-nearest neighbors (kNN) is a Mar 23, 2022 · It is a simple, easy-to-implement supervised Machine Learning (ML) algorithm that can be used to solve both classification and regression problems. Copy & Edit. Aug 8, 2021 · KNN (K-Nearest Neighbours) is one of the very straightforward supervised learning algorithms. However, unlike the traditional supervised learning algorithms, such as Multinomial Naive Bayes algorithm, KNN doesn’t have an independent training stage, and then a stage where the labels for the test data are predicted based on the trained model. K-Nearest Neighbors, or KNN, is a family of simple: classification. Trong trang này: Nov 11, 2019 · Python Machine Learning KNN Example from CSV data. KNN Regression Classification Supervised-learning MNIST Iris. People tend to be effected by the people around them. Every simple or complex programming tasks start with importing the required packages. Read on if you are interested in Data Science and want to understand the kNN algorithm better or if you need a guide to building your own ML model Jan 11, 2023 · The K-Nearest Neighbors (KNN) algorithm is a supervised machine learning method employed to tackle classification and regression problems. imputer. Additionally, it is quite convenient to demonstrate how everything goes visually. Empower your machine learning journey with this comprehensive guide. If you explore machine learning with Python syllabus, you will realize the extent of the application of KNN. me/joinchat/G7ZZ_SsFfcNiMTA9contact me on Gmail at shraavyareddy810@gmail. 8 and 11. most similar to Monica in terms of attributes, and see what categories those 5 customers were in. Within these k, calculate the successful and unsuccessful. The K-Nearest Neighbors algorithm assumes that similar things exist in close or nearness in space. Jan 25, 2024 · The K-Nearest Neighbors (KNN) algorithm is a supervised machine learning method employed to tackle classification and regression problems. To get the most from this tutorial, you should have basic Oct 27, 2020 · This algorithm is one of the go to algorithms used in machine learning because it is easy-to-implement, non-parametric, lazy learning and has low calculation time. Classification methods from machine learning have transformed difficult data analysis. Feb 28, 2021 · KNN is a highly effective, simple, and easy-to-implemented supervised machine learning algorithm that can be used for classification and regression problems. Oct 7, 2020 · K-Nearest Neighbours is considered to be one of the most intuitive machine learning algorithms since it is simple to understand and explain. And take mean of those y values as (11+14. AI-enhanced description. Clustering algorithms have revolutionized the way data is organized and analyzed. It yields highly competitive results, despite its simplicity. Jun 1, 2016 · Machine learning techniques have been widely used in many scientific fields, but its use in medical literature is limited partly because of technical difficulties. K-Nearest Neighbors (KNN) is a simple and powerful machine learning algorithm used for both classification and regression problems. Its simplicity, interpretability, and effectiveness in classification and regression tasks make it a valuable asset for both beginners and experts. The document discusses the K-nearest neighbor (K-NN) classifier, a machine learning algorithm where data is classified based on its similarity to its nearest neighbors. Our behaviour is guided by the friends we grew up with. Calculate the distance between the query-instance and all the training samples. Also, you will find a lot of intense application of K-NN in data mining, pattern recognition, semantic searching Mar 18, 2024 · It leverages powerful machine learning algorithms to make data useful. # fit on the dataset. Jan 30, 2022 · Solved Example K Nearest Neighbors Algorithm Weighted KNN to classify New Instance by Dr. Dec 30, 2018 · 5- The knn algorithm does not works with ordered-factors in R but rather with factors. . fit(X) Then, the fit imputer is applied to a dataset to create a copy of the dataset with all missing values for each column replaced with an estimated value. efficiency - being a lazy learning method Oct 30, 2021 · The algorithm can be used in both classification and regression tasks. Compute d(x’,x), the distance between z and every example, (x,y) ϵ D 3. be/ Aug 21, 2021 · Telegram group : https://t. The nearest neighbors are found by calculating the distance between the given data point and the data points in the initial dataset. Nov 23, 2020 · KNN. [2] It is used for classification and regression. def find_neighbors(X_train, query_point, k): """. Apr 1, 2024 · From classification to regression, here are 10 types of machine learning algorithms you need to know in the field of machine learning: 1. We evaluate the closest data points through the use of a distance metric, of which there are a variety of options. Machine Learning - K-Nearest Neighbors (KNN) - KNN is a supervised learning algorithm that can be used for both classification and regression problems. Explore intuitive examples, grasp distance metrics, uncover the role of 'k', and master its use for both classification and regression tasks. K-Nearest Neighbour is one of the simplest Machine Learning algorithms based on Supervised Learning technique. This is a popular supervised model used for both classification and regression and is a useful way to understand distance functions, voting systems, and hyperparameter optimization. It's a smoother algorithm . To determine the gender of an unknown input Feb 14, 2024 · kNN (k-Nearest Neighbors) is a supervised machine learning algorithm. Select D z ⊆ D, the set of k closest training examples to z. K-NN is an instance-based learning algorithm. When we say a technique is non-parametric, it means that it does not make any assumptions about the underlying data. A novel Clustering algorithm by measuring Direction Centrality (CDC) locally. Machine learning algorithms can be broadly classified into two: 1. 3. By understanding the basics of machine learning, implementing the KNN algorithm step-by-step, and evaluating its performance using appropriate metrics, you can become a machine learning master. In this tutorial, let’s pick up a dataset example with raw value, label encode them and let’s see if we can get any interesting insights. kNN Problems and ML Terminology Learning Goals Describe how to speed rup kNN Define non rparametric and parametric and describe differences Describe curse of dimensionality Speeding up k rNN k rNN is a “lazy” learning algorithm ±does virtually nothing at training time But classification / prediction can be costly when training set is large Jun 26, 2020 · Common machine learning algorithms; Introduction to kNN – simplified; We’ll also discuss a case study which describes the step by step process of implementing kNN in building models. In conclusion, the K-Nearest Neighbor algorithm is a powerful tool for machine learning tasks, and mastering it can open up a world of possibilities. One of those is K Nearest Neighbors, or KNN—a popular supervised machine learning algorithm used for solving classification and regression problems. 8 and 10 if we take k = 3 nearest neighbors. Now find selected neighbors corresponding y value those are 13. In order to determine the which samples are closest to the new sample, the Euclidean distance is commonly used. csv file it computes the outcome whether a company will be succesful or not using the k nearest neighbours method. Aug 3, 2023 · My first machine learning algorithm was a K-nearest-neighbors (KNN) model. K-Nearest Neighbors. They are crucial tools in the field of machine learning and data science, helping us make sense of complex datasets by grouping similar observations together. The main idea behind KNN is to find the k-nearest data points to a given test data point and use these nearest neighbors to make a prediction. In our simplest nearest neighbor example, this value for k was simply 1 — we looked at the nearest neighbor and that was it. K in KNN is a parameter that refers to the number of the nearest neighbours to include KNN vs K-means: Unveiling the Contrasts in Clustering Algorithms. This is done by calculating the distance between the test data and training data Sep 17, 2021 · Sep 17, 2021. Find Aug 17, 2020 · imputer = KNNImputer(n_neighbors=5, weights='uniform', metric='nan_euclidean') Then, the imputer is fit on a dataset. To calculate the distance the attribute values must be real numbers. The K-nearest Neighbors. This article is a continuation of the series that provides an in-depth look into different Machine Learning algorithms. The model is built during the prediction phase. bp ll ij fp iz tj zp fz mi xo