Machine Learning in Action

Machine Learning in Action

2019/5/15 by DKZ

学习了Andrew Ng的Machine Learing入门视频课程,结合了Machine Learning in Action这本书的代码实践。

以下代码整理自Machine Learning in Action,少数地方为使用python3做了改动。

kNN

distance=sqrt(sum((target-train)**2))

  1. data [x,y,...] labal
  2. train data matrix [data,...] and [labal,]
  3. normMat(trainMat) and normVec(targetData)
  4. kNN(targetVec,trainMat,labals,k) return nearist labal
    1. calc distance
    2. sort
    3. find max count label
def normMat(dataMat):
    minVals = dataMat.min(0)
    maxVals = dataMat.max(0)
    ranges = maxVals - minVals
    normDataSet = zeros(shape(dataMat))
    m = dataMat.shape[0]
    normDataSet = dataMat - tile(minVals, (m,1))
    normDataSet = normDataSet/tile(ranges, (m,1))
    return normDataSet, ranges, minVals

def normVec(dataVec,minVals,ranges):
    return (dataVec-minVals)/ranges

def kNN(targetVec, trainMat, labels, k):
    """
    targetVec [num,...] 
    trainMat [[num,...],[num,...],...] 
    labels [str,str,...] train data label
    k int count range
    """
    trainMatSize = trainMat.shape[0]
    diffMat = tile(targetVec, (trainMatSize,1)) - trainMat # targetArr to targetMat [target,...] then [[target-train],...] 
    sqDiffMat = diffMat**2 # [[(target-train)**2]]
    sqDistances = sqDiffMat.sum(axis=1) # [sum([(target-train)**2]),...]
    distances = sqDistances**0.5 # useless?
    sortedDistIndicies = distances.argsort() # sort distance array [index,...]
    # find k nearist train data count label return max
    classCount={} 
    for i in range(k):
        voteIlabel = labels[sortedDistIndicies[i]]
        classCount[voteIlabel] = classCount.get(voteIlabel,0) + 1
    sortedClassCount = sorted(classCount.items(), key=operator.itemgetter(1), reverse=True)
    return sortedClassCount[0][0]

Decision Tree

ID3

entropy=-sum(log2(prob)*prob)

  1. data [feature,...,cls]
  2. train data matrix [[feature,...,cls],...] feature labels [feature_name,...]
  3. creatTree(trainMat,labels)
    1. get sub matrix by every unique type in features
    2. calc entropy*prob find smallest as best feature
    3. splic sub matrix by best feature
    4. recursive creat sub tree
  4. classify by tree
def calcShannonEnt(dataMat):
    numEntries = len(dataMat)
    labelCounts = {}
    for featVec in dataMat: #the the number of unique elements and their occurance
        currentLabel = featVec[-1]
        if currentLabel not in labelCounts.keys(): labelCounts[currentLabel] = 0
        labelCounts[currentLabel] += 1
    shannonEnt = 0.0
    for key in labelCounts:
        prob = float(labelCounts[key])/numEntries
        shannonEnt -= prob * log(prob,2) #log base 2
    return shannonEnt # -sum(log2(prob)*prob) average infomation
    
def splitDataSet(dataMat, axis, value):
    resultDataMat = []
    for featVec in dataMat:
        if featVec[axis] == value:
            reducedFeatVec = featVec[:axis]     #chop out axis used for splitting
            reducedFeatVec.extend(featVec[axis+1:])
            resultDataMat.append(reducedFeatVec)
    return resultDataMat
    
def chooseBestFeatureToSplit(dataMat):
    numFeatures = len(dataMat[0]) - 1      #the last column is used for the class
    baseEntropy = calcShannonEnt(dataMat)
    bestInfoGain = 0.0; bestFeature = -1
    for i in range(numFeatures):        #iterate over all the features
        featList = [example[i] for example in dataMat] # [feature_i,...]
        uniqueVals = set(featList) # unique type in feature_i {feature_it,...} featurn_i 
        newEntropy = 0.0
        for value in uniqueVals:
            subDataMat = splitDataSet(dataMat, i, value) # featurn_it => [[feature_except_i,...,cls],...]
            prob = len(subDataMat)/float(len(dataMat))
            newEntropy += prob * calcShannonEnt(subDataMat) # smaller better    
        infoGain = baseEntropy - newEntropy     # calculate the info gain; ie reduction in entropy
        if (infoGain > bestInfoGain):       
            bestInfoGain = infoGain         
            bestFeature = i
    return bestFeature                      # returns best feature index

def createTree(dataMat,labels):
    """
    ID3
    dataMat [[feature,...,cls],...]
    labels [feature_name,...] featurn label
    """
    classList = [example[-1] for example in dataMat] # class array [cls,...]
    # stop splitting when all of the classes are equal
    if classList.count(classList[0]) == len(classList): 
        return classList[0]
    # stop splitting when there are no more features in dataMat
    if len(dataMat[0]) == 1: 
        return majorityCnt(classList)
    bestFeat = chooseBestFeatureToSplit(dataMat)
    bestFeatLabel = labels[bestFeat]
    theTree = {bestFeatLabel:{}}
    del(labels[bestFeat])
    # subtree
    featValues = [example[bestFeat] for example in dataMat]
    uniqueVals = set(featValues)
    for value in uniqueVals:
        subLabels = labels[:]       #copy all of labels, so trees don't mess up existing labels
        theTree[bestFeatLabel][value] = createTree(splitDataSet(dataMat, bestFeat, value),subLabels)
    return theTree # {feature_label_i:{feature_i_a:subtree|cls,...}} 

def classify(tree,featureLabel,targetVec):
    firstStr = list(tree.keys())[0]
    secondDict = tree[firstStr]
    featIndex = featureLabel.index(firstStr)
    key = targetVec[featIndex]
    valueOfFeat = secondDict[key]
    if isinstance(valueOfFeat, dict): 
        classLabel = classify(valueOfFeat, featureLabel, targetVec)
    else: classLabel = valueOfFeat
    return classLabel

Naive Bayes

P(A|B) = P(B|A)P(A)/P(B)
  1. creat dictionary (a unique word vector)
    • calculate most frequence word and delect from dictionary
    • or remove from stop word list
  2. transform wordVec to dataVec
    • set-of-words model or bag-of-words model
    • mark in or not at dictionary
    • dataVec to dataMat
def createDictionary(wordMat):
    vocabSet = set([])  #create empty set
    for document in wordMat:
        vocabSet = vocabSet | set(document) #union of the two sets
    return list(vocabSet)

def wordVecToDataVec(dictionary, wordVec):
    returnVec = [0]*len(dictionary)
    for word in wordVec:
        if word in dictionary:
            # returnVec[dictionary.index(word)] = 1
            returnVec[dictionary.index(word)] += 1
        else: print("the word: %s is not in my Vocabulary!" % word)
    return returnVec    
  1. train naive bayes
  2. classify
def trainNaiveBayes(trainMat,labels):
    numTrainDocs = len(trainMat)
    numWords = len(trainMat[0])
    pClass1 = sum(labels)/float(numTrainDocs)
    p0Num = ones(numWords); p1Num = ones(numWords)      #change to ones() 
    p0Denom = 2.0; p1Denom = 2.0                        #change to 2.0
    # p0Denom = 0; p1Denom =0                       
    for i in range(numTrainDocs):
        if labels[i] == 1:
            p1Num += trainMat[i]
            p1Denom += sum(trainMat[i])
        else:
            p0Num += trainMat[i]
            p0Denom += sum(trainMat[i])
    p1Vect = log(p1Num/p1Denom)          #change to log() for better distribution
    p0Vect = log(p0Num/p0Denom)          
    # p1Vect = p1Num/p1Denom         
    # p0Vect = p0Num/p0Denom         
    return p0Vect,p1Vect,pClass1

def classifyNB(targetVec, p0Vec, p1Vec, pClass1):
    p1 = sum(targetVec * p1Vec) + log(pClass1)    #element-wise mult
    p0 = sum(targetVec * p0Vec) + log(1.0 - pClass1)
    if p1 > p0:
        return 1
    else: 
        return 0

Logistics Regres

sigmoid(inX)=1/(1+exp(-inX))

weights=weights+alpha*error*dataMat.transpose()

  1. calculate sigmoid result
  2. find error and new weight
  3. regres weight
def sigmoid(inX):
    return 1.0/(1+exp(-inX))

def gradAscent(dataMatIn, classLabels):
    dataMatrix = mat(dataMatIn)             #convert to NumPy matrix
    labelMat = mat(classLabels).transpose() #convert to NumPy matrix
    m,n = shape(dataMatrix)
    alpha = 0.001
    maxCycles = 500
    weights = ones((n,1))
    for k in range(maxCycles):              #heavy on matrix operations
        h = sigmoid(dataMatrix*weights)     #matrix mult
        error = (labelMat - h)              #vector subtraction
        weights = weights + alpha * dataMatrix.transpose()* error #matrix mult
    return weights

# random optimized
def stocGradAscent(dataMatrix, classLabels, numIter=150):
    m,n = shape(dataMatrix)
    weights = ones(n)   #initialize to all ones
    for j in range(numIter):
        dataIndex = list(range(m))
        for i in range(m):
            alpha = 4/(1.0+j+i)+0.0001    #apha decreases with iteration, does not 
            randIndex = int(random.uniform(0,len(dataIndex)))#go to 0 because of the constant
            h = sigmoid(sum(dataMatrix[randIndex]*weights))
            error = classLabels[randIndex] - h
            weights = weights + alpha * error * dataMatrix[randIndex]
            del(dataIndex[randIndex])
    return weights

def classifyVector(inX, weights):
    prob = sigmoid(sum(inX*weights))
    if prob > 0.5: return 1.0
    else: return 0.0

SVN

simple SMO

def selectJrand(i,m):
    j=i #we want to select any J not equal to i
    while (j==i):
        j = int(random.uniform(0,m))
    return j

def clipAlpha(aj,H,L):
    if aj > H: 
        aj = H
    if L > aj:
        aj = L
    return aj

def smoSimple(dataMatIn, classLabels, C, toler, maxIter):
    """
    C:float bigger err less overfitting, C smaller margin bigger
    toler:float max error
    """
    dataMatrix = mat(dataMatIn); labelMat = mat(classLabels).transpose()
    b = 0; m,n = shape(dataMatrix)
    alphas = mat(zeros((m,1)))
    iter = 0
    while (iter < maxIter):
        alphaPairsChanged = 0
        for i in range(m):
            fXi = float(multiply(alphas,labelMat).T*(dataMatrix*dataMatrix[i,:].T)) + b
            Ei = fXi - float(labelMat[i])#if checks if an example violates KKT conditions
            if ((labelMat[i]*Ei < -toler) and (alphas[i] < C)) or ((labelMat[i]*Ei > toler) and (alphas[i] > 0)):
                j = selectJrand(i,m)
                fXj = float(multiply(alphas,labelMat).T*(dataMatrix*dataMatrix[j,:].T)) + b
                Ej = fXj - float(labelMat[j])
                alphaIold = alphas[i].copy(); alphaJold = alphas[j].copy();
                if (labelMat[i] != labelMat[j]):
                    L = max(0, alphas[j] - alphas[i])
                    H = min(C, C + alphas[j] - alphas[i])
                else:
                    L = max(0, alphas[j] + alphas[i] - C)
                    H = min(C, alphas[j] + alphas[i])
                if L==H: print("L==H"); continue
                eta = 2.0 * dataMatrix[i,:]*dataMatrix[j,:].T - dataMatrix[i,:]*dataMatrix[i,:].T - dataMatrix[j,:]*dataMatrix[j,:].T
                if eta >= 0: print("eta>=0"); continue
                alphas[j] -= labelMat[j]*(Ei - Ej)/eta
                alphas[j] = clipAlpha(alphas[j],H,L)
                if (abs(alphas[j] - alphaJold) < 0.00001): 
                    print("j not moving enough") 
                    continue
                alphas[i] += labelMat[j]*labelMat[i]*(alphaJold - alphas[j])#update i by the same amount as j
                                                                        #the update is in the oppostie direction
                b1 = b - Ei- labelMat[i]*(alphas[i]-alphaIold)*dataMatrix[i,:]*dataMatrix[i,:].T - labelMat[j]*(alphas[j]-alphaJold)*dataMatrix[i,:]*dataMatrix[j,:].T
                b2 = b - Ej- labelMat[i]*(alphas[i]-alphaIold)*dataMatrix[i,:]*dataMatrix[j,:].T - labelMat[j]*(alphas[j]-alphaJold)*dataMatrix[j,:]*dataMatrix[j,:].T
                if (0 < alphas[i]) and (C > alphas[i]): b = b1
                elif (0 < alphas[j]) and (C > alphas[j]): b = b2
                else: b = (b1 + b2)/2.0
                alphaPairsChanged += 1
                print("iter: %d i:%d, pairs changed %d" % (iter,i,alphaPairsChanged))
        if (alphaPairsChanged == 0): iter += 1
        else: iter = 0
        print("iteration number: %d" % iter)
    return b,alphas#alphas[i]>0  i is support vecter

def calcWs(alphas,dataArr,classLabels):
    X = mat(dataArr); labelMat = mat(classLabels).transpose()
    m,n = shape(X)
    w = zeros((n,1))
    for i in range(m):
        w += multiply(alphas[i]*labelMat[i],X[i,:].T)
    return w

p0=dataMat[0]*mat(w)+b

Platt SMO

def kernelTrans(X, A, kTup): #calc the kernel or transform data to a higher dimensional space
    m,n = shape(X)
    K = mat(zeros((m,1)))
    if kTup[0]=='lin': K = X * A.T   #linear kernel
    elif kTup[0]=='rbf':
        for j in range(m):
            deltaRow = X[j,:] - A
            K[j] = deltaRow*deltaRow.T
        K = exp(K/(-1*kTup[1]**2)) #divide in NumPy is element-wise not matrix like Matlab
    else: raise NameError('Houston We Have a Problem -- \
    That Kernel is not recognized')
    return K

class optStruct:
    def __init__(self,dataMatIn, classLabels, C, toler, kTup):  # Initialize the structure with the parameters 
        self.X = dataMatIn
        self.labelMat = classLabels
        self.C = C
        self.tol = toler
        self.m = shape(dataMatIn)[0]
        self.alphas = mat(zeros((self.m,1)))
        self.b = 0
        self.eCache = mat(zeros((self.m,2))) #first column is valid flag
        self.K = mat(zeros((self.m,self.m)))
        for i in range(self.m):
            self.K[:,i] = kernelTrans(self.X, self.X[i,:], kTup)
        
def calcEk(oS, k):
    fXk = float(multiply(oS.alphas,oS.labelMat).T*oS.K[:,k] + oS.b)
    Ek = fXk - float(oS.labelMat[k])
    return Ek
        
def selectJ(i, oS, Ei):         #this is the second choice -heurstic, and calcs Ej
    maxK = -1; maxDeltaE = 0; Ej = 0
    oS.eCache[i] = [1,Ei]  #set valid #choose the alpha that gives the maximum delta E
    validEcacheList = nonzero(oS.eCache[:,0].A)[0]
    if (len(validEcacheList)) > 1:
        for k in validEcacheList:   #loop through valid Ecache values and find the one that maximizes delta E
            if k == i: continue #don't calc for i, waste of time
            Ek = calcEk(oS, k)
            deltaE = abs(Ei - Ek)
            if (deltaE > maxDeltaE):
                maxK = k; maxDeltaE = deltaE; Ej = Ek
        return maxK, Ej
    else:   #in this case (first time around) we don't have any valid eCache values
        j = selectJrand(i, oS.m)
        Ej = calcEk(oS, j)
    return j, Ej

def updateEk(oS, k):#after any alpha has changed update the new value in the cache
    Ek = calcEk(oS, k)
    oS.eCache[k] = [1,Ek]
        
def innerL(i, oS):
    Ei = calcEk(oS, i)
    if ((oS.labelMat[i]*Ei < -oS.tol) and (oS.alphas[i] < oS.C)) or ((oS.labelMat[i]*Ei > oS.tol) and (oS.alphas[i] > 0)):
        j,Ej = selectJ(i, oS, Ei) #this has been changed from selectJrand
        alphaIold = oS.alphas[i].copy(); alphaJold = oS.alphas[j].copy();
        if (oS.labelMat[i] != oS.labelMat[j]):
            L = max(0, oS.alphas[j] - oS.alphas[i])
            H = min(oS.C, oS.C + oS.alphas[j] - oS.alphas[i])
        else:
            L = max(0, oS.alphas[j] + oS.alphas[i] - oS.C)
            H = min(oS.C, oS.alphas[j] + oS.alphas[i])
        if L==H: 
            # print("L==H") 
            return 0
        eta = 2.0 * oS.K[i,j] - oS.K[i,i] - oS.K[j,j] #changed for kernel
        if eta >= 0: 
            # print("eta>=0")
            return 0
        oS.alphas[j] -= oS.labelMat[j]*(Ei - Ej)/eta
        oS.alphas[j] = clipAlpha(oS.alphas[j],H,L)
        updateEk(oS, j) #added this for the Ecache
        if (abs(oS.alphas[j] - alphaJold) < 0.00001): 
            # print("j not moving enough")
            return 0
        oS.alphas[i] += oS.labelMat[j]*oS.labelMat[i]*(alphaJold - oS.alphas[j])#update i by the same amount as j
        updateEk(oS, i) #added this for the Ecache                    #the update is in the oppostie direction
        b1 = oS.b - Ei- oS.labelMat[i]*(oS.alphas[i]-alphaIold)*oS.K[i,i] - oS.labelMat[j]*(oS.alphas[j]-alphaJold)*oS.K[i,j]
        b2 = oS.b - Ej- oS.labelMat[i]*(oS.alphas[i]-alphaIold)*oS.K[i,j]- oS.labelMat[j]*(oS.alphas[j]-alphaJold)*oS.K[j,j]
        if (0 < oS.alphas[i]) and (oS.C > oS.alphas[i]): oS.b = b1
        elif (0 < oS.alphas[j]) and (oS.C > oS.alphas[j]): oS.b = b2
        else: oS.b = (b1 + b2)/2.0
        return 1
    else: return 0

def smoP(dataMatIn, classLabels, C, toler, maxIter,kTup=('lin', 0)):    #full Platt SMO
    oS = optStruct(mat(dataMatIn),mat(classLabels).transpose(),C,toler, kTup)
    iter = 0
    entireSet = True; alphaPairsChanged = 0
    while (iter < maxIter) and ((alphaPairsChanged > 0) or (entireSet)):
        alphaPairsChanged = 0
        if entireSet:   #go over all
            for i in range(oS.m):        
                alphaPairsChanged += innerL(i,oS)
                # print("fullSet, iter: %d i:%d, pairs changed %d" % (iter,i,alphaPairsChanged))
            iter += 1
        else:#go over non-bound (railed) alphas
            nonBoundIs = nonzero((oS.alphas.A > 0) * (oS.alphas.A < C))[0]
            for i in nonBoundIs:
                alphaPairsChanged += innerL(i,oS)
                # print("non-bound, iter: %d i:%d, pairs changed %d" % (iter,i,alphaPairsChanged))
            iter += 1
        if entireSet: entireSet = False #toggle entire set loop
        elif (alphaPairsChanged == 0): entireSet = True  
        # print("iteration number: %d" % iter)
    return oS.b,oS.alphas

datMat=mat(dataMatIn)
labelMat = mat(classLabels).transpose()
svInd=nonzero(alphas.A>0)[0]# support vecters index
sVs=datMat[svInd] # get matrix of only support vectors
labelSV = labelMat[svInd] #support vecters labels
m,n = shape(datMat)
errorCount = 0
for i in range(m):
    kernelEval = kernelTrans(sVs,datMat[i,:],('rbf', k1))
    predict=kernelEval.T * multiply(labelSV,alphas[svInd]) + b # predict
    if sign(predict)!=sign(classLabels[i]): errorCount += 1

AdaBoost

def stumpClassify(dataMatrix,dimen,threshVal,threshIneq):#just classify the data
    retArray = ones((shape(dataMatrix)[0],1))
    if threshIneq == 'lt':
        retArray[dataMatrix[:,dimen] <= threshVal] = -1.0
    else:
        retArray[dataMatrix[:,dimen] > threshVal] = -1.0
    # print('retArray',retArray)#
    return retArray

def buildStump(dataArr,classLabels,D):
    dataMatrix = mat(dataArr); labelMat = mat(classLabels).T
    m,n = shape(dataMatrix)
    numSteps = 10.0; bestStump = {}; bestClasEst = mat(zeros((m,1)))
    minError = inf #init error sum, to +infinity
    for i in range(n):#loop over all dimensions
        rangeMin = dataMatrix[:,i].min(); rangeMax = dataMatrix[:,i].max();
        stepSize = (rangeMax-rangeMin)/numSteps
        for j in range(-1,int(numSteps)+1):#loop over all range in current dimension
            for inequal in ['lt', 'gt']: #go over less than and greater than
                threshVal = (rangeMin + float(j) * stepSize)
                predictedVals = stumpClassify(dataMatrix,i,threshVal,inequal)#call stump classify with i, j, lessThan
                errArr = mat(ones((m,1)))
                errArr[predictedVals == labelMat] = 0
                weightedError = D.T*errArr  #calc total error multiplied by D
                # print("split: dim %d, thresh %.2f, thresh ineqal: %s, the weighted error is %.3f" % (i, threshVal, inequal, weightedError))
                if weightedError < minError:
                    minError = weightedError
                    bestClasEst = predictedVals.copy()
                    bestStump['dim'] = i
                    bestStump['thresh'] = threshVal
                    bestStump['ineq'] = inequal
    return bestStump,minError,bestClasEst

def adaBoostTrainDS(dataArr,classLabels,numIt=40):
    weakClassArr = []
    m = shape(dataArr)[0]
    D = mat(ones((m,1))/m)   #init D to all equal
    aggClassEst = mat(zeros((m,1)))
    for i in range(numIt):
        bestStump,error,classEst = buildStump(dataArr,classLabels,D)#build Stump
        # print("D:",D.T)
        alpha = float(0.5*log((1.0-error)/max(error,1e-16)))#calc alpha, throw in max(error,eps) to account for error=0
        bestStump['alpha'] = alpha  
        weakClassArr.append(bestStump)                  #store Stump Params in Array
        # print("classEst: ",classEst.T)
        expon = multiply(-1*alpha*mat(classLabels).T,classEst) #exponent for D calc, getting messy
        D = multiply(D,exp(expon))                              #Calc New D for next iteration
        D = D/D.sum()
        #calc training error of all classifiers, if this is 0 quit for loop early (use break)
        aggClassEst += alpha*classEst
        # print("aggClassEst: ",aggClassEst.T)
        aggErrors = multiply(sign(aggClassEst) != mat(classLabels).T,ones((m,1)))
        errorRate = aggErrors.sum()/m
        # print("total error: ",errorRate)
        if errorRate == 0.0: break
    return weakClassArr,aggClassEst

def adaClassify(datToClass,classifierArr):#dataMat[i],weakClassArr
    dataMatrix = mat(datToClass)#do stuff similar to last aggClassEst in adaBoostTrainDS
    m = shape(dataMatrix)[0]
    aggClassEst = mat(zeros((m,1)))
    for i in range(len(classifierArr)):
        classEst = stumpClassify(dataMatrix,classifierArr[i]['dim'],\
                                 classifierArr[i]['thresh'],\
                                 classifierArr[i]['ineq'])#call stump classify
        aggClassEst += classifierArr[i]['alpha']*classEst
        # print(aggClassEst)
    return sign(aggClassEst)

Linear Regression

Ordinary Least Squares Methods

err=sum(yi-xi.T*w)^2
w=(X.T*X)^-1*X.T*y #min err

y=x*w
def standRegres(xData,yArr):
    xMat = mat(xData); yMat = mat(yArr).T
    xTx = xMat.T*xMat
    if linalg.det(xTx) == 0.0:
        print("This matrix is singular, cannot do inverse")
        return
    ws = xTx.I * (xMat.T*yMat)
    return ws

y=xData*ws
corr=corrcoef(y.T,yArr)

Locally Weighted Linear Regression

w=(X.T*W*X)^-1*X.T*W*y

def lwlr(testPoint,xData,yArr,k=1.0): # k smaller near point weight biger
    xMat = mat(xData); yMat = mat(yArr).T
    m = shape(xMat)[0]
    weights = mat(eye((m)))
    for j in range(m):                      #next 2 lines create weights matrix
        diffMat = testPoint - xMat[j,:]     #
        weights[j,j] = exp(diffMat*diffMat.T/(-2.0*k**2))
    xTx = xMat.T * (weights * xMat)
    if linalg.det(xTx) == 0.0:
        print("This matrix is singular, cannot do inverse")
        return
    ws = xTx.I * (xMat.T * (weights * yMat))
    return testPoint * ws

Ridge Regression

feature > sample

w=(X.T*X+lamda*I)^-1*X.T*y

def ridgeRegres(xMat,yMat,lam=0.2):# xMat=mat(xData) yMat=mat(yArr).T
    xTx = xMat.T*xMat
    denom = xTx + eye(shape(xMat)[1])*lam
    if linalg.det(denom) == 0.0:
        print("This matrix is singular, cannot do inverse")
        return
    ws = denom.I * (xMat.T*yMat)
    return ws

Stage Regres

def stageWise(xArr,yArr,eps=0.01,numIt=100):
    xMat = mat(xArr); yMat=mat(yArr).T
    yMean = mean(yMat,0)
    yMat = yMat - yMean     #can also regularize ys but will get smaller coef
    xMat = regularize(xMat)
    m,n=shape(xMat)
    ws = zeros((n,1)); wsTest = ws.copy(); wsMax = ws.copy()
    for i in range(numIt):
        # print(ws.T)
        lowestError = inf; 
        for j in range(n):
            for sign in [-1,1]:
                wsTest = ws.copy()
                wsTest[j] += eps*sign
                yTest = xMat*wsTest
                rssE = rssError(yMat.A,yTest.A)
                if rssE < lowestError:
                    lowestError = rssE
                    wsMax = wsTest
        ws = wsMax.copy()
    return ws.T

CART

1.create tree use train data

2.tree pruning use test data

3.forecast

def binSplitDataSet(dataSet, feature, value):
    mat0 = dataSet[nonzero(dataSet[:,feature] > value)[0],:]
    mat1 = dataSet[nonzero(dataSet[:,feature] <= value)[0],:]
    return mat0,mat

def chooseBestSplit(dataSet, leafType=regLeaf, errType=regErr, ops=(1,4)):
    tolS = ops[0]# spiit min error
    tolN = ops[1]# split min item number
    #if all the target variables are the same value: quit and return value
    if len(set(dataSet[:,-1].T.tolist()[0])) == 1: #exit cond 1
        return None, leafType(dataSet)
    m,n = shape(dataSet)
    #the choice of the best feature is driven by Reduction in RSS error from mean
    S = errType(dataSet)
    bestS = inf; bestIndex = 0; bestValue = 0
    for featIndex in range(n-1):
        for splitVal in set((dataSet[:, featIndex].T.A.tolist())[0]):
            mat0, mat1 = binSplitDataSet(dataSet, featIndex, splitVal)
            if (shape(mat0)[0] < tolN) or (shape(mat1)[0] < tolN): continue
            newS = errType(mat0) + errType(mat1)
            if newS < bestS: 
                bestIndex = featIndex
                bestValue = splitVal
                bestS = newS
    #if the decrease (S-bestS) is less than a threshold don't do the split
    if (S - bestS) < tolS: 
        return None, leafType(dataSet) #exit cond 2
    mat0, mat1 = binSplitDataSet(dataSet, bestIndex, bestValue)
    if (shape(mat0)[0] < tolN) or (shape(mat1)[0] < tolN):  #exit cond 3
        return None, leafType(dataSet)
    return bestIndex,bestValue#returns the best feature to split on
                              #and the value used for that split

def createTree(dataSet, leafType=regLeaf, errType=regErr, ops=(1,4)):#assume dataSet is NumPy Mat so we can array filtering
    feat, val = chooseBestSplit(dataSet, leafType, errType, ops)#choose the best split
    if feat == None: return val #if the splitting hit a stop condition return val
    retTree = {}
    retTree['spInd'] = feat
    retTree['spVal'] = val
    lSet, rSet = binSplitDataSet(dataSet, feat, val)
    retTree['left'] = createTree(lSet, leafType, errType, ops)
    retTree['right'] = createTree(rSet, leafType, errType, ops)
    return retTree # {spInd:split_feat_index,spVal:split_feat_value,left:tree|leafType,right:tree|leafType}

regression tree

def regLeaf(dataSet):#returns the value used for each leaf
    return mean(dataSet[:,-1])

def regErr(dataSet):
    return var(dataSet[:,-1]) * shape(dataSet)[0]

TreePruning

for regression tree

def isTree(obj):
    return (type(obj).__name__=='dict')

def getMean(tree):
    if isTree(tree['right']): tree['right'] = getMean(tree['right'])
    if isTree(tree['left']): tree['left'] = getMean(tree['left'])
    return (tree['left']+tree['right'])/2.0
    
def prune(tree, testData):
    if shape(testData)[0] == 0: return getMean(tree) #if we have no test data collapse the tree
    if (isTree(tree['right']) or isTree(tree['left'])):#if the branches are not trees try to prune them
        lSet, rSet = binSplitDataSet(testData, tree['spInd'], tree['spVal'])
    if isTree(tree['left']): tree['left'] = prune(tree['left'], lSet)
    if isTree(tree['right']): tree['right'] =  prune(tree['right'], rSet)
    #if they are now both leafs, see if we can merge them
    if not isTree(tree['left']) and not isTree(tree['right']):
        lSet, rSet = binSplitDataSet(testData, tree['spInd'], tree['spVal'])
        errorNoMerge = sum(power(lSet[:,-1] - tree['left'],2)) +\
            sum(power(rSet[:,-1] - tree['right'],2))
        treeMean = (tree['left']+tree['right'])/2.0
        errorMerge = sum(power(testData[:,-1] - treeMean,2))
        if errorMerge < errorNoMerge: 
            print("merging")
            return treeMean
        else: return tree
    else: return tree
def regTreeEval(model, inDat):
    return float(model)

model tree

def linearSolve(dataSet):   #helper function used in two places
    m,n = shape(dataSet)
    X = mat(ones((m,n))); Y = mat(ones((m,1)))#create a copy of data with 1 in 0th postion
    X[:,1:n] = dataSet[:,0:n-1]; Y = dataSet[:,-1]#and strip out Y
    xTx = X.T*X
    if linalg.det(xTx) == 0.0:
        raise NameError('This matrix is singular, cannot do inverse,\n\
        try increasing the second value of ops')
    ws = xTx.I * (X.T * Y)
    return ws,X,Y

def modelLeaf(dataSet):#create linear model and return coeficients
    ws,X,Y = linearSolve(dataSet)
    return ws

def modelErr(dataSet):
    ws,X,Y = linearSolve(dataSet)
    yHat = X * ws
    return sum(power(Y - yHat,2))
def modelTreeEval(model, inDat):
    n = shape(inDat)[1]
    X = mat(ones((1,n+1)))
    X[:,1:n+1]=inDat
    return float(X*model)

Forecast

def treeForeCast(tree, inData, modelEval=regTreeEval):
    if not isTree(tree): return modelEval(tree, inData)
    if inData[tree['spInd']] > tree['spVal']:
        if isTree(tree['left']): return treeForeCast(tree['left'], inData, modelEval)
        else: return modelEval(tree['left'], inData)
    else:
        if isTree(tree['right']): return treeForeCast(tree['right'], inData, modelEval)
        else: return modelEval(tree['right'], inData)
        
def createForeCast(tree, testData, modelEval=regTreeEval):
    m=len(testData)
    yHat = mat(zeros((m,1)))
    for i in range(m):
        yHat[i,0] = treeForeCast(tree, mat(testData[i]), modelEval)
    return yHat

kMeans

  1. for each data point assign it to the closest centroid
  2. for each centriod recalculate it to mean
  3. loop until centriod dont change
def distEclud(vecA, vecB):
    return sqrt(sum(power(vecA - vecB, 2))) #la.norm(vecA-vecB)

def randCent(dataSet, k):
    n = shape(dataSet)[1]
    centroids = mat(zeros((k,n)))#create centroid mat
    for j in range(n):#create random cluster centers, within bounds of each dimension
        minJ = min(dataSet[:,j]) 
        rangeJ = float(max(dataSet[:,j]) - minJ)
        centroids[:,j] = mat(minJ + rangeJ * random.rand(k,1))
    return centroids

def kMeans(dataSet, k, distMeas=distEclud, createCent=randCent):
    m = shape(dataSet)[0]
    clusterAssment = mat(zeros((m,2)))#create mat to assign data points 
                                      #to a centroid, also holds SE of each point
    centroids = createCent(dataSet, k)
    clusterChanged = True
    while clusterChanged:
        clusterChanged = False
        for i in range(m):#for each data point assign it to the closest centroid
            minDist = inf; minIndex = -1
            for j in range(k):
                distJI = distMeas(centroids[j,:],dataSet[i,:])
                if distJI < minDist:
                    minDist = distJI; minIndex = j
            if clusterAssment[i,0] != minIndex: clusterChanged = True
            clusterAssment[i,:] = minIndex,minDist**2
        # print(centroids)
        for cent in range(k):#recalculate centroids
            ptsInClust = dataSet[nonzero(clusterAssment[:,0].A==cent)[0]]#get all the point in this cluster
            centroids[cent,:] = mean(ptsInClust, axis=0) #assign centroid to mean 
    return centroids, clusterAssment# mat [index,distance] 
# dichotomy optimize
def biKmeans(dataSet, k, distMeas=distEclud):
    m = shape(dataSet)[0]
    clusterAssment = mat(zeros((m,2)))
    centroid0 = mean(dataSet, axis=0).tolist()[0]
    centList =[centroid0] #create a list with one centroid
    for j in range(m):#calc initial Error
        clusterAssment[j,1] = distMeas(mat(centroid0), dataSet[j,:])**2
    while (len(centList) < k):
        lowestSSE = inf
        for i in range(len(centList)):
            ptsInCurrCluster = dataSet[nonzero(clusterAssment[:,0].A==i)[0],:]#get the data points currently in cluster i
            centroidMat, splitClustAss = kMeans(ptsInCurrCluster, 2, distMeas)
            sseSplit = sum(splitClustAss[:,1])#compare the SSE to the currrent minimum
            sseNotSplit = sum(clusterAssment[nonzero(clusterAssment[:,0].A!=i)[0],1])
            # print("sseSplit, and notSplit: ",sseSplit,sseNotSplit)
            if (sseSplit + sseNotSplit) < lowestSSE:
                bestCentToSplit = i
                bestNewCents = centroidMat
                bestClustAss = splitClustAss.copy()
                lowestSSE = sseSplit + sseNotSplit
        bestClustAss[nonzero(bestClustAss[:,0].A == 1)[0],0] = len(centList) #change 1 to 3,4, or whatever
        bestClustAss[nonzero(bestClustAss[:,0].A == 0)[0],0] = bestCentToSplit
        # print('the bestCentToSplit is: ',bestCentToSplit)
        # print('the len of bestClustAss is: ', len(bestClustAss))
        centList[bestCentToSplit] = bestNewCents[0,:].tolist()[0]#replace a centroid with two best centroids 
        centList.append(bestNewCents[1,:].tolist()[0])
        clusterAssment[nonzero(clusterAssment[:,0].A == bestCentToSplit)[0],:]= bestClustAss#reassign new clusters, and SSE
    return mat(centList), clusterAssment

Apriori

def createC1(dataSet):
    C1 = []
    for transaction in dataSet:
        for item in transaction:
            if not [item] in C1:
                C1.append([item])
                
    C1.sort()
    return list(map(frozenset, C1))#use frozen set so we
                            #can use it as a key in a dict    

def scanD(D, Ck, minSupport):
    ssCnt = {}
    for tid in D:
        for can in Ck:
            if can.issubset(tid):
                if not can in ssCnt: ssCnt[can]=1
                else: ssCnt[can] += 1
    numItems = float(len(D))
    retList = []
    supportData = {}
    for key in ssCnt:
        support = ssCnt[key]/numItems # issubset/total 
        if support >= minSupport:
            retList.insert(0,key)
        supportData[key] = support
    return retList, supportData

def aprioriGen(Lk, k): #creates Ck
    retList = []
    lenLk = len(Lk)
    for i in range(lenLk):
        for j in range(i+1, lenLk): 
            L1 = list(Lk[i])[:k-2]; L2 = list(Lk[j])[:k-2]
            L1.sort(); L2.sort()
            if L1==L2: #if first k-2 elements are equal
                retList.append(Lk[i] | Lk[j]) #set union
    return retList

def apriori(dataSet, minSupport = 0.5):
    C1 = createC1(dataSet) # set len = 1
    D = list(map(set, dataSet))
    L1, supportData = scanD(D, C1, minSupport)
    L = [L1]
    k = 2
    while (len(L[k-2]) > 0):
        Ck = aprioriGen(L[k-2], k) # set len = k
        Lk, supK = scanD(D, Ck, minSupport)#scan DB to get Lk
        supportData.update(supK)
        L.append(Lk)
        k += 1
    return L, supportData # [[Ck>minSupport],] , {set:support}

def generateRules(L, supportData, minConf=0.7):
    bigRuleList = []
    for i in range(1, len(L)):#only get the sets with two or more items ,no C1
        for freqSet in L[i]:
            H1 = [frozenset([item]) for item in freqSet] #[1 item frozen set]
            if (i > 1):
                rulesFromConseq(freqSet, H1, supportData, bigRuleList, minConf)
            else:
                calcConf(freqSet, H1, supportData, bigRuleList, minConf)
    return bigRuleList         

def calcConf(freqSet, H, supportData, brl, minConf=0.7):
    prunedH = [] #create new list to return
    for conseq in H:
        conf = supportData[freqSet]/supportData[freqSet-conseq] #calc confidence
        if conf >= minConf: 
            print(freqSet-conseq,'-->',conseq,'conf:',conf)
            brl.append((freqSet-conseq, conseq, conf))
            prunedH.append(conseq)
    return prunedH

def rulesFromConseq(freqSet, H, supportData, brl, minConf=0.7):
    m = len(H[0])
    if (len(freqSet) > (m + 1)): #try further merging
        Hmp1 = aprioriGen(H, m+1)#create Hm+1 new candidates
        Hmp1 = calcConf(freqSet, Hmp1, supportData, brl, minConf)
        if (len(Hmp1) > 1):    #need at least two sets to merge
            rulesFromConseq(freqSet, Hmp1, supportData, brl, minConf)

FP-Growth

class treeNode:
    def __init__(self, nameValue, numOccur, parentNode):
        self.name = nameValue
        self.count = numOccur
        self.nodeLink = None
        self.parent = parentNode      #needs to be updated
        self.children = {} 
    
    def inc(self, numOccur):
        self.count += numOccur
        
    def disp(self, ind=1):
        print('  '*ind, self.name, ' ', self.count)
        for child in self.children.values():
            child.disp(ind+1)

def createTree(dataSet, minSup=1): #create FP-tree from dataset but don't mine
    headerTable = {} # {item:[times,treenode]}
    #go over dataSet twice
    for trans in dataSet:#first pass counts frequency of occurance
        for item in trans:
            headerTable[item] = headerTable.get(item, 0) + dataSet[trans]
    for k in list(headerTable.keys()):  #remove items not meeting minSup
        if headerTable[k] < minSup: 
            del(headerTable[k])
    freqItemSet = set(headerTable.keys())
    # print('freqItemSet: ',freqItemSet)
    if len(freqItemSet) == 0: return None, None  #if no items meet min support -->get out
    for k in headerTable:
        headerTable[k] = [headerTable[k], None] #reformat headerTable to use Node link 
    # print('headerTable: ',headerTable) 
    retTree = treeNode('Null Set', 1, None) #create tree
    for tranSet, count in dataSet.items():  #go through dataset 2nd time; count always = 1
        localD = {} # {item_transet:times}
        for item in tranSet:  #put transaction items in order
            if item in freqItemSet:
                localD[item] = headerTable[item][0]
        if len(localD) > 0:
            orderedItems = [v[0] for v in sorted(localD.items(), key=lambda p: p[1], reverse=True)]
            # print('orderedItems',orderedItems,localD)
            updateTree(orderedItems, retTree, headerTable, count)#populate tree with ordered freq itemset
    return retTree, headerTable #return tree and header table

def updateTree(items, inTree, headerTable, count):
    if items[0] in inTree.children:#check if orderedItems[0] in retTree.children
        inTree.children[items[0]].inc(count) #incrament count
    else:   #add items[0] to inTree.children
        inTree.children[items[0]] = treeNode(items[0], count, inTree)
        if headerTable[items[0]][1] == None: #update header table 
            headerTable[items[0]][1] = inTree.children[items[0]]
        else:
            updateHeader(headerTable[items[0]][1], inTree.children[items[0]])
    if len(items) > 1:#call updateTree() with remaining ordered items
        updateTree(items[1::], inTree.children[items[0]], headerTable, count)
        
def updateHeader(nodeToTest, targetNode):   #this version does not use recursion
    while (nodeToTest.nodeLink != None):    #Do not use recursion to traverse a linked list!
        nodeToTest = nodeToTest.nodeLink
    nodeToTest.nodeLink = targetNode
        
def ascendTree(leafNode, prefixPath): #ascends from leaf node to root
    if leafNode.parent != None:
        prefixPath.append(leafNode.name)
        ascendTree(leafNode.parent, prefixPath)
    
def findPrefixPath(basePat, treeNode): #treeNode comes from header table
    condPats = {}
    while treeNode != None:
        prefixPath = []
        ascendTree(treeNode, prefixPath)
        if len(prefixPath) > 1: 
            condPats[frozenset(prefixPath[1:])] = treeNode.count
        treeNode = treeNode.nodeLink
    return condPats

def mineTree(inTree, headerTable, minSup, preFix, freqItemList):
    bigL = [v[0] for v in sorted(headerTable.items(), key=lambda p: str(p[1]))]#(sort header table);[item]
    # print('bigL',bigL)
    for basePat in bigL:  #start from bottom of header table
        newFreqSet = preFix.copy()
        newFreqSet.add(basePat)
        # print('finalFrequent Item: ',newFreqSet)    #append to set
        freqItemList.append(newFreqSet)
        condPattBases = findPrefixPath(basePat, headerTable[basePat][1])
        # print('condPattBases :',basePat, condPattBases)
        #2. construct cond FP-tree from cond. pattern base
        myCondTree, myHead = createTree(condPattBases, minSup)
        # print('head from conditional tree: ', myHead)
        if myHead != None: #3. mine cond. FP-tree
            print('conditional tree for: ',newFreqSet)
            myCondTree.disp(1)            
            mineTree(myCondTree, myHead, minSup, newFreqSet, freqItemList)

PCA

def pca(dataMat, topNfeat=9999999):
    meanVals = mean(dataMat, axis=0)
    meanRemoved = dataMat - meanVals #remove mean
    covMat = cov(meanRemoved, rowvar=0)
    eigVals,eigVects = linalg.eig(mat(covMat))
    eigValInd = argsort(eigVals)            #sort, sort goes smallest to largest
    eigValInd = eigValInd[:-(topNfeat+1):-1]  #cut off unwanted dimensions
    redEigVects = eigVects[:,eigValInd]       #reorganize eig vects largest to smallest
    lowDDataMat = meanRemoved * redEigVects #transform data into new dimensions
    reconMat = (lowDDataMat * redEigVects.T) + meanVals
    return lowDDataMat, reconMat

SVD

U,Sigma,VT=svd(datamat)
lowdatamat=Uk*Sigmak*VTk

Recommend Engine

collaborative filtering

#datamat=[user]=[[itemscore]]
def ecludSim(inA,inB):
    return 1.0/(1.0 + la.norm(inA - inB))

def pearsSim(inA,inB):
    if len(inA) < 3 : return 1.0
    return 0.5+0.5*corrcoef(inA, inB, rowvar = 0)[0][1]

def cosSim(inA,inB):
    num = float(inA.T*inB)
    denom = la.norm(inA)*la.norm(inB)
    return 0.5+0.5*(num/denom)

def standEst(dataMat, user, simMeas, item):
    n = shape(dataMat)[1]
    simTotal = 0.0; ratSimTotal = 0.0
    for j in range(n):
        userRating = dataMat[user,j]
        if userRating == 0: continue
        overLap = nonzero(logical_and(dataMat[:,item].A>0, \
                                      dataMat[:,j].A>0))[0]#[userindex]
        print(overLap,userRating)
        if len(overLap) == 0: similarity = 0
        else: similarity = simMeas(dataMat[overLap,item], \
                                   dataMat[overLap,j])
        print('the %d and %d similarity is: %f' % (item, j, similarity))
        simTotal += similarity
        ratSimTotal += similarity * userRating
    if simTotal == 0: return 0
    else: return ratSimTotal/simTotal
    
def svdEst(dataMat, user, simMeas, item):
    n = shape(dataMat)[1]
    simTotal = 0.0; ratSimTotal = 0.0
    U,Sigma,VT = la.svd(dataMat)
    Sig4 = mat(eye(4)*Sigma[:4]) #arrange Sig4 into a diagonal matrix
    xformedItems = dataMat.T * U[:,:4] * Sig4.I  #create transformed items
    for j in range(n):
        userRating = dataMat[user,j]
        if userRating == 0 or j==item: continue
        similarity = simMeas(xformedItems[item,:].T,\
                             xformedItems[j,:].T)
        print('the %d and %d similarity is: %f' % (item, j, similarity))
        simTotal += similarity
        ratSimTotal += similarity * userRating
    if simTotal == 0: return 0
    else: return ratSimTotal/simTotal

def recommend(dataMat, user, N=3, simMeas=cosSim, estMethod=standEst):
    unratedItems = nonzero(dataMat[user,:].A==0)[1]#find unrated items [itemindex]
    if len(unratedItems) == 0: return 'you rated everything'
    itemScores = []#[(itemindex,score)]
    for item in unratedItems:
        estimatedScore = estMethod(dataMat, user, simMeas, item)
        itemScores.append((item, estimatedScore))
    return sorted(itemScores, key=lambda jj: jj[1], reverse=True)[:N]

Image Compress

def imgCompress(dataMat,numSV=3):
    U,Sigma,VT = la.svd(dataMat)
    SigRecon = mat(zeros((numSV, numSV)))
    for k in range(numSV):#construct diagonal matrix from vector
        SigRecon[k,k] = Sigma[k]
    
    reconMat = U[:,:numSV]*SigRecon*VT[:numSV,:]
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