I'm studying Perceptron algorithm. Some books use this step function 1 if x>=0 else -1 where x is a dot product between the weights w and a sample x. Other books use: 1 if x>=0 else 0 What are the practical differences between these step functions?
I am a beginner and I am designing an binary classifier using Perceptron algorithm using FASHION-MNIST dataset. While designing the same I have written the following code: import pandas as pd import numpy as np import matplotlib.pyplot as plt import matplotlib.image as mpimg import seaborn as sns np.random.seed(2) from sklearn.model_selection import train_test_split from sklearn.metrics import confusion_matrix import itertools from keras.utils.np_utils import to_categorical from keras.models import Sequential from keras.optimizers import RMSprop,Adam from keras.layers import Dense, Dropout, Flatten, Conv2D, MaxPool2D from keras.optimizers …
Consider the modification of Perceptron algorithm with the following update rule: $$ w_t+1 ← w_t + η_ty_tx_t $$ whenever $\hat{y_t } \neq y_t$ ($w_t+1 ← w_t$ otherwise).for $η_t = 1 /\sqrt{t}$ i need to prove that the bound of mistake number is $$4/γ *\log^2(1/γ)$$ can for simplicity assume $ ∥x_t∥ = 1 $for all t. and the algorithm makes M mistakes at the first M rounds, after which it has no mistakes. my try first i notice that the following …
I have a dataset in which the response variable is Sick(1) or not sick (2). As for the variables, there are a few numeric ones (2/14), all the others are variables by levels (example: 1-Abdominal pain, 2-Throat pain...). I had two questions: 1-Can a multilayer perceptron classify a binary variable? Or can it only return numerical values? 2-Can binary or leveled variables be passed as training to the multilayer perceptron? Thank you very much.
Machine Learning books generally explains that the error calculated for a given sample $i$ is: $e_i = y_i - \hat{y_i}$ Where $\hat{y}$ is the target output and $y$ is the actual output given by the network. So, a loss function $L$ is calculated: $L = \frac{1}{2N}\sum^{N}_{i=1}(e_i)^2$ The above scenario is explained for a binary classification/regression problem. Now, let's assume a MLP network with $m$ neurons in the output layer for a multiclass classification problem (generally one neuron per class). What …
If we change the $ywx<0$ condition (for performing update) to $ywx<1$ like in SVM (but without adding regularization to maximize the margin), is there any difference from the basic perceptron (the one with the aforementioned $ywx<0$ condition)?
I have been asked to implement the Pegasos algorithm as below. It is similar to the Peceptron algorithm but includes eta and lambda terms. However, there is no bias term below and I don't know how to include it in either the condition or the update. I think the update is just W0 -> W0 + eta*y[i,t], but it should only be updated if the condition is satisfied, and I used the condition below which ignores bias. Any ideas how …
So I'm trying to write an averaged perceptron algorithm (page 48 here for the equation) in python. Instead of storing the historical weights, I simply accumulate the weights and then multiply consistency counter, $c$, that is the variable w_accum. My implementation initially had the weight vectors and x represented as dictionaries where a feature is in the dictionary only if it's active, that was supposed to be the most efficient way I could think of. Here is that code: def …
I'm trying to get a better understanding of basic neural networks by implementing a little framework in C++. I've started with the classical MNIST exercise. I get to 91% accuracy on the test sample which I'm already pretty happy about. The thing is, the maximum accuracy is almost reached after just one epoch. The next epochs do not seem to improve the situation much. I am optimizing using stochastic gradient descent with a batch size of 40. During the training, …
I read that the equation perceptron decision boundary is given as follows:$$w^Tx-w_0=0$$ This can be proven as follows: Assuming $w$ is a unit vector (as we can multiply above equation with a constant to make $w$ a unit vector and the equation will still hold), by the definition of vector dot product, $$w^T.x=\Vert w\Vert.p_{x\rightarrow w}=1.w_0$$ where $p_{x\rightarrow w}$ is a projection of $x$ on $w$ and $\Vert w\Vert$ is a magnitude of $w$. This gives: $$w^Tx-w_0=0$$ But I also came …
The convergence of the "simple" perceptron says that: $$k\leqslant \left ( \frac{R\left \| \bar{\theta} \right \|}{\gamma } \right )^{2}$$ where $k$ is the number of iterations (in which the weights are updated), $R$ is the maximum distance of a sample from the origin, $\bar{\theta}$ is the final weights vector, and $\gamma$ is the smallest distance from $\bar{\theta}$ to a sample (= the margin of hyperplane). Many books implicitly say that $\left \| \bar{\theta} \right \|$ is equal to 1. But …
I came across following neural networks emulating logical XOR gate: Approach 1: Approach 2: But today, I came across below one: I dont get how this behaves as XOR, especially what does those numbers 1.5 and 0.9 on neurons mean? Assuming those behave as scaling neurons, I tried to code the behavior in python: x1 = 0 x2 = 0 y = -2*(1.5*(x1+x2))+x1+x2 print("(%s,%s:%s)"%(x1,x2,y)) x1 = 0 x2 = 1 y = -2*(1.5*(x1+x2))+x1+x2 print("(%s,%s:%s)"%(x1,x2,y)) x1 = 1 x2 = 0 …
I am using keras currently, and I want to see which inputs the model is "looking at". It would be like a saliency map, but my model is a simple two-layered perceptron for classification, so the input and ouput vectors are one dimensional. There is any library to do it easily? I don't quite understand the full programming of saliency maps.
The Perceptron Training Rule is basically applying Stochastic Gradient Descent for finding the coefficients of a hyperplane (which works as a Decision Boundary) for doing binary classification of data points (instances). I read that the Stochastic Gradient Descent algorithm could be proved to work accurately for finding the coefficients (aka weights) of a hyperplane Decision Boundary, given the following: Provided the training examples are linearly separable. Provided a sufficiently small Learning Rate is used. Could anyone please prove the above?
I perceive a single perceptron as a single linear function $y = a_1x_1 + a_2x_2 + ... + a_nx_n + b_0$ with a goal to calculate the best weights combination $ w_1, w_2, ..., w_n $ that minimizes the given loss function. The problem with this type of network is that it would not be able to perform well on a non linear dataset, thus an activation function would be used in order to tackle this. I am wandering what …
https://www.mathworks.com/help/deeplearning/ref/fitnet.html is the tutorial that I am following to understand fitting data to a function. I have few doubts regarding structure and terminologies which are the following: 1. Model & number of hidden layers By hidden layer we mean the layer that is inbetween the input and output. If number of layers = 1 with 10 hidden neurons (as shown in second figure) then is it essentially a neural network which is termed as an MLP. Is my understanding correct? …
I wanted to visualize how a perceptron learns, so I made a class that performs gradient descent. To show the decision, I plot a plane showing where positive examples and negative examples are, according to the perception. I also plot the decision line. Right now, this is the output: As you can see, the line appears to be incorrect, but the plane appears to be correct. A decision line of a perception, as I understand it, can be represented like …
Suppose we have the following fully connected network made of perceptrons with a sign function as the activation unit, what issue arises, when trying to train this network with gradient descent?
why should I prefer L1 over L2, in fully-connected-layer or convolution? why use dropout between 2 layers, when there is the option of regularising a layer(or both) with something like L1 or L2? and one would also have the flexibility to use different regularisation techniques at each layer? A lot of the times, trying out different techniques and comparing performance may cost time and money. So, when should I use(or prefer) one regularisation technique over other?