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| Removes drift and prevents aliasing and/or emphasize a particular frequency range |
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| remove a particular frequency range e.g. 60Hz |
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| is the Probability of rejecting the Null when it is actually true |
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= E ((X-mu)(X-mu)')
=1/n \sum(X-mu)(X-mu)') |
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m = mean(hw3data, 2);
centeredData = hw3data - repmat(m, 1, numSamples); |
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| Compute Covariance Matrix (PCA) |
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| C = (1 / (numSamples )) * centeredData * centeredData'; |
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| Compute Eigenvectors of Covariance Matrix (and sort by decreasing eigenvalue) |
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[V, D] = eig(C);
[V, D] = eigsort(V, D); |
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| V(:,1:N)*projectedData(1:10) + m |
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A\B is the matrix division of A into B,
same as INV(A)*B , |
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| What does the minimum square error solution minimize? |
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| \sum_{(x,y) pairs} (y-mx-b)^2 |
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* Reflect the point with the highest WSS through centroid (center) of the simplex
* If this produces the lowest WSS (best point) expand the simplex and reflect further
* If this is just a good point start at the top and reflect again
* If this the highest WSS (worst point) compress the simplex and reflect closer |
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| What are the three activation functions? |
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1.)sigmoid
2.)linear
3.)threshold |
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| the boundary between where the neuron outputs 0 or 1 (for threshold units), crosses through .5 for linear/sigmoid units |
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| When does Nelder Mead finish running? |
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| Rules are repeated until the convergence criteria are meet. The simplex moves over WSS surface and should contracts around minimum. |
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| What does fminsearch do to find a good fit to data? |
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| It minimizes the mean square error of the fit |
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| Why is the weight vector perpendicular to the decision given by the network? |
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| bias weight can be dealt with as a weight from a unit with activation always 1 |
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| What is the perceptron learning rule? |
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| Why does the Perceptron Learning Rule make sense? |
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| When does the Perceptron Learning Rule converge? |
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| Can the Perceptron Learning Rule work for every case? |
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| No, the Perceptron Learning Rule only works for linearly separable problems |
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| What does the perceptron learning rule do when the inputs are classified correctly? |
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| What does the Perceptron learning rules do for inputs that have outputs 0 but should be 1? |
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| It moves the weight vector towards the input by adding the input vector to the weight vector |
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| What does the perceptron learning rule do for inputs that have output 1 but should be 0 |
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It moves the weight vecotr away from the output by subtracting
w_1^new = w_1^old + (target-output) x_1 |
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| What is the Perceptron Convergence Theorem? |
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for any data set which is linearly
separable, the PLA is guaranteed to find a solution in a finite number
of steps |
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| What does the perceptron learning rule do for non-linearly separable problems? |
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| will not converge (continually bounces around) |
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| What is the pocket algorithm? |
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| The pocket algorithm is a variant on the PLA -- stores best solution and only stores new weights if the solution is better the previous ones |
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| Why do we need to havemulti-layer perceptrons with non-linear activation units? |
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| What is a commonly used activation function? |
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| f(x) = 1/(1+e^{-x}) = sigma(x) |
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| What is a gradient vector? |
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| The vector of partial derivatives with respect to each parameter Gradient(f(x_1,x_2)) = [ df/dx_1 df/dx_2 ]' |
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| What is the gradient descent algorithm? |
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| x_1 (new) = x_1 (old) - eta (df/dx_1) |
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| What is the derivative of the sigmoid function? |
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| What are the disadvantages of the Nelder Mead algorithm? |
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