Jan 12, 2014 · This example network has a single output neuron, so it is making a binary classification (e. A logical matrix, binary matrix, relation matrix, Boolean matrix, or (0,1) matrix is a matrix with entries from the Boolean domain B = {0, 1}. Each row of M corresponds to a certain class. Diagonal values represent accurate predictions, while non-diagonal elements are inaccurate predictions. In the first row, there are 137 examples of class 1 that were classified as class 1, and 13 examples of class 1 that were classified as class 2. All? Because on these confusion matrices, the reports says the false positives for each class. xgboost package import matplotlib. binary_operators. It is a direct extension of class itemMatrix to store a binary incidence matrix, item labels, and optionally transaction IDs and user IDs. Matrix multiplication. the formula to calculate them are as follows: Synonym for (0,1)-matrix, binary matrix or Boolean matrix. atoms. Oct 20, 2014 · Computing Precisio n and Recall for the Multi-Class Problem While it is fairly straightforward to compute precision and recall for a binary classification problem, it can be quite confusing as to how to compute these values for a multi-class classifcation problem. Here is an example of Calculate a confusion matrix: As you saw in the video, a confusion matrix is a very useful tool for calibrating the output of a model and examining all possible outcomes of your predictions (true positive, true negative, false positive, false negative). The method to use depends on whether the classes are mutually exclusive or not. Dec 28, 2014 · i have a binary class confusion matrix of a given classifiers says J48. Skip to content. The rows present the number of actual Can someone help me to calculate accuracy, sensitivity, of a 6*6 confusion matrix? for binary classification, not multi-classes, but I do not know why some reviewers normally ask for these Apr 25, 2015 · Remember the Confusion Matrix from the previous post. Class vector to be converted into a matrix (integers from 0 to num_classes). Toy binary classification dataset . BufferedReader class comes with functions like read(), write(), peek(), getvalue(). It is a direct extension of class '>itemMatrix to store a binary incidence matrix, item labels, and optionally transaction IDs and user IDs. Type of Overloading ; What is the difference between an Object and a Class ; How to Creating Objects and Allocate Memory for Objects in c++ Using vectors and matrices in R. The methods in this class all throw a NullPointerException, if the specified array reference is null, except where noted. Please see the cat and dog classification example listed at the end of this article. pyplot as plt from mlxtend. F1Score Gets the F1 score of the classifier. Binary Ordering Algorithm • Consider the rows and columns as binary strings • To get block diagonal form, the similar rows should be brought together and similarly similar columns • A row is a binary number, then similar rows have similar values; similarly we can envision columns I want to use a binary matrix to build a phylogenetic tree using the R package phangorn as done in this paper:Tracking the Genomic Evolution of Esophageal Adenocarcinoma through Neoadjuvant Chemotherapy. While scikit-learn offers a nice method to compute this matrix (for multiclass classification, as well), I’m not aware of a built-in method that shows the relevant statistics from the confusion matrix. The Bluebit . If the data are multiclass or multilabel, this will be ignored; setting labels=[pos_label] and average != 'binary' will report scores for that label only. show() Example 3 - Multi-class to binary. This class also contains a static factory that allows arrays to be viewed as lists. One important class is latent structure analysis (LSA), which in-cludes latent class analysis, latent trait analysis and various forms of factor analysis for binary data. Classification for classes that are not mutually exclusive is called any-of, multilabel, or multivalue classification. Slots data: the dataset, class "matrix". A binary relation R between arbitrary sets (or classes) X (the set of departure) and Y (the set of destination or codomain) is specified by its graph G, which is a subset of the Cartesian product X × Y. Approaching a new data set using different models is one way of Confusion Matrix. The dimension of this matrix is 2*2 because this model is binary classification. 5 Numerical Solutions *****/ final public class Matrix {private final int M; // number of rows Model: For an example , the class scores are given by vector , where is a matrix and is a length vector of biases. Write A C++ Program For Addition & Multiplication Of Two Matrices By Overloading + And * Operators. , penalty function algorithm and Nov 30, 2012 · Data types part 4: Logical class. Furthermore, if *reality is unbalanced*, then you want your algorithm to learn that! Consider the problem of trying to predict two outcomes, one of which is much more common than the other. class cvxpy. The diagonal of the confusion matrix consists of True Negatives (TN) and True Positives (TP). 5 are considered. The confusion matrix is an mxm, where m is the number of classes to be predicted. num_classes: total number of classes. The number of correct and incorrect predictions are summarized with count values and broken down by each class. There’s no statistical method or machine learning algorithm I know of that requires balanced data classes. MulExpression (lh_exp, rh_exp) [source] ¶ Bases: cvxpy. The correct values are organized in a diagonal line from top left to bottom-right of the matrix (3 + 4). Explore Popular Topics Like Government, Sports, Medicine, Fintech, Food, More. Input values are of the class specified by source. The confusion matrix is a table that shows each class in the evaluation data and the number or percentage of correct predictions and incorrect predictions. A simple class in Python representing a Matrix with basic operations, operator overloading and class factory methods to make Matrices from different sources. e. The normed confusion matrix coefficients give the proportion of training examples per class that are assigned the correct label. BytesIO inherits from io. You have two classes 0 and 1. A Python class for computing the rank of a binary matrix. Write a program to add two matrices of mxn size using binary operator overloading. A binary outcome is a result that has two possible values - true or false, alive or dead, etc. ). The confusion matrix itself is relatively simple to understand, but the related terminology can be confusing. 1/0) or non-binary ratings. As in the binary case, however, we frequently seek a discrete probability distribution over the possible classes. Train a binary, linear classification model using the training set that can identify whether the word counts in a documentation web page are from the Statistics and Machine Learning Toolbox™ documentation. So a binary matrix is such an array of 0's and 1's. Dec 31, 2017 · How to plot a Confusion Matrix in Python. As seen below, the data are stored in a dgCMatrix which is a sparse matrix and label vector is a numeric vector ( {0,1} ): M = designecoc(K,name) returns the coding matrix M that reduces the error-correcting output code (ECOC) design specified by name and K classes to a binary problem. For most sets, we linearly scale each attribute to [-1,1] or [0,1]. Thus, all these cases are handled by just two operators: binary operator * as in a*b Before going into the details of such metrics, it is important to understand the confusion matrix of a binary classification evaluation. May 17, 2018 · Let’s try and understand the confusion matrix on a very basic level. There is a binarySearch method in Arrays class which can also be used. or you formulate it as one-vs-one, where you will have a ROC curve for all class-pair combinations. affine. Alternatively, by recoding the data as a 2m table, log-linear decompositions and other approximations of the multivariate bi-nary distribution become available. How to create a confusion matrix in Python. Receiver operating characteristic curve (ROC)– This curve is typically used for binary classifications. Binary to Decimal Binary to Octal Binary to HexaDecimal Matrix (Two Dimensional Array) Creation in Java; Matrix Addition in Java; public class Matrix_Create Given a binary tree whose nodes are labelled from 0 to n-1, construct an ancestor matrix from it. The parity check matrix for a given binary linear code can be derived from its generator matrix (and vice versa). The class to report if average='binary' and the data is binary. 2. Shortest Path in Binary Matrix. The binary relation R itself is usually identified with its graph G, Returns a matrix from an array-like object, or from a string of data. We want to define addition of matrices of the same size, and multiplication of certain "compatible" matrices. Introduction ¶. The Target class actually has three choices, to simplify our task and narrow it down to a binary classifier I will pick Versicolor to narrow our classification classes to (0 or 1): either it is versicolor (1) or it is Not versicolor (0). This amounts to estimating a region of the form {η(x) >c}. 13. This matrix contains M binary feature vectors stored in N uint8 containers. With features such as HDMI 1. Each row of the confusion matrix represents the instances of an actual class and each column represents the instances of a predicted class. Based on the entries in the confusion matrix, the total # Final layer is a Dense output layer with single unit and sigmoid activation since this is a binary classification problem. Confusion Matrix is applicable for both binary and multi class classification. This class contains various methods for manipulating arrays (such as sorting and searching). NumBits — Number of bits per feature integer Number of bits per feature, saved as an integer. binary: class "logical", determines if the item dataset contains binary (i. Total number of classes. Instead of two classes, we have multiple classes. Set to NULL to autodetect from the input. public class Solution I think it is better to binary search by row first, then binary search by column. Initially, all the element of the third matrix will be zero. NET Matrix Library provides classes for object-oriented linear algebra in the . The io. As the target variable is not continuous, binary classification model predicts the probability of a target variable to be Yes/No. binary_stream = io. An object oriented language as C#, lets you define very elegant matrix classes, that encapsulate element access, and with the mechanism of operator overloading you can write easily: Matrix m = new Matrix( 10 , 5 ); Matrix n = new Matrix( 10 , 5 ); Matrix r; double d = 2 ; r = m + n; r = n*2; Class Matrix { int a[3][3]; Public: //methods; }; Let m1 and m2 are two matrices. class Solution {2 Hi, i need to create a binary matrix (one which elements can only be 1 or 0) in openCV. Markov matrix: A matrix of non-negative real numbers, such that the entries in each row sum to 1. We use standard methods of matrix analysis to prove directly that there exist two congruence classes. To evaluate such a model, a metric called the confusion matrix is used, also called the classification or co-incidence matrix. There are two main reasons why treating the matrix as In data structures, a binary tree is represented using an array presentation and linked list representation. This latter quantity is known as the class-conditional density of the features on the class and requires that we make assumptions on the form of X. For our Target/dependent variable (Y) we can pick the Versicolor class. Confusion matrix is nice, but it is not statistically significant as it is a point estimate, Matrix-matrix multiplication is again done with operator*. 131 23 Favorite Share. An instance of the generative model Output of program: Download Binary Search Java program class file. At least one of show_absolute or show_normed must be True. to_categorical(y, num_classes = NULL) Class vector to be converted into a matrix (integers from 0 to num_classes). If the generator matrix for an [n,k]-code is in Welcome to the website, this is a variation of a commonly asked question. Medium. The transactions class represents transaction data used for mining itemsets or rules. It can be used to solve systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalues and eigenvectors problems, and singular value problems. Extends _ds. We thank their efforts. You can definitely convert a multi class matrix to a binary conf matrix. By setting binary=True, all class labels that are not the positive class label are being summarized to class 0. Only detections with a score greater or equal than 0. And this is the plot I got as required. Converts a class vector (integers) to binary class matrix. Unlike linear regression which outputs continuous number values, logistic regression transforms its output using the logistic sigmoid function to return a probability value which can then be mapped to two or more discrete classes. Example: 'int8=>char' *source: The input values and the output matrix, A, are of the class specified by source. (' Convert class vector to binary class matrix ' ' Jul 20, 2011 · this is not possible in MATLAB and in other languages too like C or C++. To perform matrix multiplication or to multiply two matrices in python, you have to choose three matrices. A very common way of storing data is in a matrix, which is basically a two-way Mar 11, 2016 · In the following script, we will compute the one-vs-all confusion matrix for each class (3 matrices in this case). Addition is a binary operation on Q because Division is NOT a binary operation on Z because Division is a binary operation on Classi cation of binary operations by their properties is the conditional class 1 probability given x: η(x) = P[Y = 1|X = x]. dtype: The data type expected by the input, as a string In general, a matrix is just a rectangular array or table of numbers. An ancestor matrix is a boolean matrix, whose cell (i, j) is true if i is ancestor of j in the binary tree. Create two objects of the class and each of which refers one 2D matrix. py Dataset loading ¶. It also calculates Cohen's kappa to get the overall 'rater' agreement between the classifeir and the actual class (of • want good performance on binary problems (so that ε small) • want rows far apart from each other (so ρ large) • ρ ≈ 1/2 for ECOC • ρ = 2/k for one-against-all • but: making ρ large may mean making binary problems more difficult to solve • many zeros in matrix makes binary problems easier and faster to solve Below is the syntax highlighted version of Matrix. A confusion matrix displays the number of correct and incorrect predictions made by the model compared with the actual classifications in the test data. The nearest that I was getting is creating a matrix which elements are 8-bit values using the CV_8UC1 dataType. In the case when the binary labels are fractional (probabilistic), inverse_transform chooses the class with the greatest value. depicts the confusion matrix for a binary classification problem. minimum: class "numeric", defines the minimal value present in the dataset. The class of the output matrix, A, is specified by output. In this section, we extend the standard NMF to BMF: given a binary matrix X,we want to factorize X into two binary matrices W,H (thus conserving the most impor-tant integer property of the objective matrix X) satisfying X ≈ WH. Our proof gives explicit algorithms to compute the congruence classes. SAS programmers sometimes ask, "How do I create a design matrix in SAS?" A design matrix is a numerical matrix that represents the explanatory variables in regression models. This dataset is very small to not make the R package too heavy, however XGBoost is built to manage huge dataset very efficiently. Representation of equivalence Class Definition 4: (HR-minimal, HC-minimal, H-minimal) A binary matrix A is a Hadamard-row-minimal matrix (or simply HR-minimal) if ρ(A) ≤ ρ(B) for all B which are hadamard-equivalent with A A binary matrix A is a Hadamard-column-minimal matrix (or simply HC-minimal) if AT is an HR-minimal Classification with more than two classes We can extend two-class linear classifiers to classes. There must be another dataType which specifies that the matrix elements are 1 bit values, but I can The strategy we’ll use is super easy: Start performing matrix multiplication with the same matrix (adding the sum of a row with a column) to determine each element. 4a 3D support, sophisticated EDID handling, IR, RS232 and Ethernet (8x8 only) control, they are ideal for residential and commercial media distribution systems. Write A C++ Program For A Simple Constructor And Destructor. May 02, 2019 · class vector to be converted into a matrix (integers from 0 to num_classes). Table 3 shows an example for K = 5 classes and N = 7 bit codewords. A connection is established between the cardinal number of this set and the cardinal number of its subset of matrices containing 1 in the lower right corner. Computing the size of the stabilizer group of a matrix is thus equivalent to computing the automorphism group of the associated graph. A prominent class of these matrices over the simplest finite or Galois field GF (2) is the class of involutory or Self-Inverse (SI) matrices, which are matrices for which an inverse exists and is equal to the original matrix. The positive class label becomes class 1. I am interested in searching information related to a certain class of binary matrices that accomplish all following conditions: Upper left box (non-fixed sizes) formed by 0's Last column in box d Aug 26, 2018 · The concept of Confusion Matrix is generic and can be extended to multiple classes also. A confusion matrix of binary classification is a two by two table formed by counting of the number of the four outcomes of a binary classifier. A binary operation on a nonempty set Ais a function from A Ato A. Flexible Data Ingestion. Examples: Download Open Datasets on 1000s of Projects + Share Projects on One Platform. is the bearing faulty or not). The dimension of this matrix is 2*2 because this model is a binary classification. I would like to find the number of misclassified items. Now I need to read matrix from file and store it then use double pointer of struct to point the matrix. It is a general buffer of bytes that you can work with. In a classification model with N classes, the confusion matrix will be NxN with the left axis showing the actual class (as known in the test set) and the top ization (NMF) is to factorize the matrix X which is of some specific class, for example, binary matrix. DEFINITION 1. In this case, a document can belong to several (a single [0;1]-valued parameter for binary classi cation) and the likelihood p(x j y) for both classes (i. Can be used to represent a k-adic relation. Of course, since this is a binary (boolean) matrix, instead of multiplication, you will AND (boolean math) the elements, and instead of adding, you will OR the elements. 1091. This is a hard problem. Metzler matrix: A matrix whose off-diagonal entries are non-negative. In simple models, the design matrix contains one column for each continuous variable and multiple columns (called dummy variables) for each classification variable. 3. The total actual women in the dataset is the sum of values in the women column (1 +4). num_classes: Total number of classes. skaccessors package; pandas_ml. Typically, this allows to use the output of a linear model’s decision_function method directly as the input of inverse_transform. 1. The confusion matrix giving the counts of the true positives, true negatives, false positives and false negatives for the two classes of data. All Answers ( 18) In multi-class classification problem, you either formulate the problem as one-vs-all, where you will have a ROC curve for each class. LIBSVM Data: Classification (Binary Class) This page contains many classification, regression, multi-label and string data sets stored in LIBSVM format. The B-100-HDMATRIX-4x4 and B-100-HDMATRIX-8x8 are state-of-the-art HDMI switchers providing true Matrix Routing for HDMI signals. Figure 5-1 shows a confusion matrix for a binary classification model. Confusion Matrix: A confusion matrix is a summary of prediction results on a classification problem. Each class is given a row of the matrix. this kind. Equivalence classes under permutations of rows/columns correspond to isomorphism classes of graphs, where the two parts are distinguished (and so are not allowed to be swapped). Confusion matrix. If vis a word in C, then vH= . In those cases it's better to find the row (binary search) first, then the column (also binary search). Oct 10, 2018 · How is the confusion matrix computed? Here is a quick outline of the algorithm to compute the confusion matrix: For each detection record, the algorithm extracts from the input file the ground-truth boxes and classes, along with the detected boxes, classes, and scores. So, the results for multi-class evaluation amount to a collection of true verses predicted binary outcome per class. A matrix His called a parity-check matrix for a linear code Cof length ngenerated by the matrix G, if the columns of H form a basis for the dual code C?. The matrix is n-by-n, where n is the number of classes. g. Each entry f ij in this table denotes the number of records from class i predicted to be of class j. How to Counting sets of 1s and 0s in a binary matrix Given a n × m binary matrix, count the number of sets where a set can be formed one or more same values in a row or column. How to calculate a confusion matrix for a 2-class classification problem from scratch. Monomial matrix Evaluating multi-class classification problems is not different than binary problems, but in this case, the metrics that were discussed above will be calculated for each class separately. The semantics of multiplication are exactly as those of NumPy’s matmul function, except here multiplication by a scalar is permitted. For instance, f 01 is the number of records from class 0 incorrectly predicted as class 1. Example of a multiclass confusion matrix. Of interest are two types of problems: • Classification: Estimate a region in predictor space in which class 1 is observed with the greatest possible majority. The rows of the confusion matrix represent the target classes while the columns represent the output classes. If we just want to predict the class label , then we just choose the class with the highest score: . So in may respects, multi-class evaluation is a straightforward extension of the methods we use in binary evaluation. In modern computer architectures, a byte is the smallest addressable unit of memory. In this paper, we extend the standard NMF to Binary Matrix Factorization (BMF for short): given a binary matrix X, we want to fac-torize X into two binary matricesW;H (thus conserving the most important integer property of the objective A Confusion Matrix is a popular representation of the performance of classification models. Find out m3=m1+m2 (use operator overloading). p(x j y = 0) and p(x j y = 1)). Class transactions --- Binary Incidence Matrix for Transactions The transactions class represents transaction data used for mining itemsets or rules. In the binary case, that is, when the number of classes is C = 2, then the confusion matrix can be written as (4) C M ≡ [m 11 m 12 m 21 m 22]. Here's my code so far: Structure that I am How to read the data from the binary file in a dynamic array in C The Matrix class takes six template parameters, but for now it's enough to learn about the first three first parameters. Many are from UCI, Statlog, StatLib and other collections. Answer: Related posts: A binary search across the entire array becomes more difficult if the matrix is sparse, such as a skyline matrix. For faster training time, orient the predictor data matrix so that the observations are in columns. A matrix is a specialized 2-D array that retains its 2-D nature through operations. core package; pandas_ml. It is useful to review the confusion matrix for multiclass problems. Now lets look at how to compute precision and recall for a multi-class problem. shape[ 2 ] Mar 26, 2017 · Contribute to keras-team/keras development by creating an account on GitHub. Use Class is the column of the dataset that has the dependent binary class value. Take a look at the Confusion Matrix for three classes: As I hope you can see, the Confusion Matrix is a great tool to measure the performance of a classifier, be it a binary classifier or a multi-class classifier. Below is some R code on how you can collapse a confusion matrix to a binary one. In general, one of the classes is called the “Positive” class and the other is named the “Negative” class. You can think of the problem as 3 binary classification tasks where one class is considered the positive class while the combination of all the other classes make up the negative class. We usually denote them as TP, FP, TN, and FN instead of “the number of true positives”, and so on. according to a binary matrix M. In the methods they say: Trees were built using binary presence/absence matrices built from the regional distribution of variants within the This is an introduction to modeling binary outcomes using the caret library. . Given an ancestor matrix, whose cell (i, j) has value true if i is ancestor of j in a binary tree, construct a binary tree from it where binary tree nodes are labelled from 0 to n-1 where n is the size of the ancestor matrix. November 30, 2012. More errors were made by predicting men as women than predicting women as men. Binary™ 120 Series HDMI Matrix Switcher with HDMI Outputs If your application calls for reliable HDMI switching, this Binary™ HDMI Matrix is the perfect solution. Confusion matrix plot with python. NET platform. non-numeric argument to binary operator. In an N by N square grid, each cell is either empty (0) or blocked (1). Other methods of searching are Linear search and Hashing. It has certain special operators, such as * (matrix multiplication) and ** (matrix power). Logistic regression is a classification algorithm used to assign observations to a discrete set of classes. class_names : array-like, shape = [n_classes] (default: None) Meet the Instructors. Addition, subtraction, multiplication are binary operations on Z. Matplotlib plot of a normalized confusion matrix; Binary confusion matrix; Matplotlib plot of a binary confusion matrix; Matplotlib plot of a normalized binary confusion matrix; Seaborn plot of a binary confusion matrix (ToDo) Confusion matrix and class statistics; pandas_ml. The following code snippets illustrate how to load a sample dataset, train a binary classification algorithm on the data, and evaluate the performance of the algorithm by several binary evaluation metrics. We’re going to use two models: gbm (Generalized Boosted Models) and glmnet (Generalized Linear Models). Since vectors are a special case of matrices, they are implicitly handled there too, so matrix-vector product is really just a special case of matrix-matrix product, and so is vector-vector outer product. Train and evaluate a simple MLP on the Reuters newswire topic classification task. This is used by the Binary Matrix Rank cryptographic test for randomness - BinaryMatrix. The time complexity is the same when the matrix is square and dense, but it also works when the matrix has different length rows. . Can i declare an Eigen matrix of unknown type, or at least declare a generic matrix and instantiate later? 0 Write BOOST sparse matrix to data file in binary format 2-Class Confusion Matrix Case Study. Binary matrices play an important role in system modeling (Warfield, 1973). The matrix (table) shows us the number of correctly and incorrectly classified examples, compared to the actual outcomes (target value) in the test data. Now perform the matrix multiplication and store the multiplication result in the third matrix one by one as shown here in the program given below. java from §9. ON A CLASS OF BINARY MATRICES Krasimir Yankov Yordzhev Abstract The paper studies the set of all square binary matrices containing an exact number of 1’s in each rows and in each column. i want to calculate five performance measures of which are true negative rate, true positive rate, false positive rate, false negative rate, and accuracy. On the x-axis, we plot the “False Positive Rate (FPR)” and on the y-axis, we plot the “True Positive Rate (TPR)” . In this tutorial, we discuss both array and linked list presentation of a binary tree with an example. For a binary classification problem the confusion matrix is a 2×2 table which shows the number of actual and predicted classes as below: Accuracy is a measure of correct classifications. Such a matrix can be used to represent a binary relation between a pair of finite sets . Oct 28, 2015 · The Confusion Matrix is a nice way to summarize the results from a binary classification problem. evaluate import confusion_matrix fig, ax = plot_confusion_matrix(conf_mat=cm) plt. When testing an unseen example, the output codeword from the N Container for a dense dataset that distinguishes between binary and non-binary feedback datasets. For binary classification problems, the number of classes is 2, thus the confusion matrix will have 2 rows and columns. This is not straightforward and two parallel methodologies (e. Abstract: We provide two congruence classes for symmetric binary matrices over a nite eld of characteristic 2. A confusion matrix is a matrix (table) that can be used to measure the performance of an machine learning algorithm, usually a supervised learning one. For the actual network with seven output neurons, each is allocated to a class (early, normal, suspect, etc. The ifelse() function is really useful, but is actually overkill when you’re just creating a binary variable. # build the network nb_features = seq_array. For bitn or ubitn precisions, the output has the smallest class that can contain the input. Figure 2: Confusion Matrix for a multiclass classification model. A confusion matrix is a table that is often used to describe the performance of a classification model (or "classifier") on a set of test data for which the true values are known. Confusion matrix is used to summarize, describe or evaluate the performance of a Binary classification task or model. BytesIO() # Binary data and strings are different types, so a str # must be encoded to binary using ascii, utf-8, or other. Each column is used to train a distinct binary classifier. M has K rows and L columns, with each row corresponding to a class and each column corresponding to a binary learner. BinaryOperator. Simultaneously route up to 8 sources to up to 8 different displays using our HDMI cables for direct connection, or use our extenders to send video to remote rooms. The three remaining parameters have default values, which for now we will leave untouched, and which we discuss below . Formal definitionEdit. What is Overloading. The class labels in the training set can take on only two possible values, which we usually refer to as positive or negative