/**
* Returns the impurity of a node.
*
* @param count the sample count in each class.
* @param n the number of samples in the node.
* @return the impurity of a node
*/
private double impurity(int[] count, int n) {
double impurity = 0.0;
switch (rule) {
case GINI:
impurity = 1.0;
for (int i = 0; i < count.length; i++) {
if (count[i] > 0) {
double p = (double) count[i] / n;
impurity -= p * p;
}
}
break;
case ENTROPY:
for (int i = 0; i < count.length; i++) {
if (count[i] > 0) {
double p = (double) count[i] / n;
impurity -= p * Math.log2(p);
}
}
break;
case CLASSIFICATION_ERROR:
impurity = 0;
for (int i = 0; i < count.length; i++) {
if (count[i] > 0) {
impurity = Math.max(impurity, count[i] / (double) n);
}
}
impurity = Math.abs(1 - impurity);
break;
}
return impurity;
}
/** Test of learn method, of class LogisticRegression. */
@Test
public void testIris() {
System.out.println("Iris");
ArffParser arffParser = new ArffParser();
arffParser.setResponseIndex(4);
try {
AttributeDataset iris =
arffParser.parse(smile.data.parser.IOUtils.getTestDataFile("weka/iris.arff"));
double[][] x = iris.toArray(new double[iris.size()][]);
int[] y = iris.toArray(new int[iris.size()]);
int n = x.length;
LOOCV loocv = new LOOCV(n);
int error = 0;
for (int i = 0; i < n; i++) {
double[][] trainx = Math.slice(x, loocv.train[i]);
int[] trainy = Math.slice(y, loocv.train[i]);
LogisticRegression logit = new LogisticRegression(trainx, trainy);
if (y[loocv.test[i]] != logit.predict(x[loocv.test[i]])) error++;
}
System.out.println("Logistic Regression error = " + error);
assertEquals(3, error);
} catch (Exception ex) {
System.err.println(ex);
}
}
/** Train L2 tree boost. */
private void train2(Attribute[] attributes, double[][] x, int[] y) {
int n = x.length;
int N = (int) Math.round(n * f);
int[] y2 = new int[n];
for (int i = 0; i < n; i++) {
if (y[i] == 1) {
y2[i] = 1;
} else {
y2[i] = -1;
}
}
y = y2;
double[] h = new double[n]; // current F(x_i)
double[] response = new double[n]; // response variable for regression tree.
double mu = Math.mean(y);
b = 0.5 * Math.log((1 + mu) / (1 - mu));
for (int i = 0; i < n; i++) {
h[i] = b;
}
int[][] order = SmileUtils.sort(attributes, x);
RegressionTree.NodeOutput output = new L2NodeOutput(response);
trees = new RegressionTree[T];
int[] perm = new int[n];
int[] samples = new int[n];
for (int i = 0; i < n; i++) {
perm[i] = i;
}
for (int m = 0; m < T; m++) {
Arrays.fill(samples, 0);
Math.permutate(perm);
for (int i = 0; i < N; i++) {
samples[perm[i]] = 1;
}
for (int i = 0; i < n; i++) {
response[i] = 2.0 * y[i] / (1 + Math.exp(2 * y[i] * h[i]));
}
trees[m] = new RegressionTree(attributes, x, response, J, order, samples, output);
for (int i = 0; i < n; i++) {
h[i] += shrinkage * trees[m].predict(x[i]);
}
}
}
@Override
public double[] project(double[] x) {
if (x.length != p) {
throw new IllegalArgumentException(
String.format("Invalid input vector size: %d, expected: %d", x.length, p));
}
double[] y = new double[scaling[0].length];
Math.atx(scaling, x, y);
Math.minus(y, smean);
return y;
}
@Override
public int predict(double[] x, double[] posteriori) {
if (posteriori.length != k) {
throw new IllegalArgumentException(
String.format("Invalid posteriori vector size: %d, expected: %d", posteriori.length, k));
}
if (k == 2) {
double y = b;
for (int i = 0; i < T; i++) {
y += shrinkage * trees[i].predict(x);
}
posteriori[0] = 1.0 / (1.0 + Math.exp(2 * y));
posteriori[1] = 1.0 - posteriori[0];
if (y > 0) {
return 1;
} else {
return 0;
}
} else {
double max = Double.NEGATIVE_INFINITY;
int y = -1;
for (int j = 0; j < k; j++) {
posteriori[j] = 0.0;
for (int i = 0; i < T; i++) {
posteriori[j] += shrinkage * forest[j][i].predict(x);
}
if (posteriori[j] > max) {
max = posteriori[j];
y = j;
}
}
double Z = 0.0;
for (int i = 0; i < k; i++) {
posteriori[i] = Math.exp(posteriori[i] - max);
Z += posteriori[i];
}
for (int i = 0; i < k; i++) {
posteriori[i] /= Z;
}
return y;
}
}
@Override
public double[][] project(double[][] x) {
double[][] y = new double[x.length][scaling[0].length];
for (int i = 0; i < x.length; i++) {
if (x[i].length != p) {
throw new IllegalArgumentException(
String.format("Invalid input vector size: %d, expected: %d", x[i].length, p));
}
Math.atx(scaling, x[i], y[i]);
Math.minus(y[i], smean);
}
return y;
}
/**
* Test the model on a validation dataset.
*
* @param x the test data set.
* @param y the test data response values.
* @return accuracies with first 1, 2, ..., decision trees.
*/
public double[] test(double[][] x, int[] y) {
double[] accuracy = new double[T];
int n = x.length;
int[] label = new int[n];
Accuracy measure = new Accuracy();
if (k == 2) {
double[] prediction = new double[n];
Arrays.fill(prediction, b);
for (int i = 0; i < T; i++) {
for (int j = 0; j < n; j++) {
prediction[j] += shrinkage * trees[i].predict(x[j]);
label[j] = prediction[j] > 0 ? 1 : 0;
}
accuracy[i] = measure.measure(y, label);
}
} else {
double[][] prediction = new double[n][k];
for (int i = 0; i < T; i++) {
for (int j = 0; j < n; j++) {
for (int l = 0; l < k; l++) {
prediction[j][l] += shrinkage * forest[l][i].predict(x[j]);
}
label[j] = Math.whichMax(prediction[j]);
}
accuracy[i] = measure.measure(y, label);
}
}
return accuracy;
}
/** Push-relabel algorithm for maximum flow */
private void push(double[][] flow, double[] excess, int u, int v) {
double send = Math.min(excess[u], graph[u][v] - flow[u][v]);
flow[u][v] += send;
flow[v][u] -= send;
excess[u] -= send;
excess[v] += send;
}
private void relabel(double[][] flow, int[] height, int u) {
int minHeight = 2 * n;
for (int v = 0; v < n; v++) {
if (graph[u][v] - flow[u][v] > 0) {
minHeight = Math.min(minHeight, height[v]);
height[u] = minHeight + 1;
}
}
}
/**
* Constructor.
*
* @param d the dimensionality of data.
* @param L the number of hash tables.
* @param k the number of random projection hash functions, which is usually set to log(N) where N
* is the dataset size.
* @param w the width of random projections. It should be sufficiently away from 0. But we should
* not choose an w value that is too large, which will increase the query time.
* @param H the size of universal hash tables.
*/
public LSH(int d, int L, int k, double w, int H) {
if (d < 2) {
throw new IllegalArgumentException("Invalid input space dimension: " + d);
}
if (L < 1) {
throw new IllegalArgumentException("Invalid number of hash tables: " + L);
}
if (k < 1) {
throw new IllegalArgumentException(
"Invalid number of random projections per hash value: " + k);
}
if (w <= 0.0) {
throw new IllegalArgumentException("Invalid width of random projections: " + w);
}
if (H < 1) {
throw new IllegalArgumentException("Invalid size of hash tables: " + H);
}
this.d = d;
this.L = L;
this.k = k;
this.w = w;
this.H = H;
keys = new ArrayList<double[]>();
data = new ArrayList<E>();
r1 = new int[k];
r2 = new int[k];
for (int i = 0; i < k; i++) {
r1[i] = Math.randomInt(MAX_HASH_RND);
r2[i] = Math.randomInt(MAX_HASH_RND);
}
hash = new ArrayList<Hash>(L);
for (int i = 0; i < L; i++) {
hash.add(new Hash());
}
}
/**
* Constructor. Learns a gradient tree boosting for classification.
*
* @param attributes the attribute properties.
* @param x the training instances.
* @param y the class labels.
* @param T the number of iterations (trees).
* @param J the number of leaves in each tree.
* @param shrinkage the shrinkage parameter in (0, 1] controls the learning rate of procedure.
* @param f the sampling fraction for stochastic tree boosting.
*/
public GradientTreeBoost(
Attribute[] attributes, double[][] x, int[] y, int T, int J, double shrinkage, double f) {
if (x.length != y.length) {
throw new IllegalArgumentException(
String.format("The sizes of X and Y don't match: %d != %d", x.length, y.length));
}
if (shrinkage <= 0 || shrinkage > 1) {
throw new IllegalArgumentException("Invalid shrinkage: " + shrinkage);
}
if (f <= 0 || f > 1) {
throw new IllegalArgumentException("Invalid sampling fraction: " + f);
}
if (attributes == null) {
int p = x[0].length;
attributes = new Attribute[p];
for (int i = 0; i < p; i++) {
attributes[i] = new NumericAttribute("V" + (i + 1));
}
}
this.T = T;
this.J = J;
this.shrinkage = shrinkage;
this.f = f;
this.k = Math.max(y) + 1;
if (k < 2) {
throw new IllegalArgumentException("Only one class or negative class labels.");
}
importance = new double[attributes.length];
if (k == 2) {
train2(attributes, x, y);
for (RegressionTree tree : trees) {
double[] imp = tree.importance();
for (int i = 0; i < imp.length; i++) {
importance[i] += imp[i];
}
}
} else {
traink(attributes, x, y);
for (RegressionTree[] grove : forest) {
for (RegressionTree tree : grove) {
double[] imp = tree.importance();
for (int i = 0; i < imp.length; i++) {
importance[i] += imp[i];
}
}
}
}
}
/** Generate a random neighbor which differs in only one medoid with current clusters. */
private double getRandomNeighbor(T[] data, T[] medoids, int[] y, double[] d) {
int n = data.length;
int index = Math.randomInt(k);
T medoid = null;
boolean dup;
do {
dup = false;
medoid = data[Math.randomInt(n)];
for (int i = 0; i < k; i++) {
if (medoid == medoids[i]) {
dup = true;
break;
}
}
} while (dup);
medoids[index] = medoid;
for (int i = 0; i < n; i++) {
double dist = distance.d(data[i], medoid);
if (d[i] > dist) {
y[i] = index;
d[i] = dist;
} else if (y[i] == index) {
d[i] = dist;
y[i] = index;
for (int j = 0; j < k; j++) {
if (j != index) {
dist = distance.d(data[i], medoids[j]);
if (d[i] > dist) {
y[i] = j;
d[i] = dist;
}
}
}
}
}
return Math.sum(d);
}
/**
* Constructor.
*
* @param keys the keys of data objects.
* @param data the data objects.
* @param w the width of random projections. It should be sufficiently away from 0. But we should
* not choose an w value that is too large, which will increase the query time.
* @param H the size of universal hash tables.
*/
public LSH(double[][] keys, E[] data, double w, int H) {
this(
keys[0].length,
Math.max(50, (int) Math.pow(keys.length, 0.25)),
Math.max(3, (int) Math.log10(keys.length)),
w,
H);
if (keys.length != data.length) {
throw new IllegalArgumentException("The array size of keys and data are different.");
}
if (H < keys.length) {
throw new IllegalArgumentException("Hash table size is too small: " + H);
}
int n = keys.length;
for (int i = 0; i < n; i++) {
put(keys[i], data[i]);
}
}
/** Test of learn method, of class FPGrowth. */
@Test
public void testKosarak() {
System.out.println("kosarak");
List<int[]> dataList = new ArrayList<int[]>(1000);
try {
InputStream stream = getClass().getResourceAsStream("/smile/data/transaction/kosarak.dat");
BufferedReader input = new BufferedReader(new InputStreamReader(stream));
String line;
for (int nrow = 0; (line = input.readLine()) != null; nrow++) {
if (line.trim().isEmpty()) {
continue;
}
String[] s = line.split(" ");
Set<Integer> items = new HashSet<Integer>();
for (int i = 0; i < s.length; i++) {
items.add(Integer.parseInt(s[i]));
}
int j = 0;
int[] point = new int[items.size()];
for (int i : items) {
point[j++] = i;
}
dataList.add(point);
}
} catch (IOException ex) {
System.err.println(ex);
}
int[][] data = dataList.toArray(new int[dataList.size()][]);
int n = Math.max(data);
System.out.format("%d transactions, %d items\n", data.length, n);
long time = System.currentTimeMillis();
FPGrowth fpgrowth = new FPGrowth(data, 1500);
System.out.format(
"Done building FP-tree: %.2f secs.\n", (System.currentTimeMillis() - time) / 1000.0);
time = System.currentTimeMillis();
List<ItemSet> results = fpgrowth.learn();
System.out.format(
"%d frequent item sets discovered: %.2f secs.\n",
results.size(), (System.currentTimeMillis() - time) / 1000.0);
assertEquals(219725, results.size());
}
@Override
public double k(double[] x, double[] y) {
if (x.length != y.length)
throw new IllegalArgumentException(
String.format("Arrays have different length: x[%d], y[%d]", x.length, y.length));
double sum = 0;
for (int i = 0; i < x.length; i++) {
sum += Math.sqrt(x[i] * y[i]);
}
return sum;
}
/**
* Returns the hash value of given vector x.
*
* @param x the vector to be hashed.
* @param m the m-<i>th</i> hash function to be employed.
* @return the hash value.
*/
int hash(double[] x, int m) {
double g = b[m];
for (int j = 0; j < d; j++) {
g += a[m][j] * x[j];
}
int h = (int) Math.floor(g / w);
if (h < 0) {
h += 2147483647;
}
return h;
}
@Override
public String toString() {
StringBuilder sb = new StringBuilder();
sb.append(String.format("CLARANS distortion: %.5f%n", distortion));
sb.append(String.format("Clusters of %d data points:%n", y.length));
for (int i = 0; i < k; i++) {
int r = (int) Math.round(1000.0 * size[i] / y.length);
sb.append(String.format("%3d\t%5d (%2d.%1d%%)%n", i, size[i], r / 10, r % 10));
}
return sb.toString();
}
@Override
public double calculate(int[] samples) {
double nu = 0.0;
double de = 0.0;
for (int i = 0; i < samples.length; i++) {
if (samples[i] > 0) {
double abs = Math.abs(y[i]);
nu += y[i];
de += abs * (2.0 - abs);
}
}
return nu / de;
}
/** Convert coordinate to a string. */
public static String coordToString(double... c) {
StringBuilder builder = new StringBuilder("(");
for (int i = 0; i < c.length; i++) {
builder.append(Math.round(c[i], 2)).append(",");
}
if (c.length > 0) {
builder.setCharAt(builder.length(), ')');
} else {
builder.append(")");
}
return builder.toString();
}
private void _cluster(double[][] data, int k) {
long clock = System.currentTimeMillis();
SpectralClustering cluster = new SpectralClustering(data, k, 0.355);
System.out.format(
"DBSCAN clusterings %d samples in %dms\n", data.length, System.currentTimeMillis() - clock);
System.out.println("getNumClusters:" + cluster.getNumClusters());
System.out.println("getClusterSize:" + cluster.getClusterSize());
// System.out.println(JSON.toJSONString(dbscan.getClusterSize()));
System.out.println("toString:" + cluster.toString());
/** ************************************************************ */
boolean more = true;
EigenValueDecomposition eigen = cluster.getEigen();
double[] lab = eigen.getEigenValues();
double sd = smile.math.Math.sd(eigen.getEigenValues());
System.out.println("sd(eigen.getEigenValues()):" + sd);
if (Math.min(eigen.getEigenValues()) > 0.3) {
result = cluster;
cluster(data, k + 1);
} else {
return;
}
}
/** Test of learn method, of class FPGrowth. */
@Test
public void testPima() {
System.out.println("pima");
List<int[]> dataList = new ArrayList<int[]>(1000);
try {
InputStream stream =
getClass().getResourceAsStream("/smile/data/transaction/pima.D38.N768.C2");
BufferedReader input = new BufferedReader(new InputStreamReader(stream));
String line;
for (int nrow = 0; (line = input.readLine()) != null; nrow++) {
if (line.trim().isEmpty()) {
continue;
}
String[] s = line.split(" ");
int[] point = new int[s.length];
for (int i = 0; i < s.length; i++) {
point[i] = Integer.parseInt(s[i]);
}
dataList.add(point);
}
} catch (IOException ex) {
System.err.println(ex);
}
int[][] data = dataList.toArray(new int[dataList.size()][]);
int n = Math.max(data);
System.out.format("%d transactions, %d items\n", data.length, n);
long time = System.currentTimeMillis();
FPGrowth fpgrowth = new FPGrowth(data, 20);
System.out.format(
"Done building FP-tree: %.2f secs.\n", (System.currentTimeMillis() - time) / 1000.0);
time = System.currentTimeMillis();
long numItemsets = fpgrowth.learn(System.out);
System.out.format(
"%d frequent item sets discovered: %.2f secs.\n",
numItemsets, (System.currentTimeMillis() - time) / 1000.0);
assertEquals(1803, numItemsets);
assertEquals(1803, fpgrowth.learn().size());
}
/** Constructor. */
Hash() {
a = new double[k][d];
b = new double[k];
GaussianDistribution gaussian = GaussianDistribution.getInstance();
for (int i = 0; i < k; i++) {
for (int j = 0; j < d; j++) {
a[i][j] = gaussian.rand();
}
b[i] = Math.random(0, w);
}
table = new HashEntry[H];
}
/** Test of learn method, of class ARM. */
@Test
public void testLearnKosarak() {
System.out.println("kosarak");
List<int[]> dataList = new ArrayList<int[]>(1000);
try {
InputStream stream = getClass().getResourceAsStream("/smile/data/transaction/kosarak.dat");
BufferedReader input = new BufferedReader(new InputStreamReader(stream));
String line;
for (int nrow = 0; (line = input.readLine()) != null; nrow++) {
if (line.trim().isEmpty()) {
continue;
}
String[] s = line.split(" ");
Set<Integer> items = new HashSet<Integer>();
for (int i = 0; i < s.length; i++) {
items.add(Integer.parseInt(s[i]));
}
int j = 0;
int[] point = new int[items.size()];
for (int i : items) {
point[j++] = i;
}
dataList.add(point);
}
} catch (IOException ex) {
System.err.println(ex);
}
int[][] data = dataList.toArray(new int[dataList.size()][]);
int n = Math.max(data);
System.out.format("%d transactions, %d items\n", data.length, n);
ARM instance = new ARM(data, 0.003);
long numRules = instance.learn(0.5, System.out);
System.out.format("%d association rules discovered\n", numRules);
assertEquals(17932, numRules);
}
@Override
public void range(double[] q, double radius, List<Neighbor<double[], E>> neighbors) {
if (radius <= 0.0) {
throw new IllegalArgumentException("Invalid radius: " + radius);
}
Set<Integer> candidates = obtainCandidates(q);
for (int index : candidates) {
double[] key = keys.get(index);
if (q == key && identicalExcluded) {
continue;
}
double distance = Math.distance(q, key);
if (distance <= radius) {
neighbors.add(new Neighbor<double[], E>(key, data.get(index), index, distance));
}
}
}
@Override
public Neighbor<double[], E>[] knn(double[] q, int k) {
if (k < 1) {
throw new IllegalArgumentException("Invalid k: " + k);
}
Set<Integer> candidates = obtainCandidates(q);
Neighbor<double[], E> neighbor = new Neighbor<double[], E>(null, null, 0, Double.MAX_VALUE);
@SuppressWarnings("unchecked")
Neighbor<double[], E>[] neighbors =
(Neighbor<double[], E>[]) java.lang.reflect.Array.newInstance(neighbor.getClass(), k);
HeapSelect<Neighbor<double[], E>> heap = new HeapSelect<Neighbor<double[], E>>(neighbors);
for (int i = 0; i < k; i++) {
heap.add(neighbor);
}
int hit = 0;
for (int index : candidates) {
double[] key = keys.get(index);
if (q == key && identicalExcluded) {
continue;
}
double distance = Math.distance(q, key);
if (distance < heap.peek().distance) {
heap.add(new Neighbor<double[], E>(key, data.get(index), index, distance));
hit++;
}
}
heap.sort();
if (hit < k) {
@SuppressWarnings("unchecked")
Neighbor<double[], E>[] n2 =
(Neighbor<double[], E>[]) java.lang.reflect.Array.newInstance(neighbor.getClass(), hit);
int start = k - hit;
for (int i = 0; i < hit; i++) {
n2[i] = neighbors[i + start];
}
neighbors = n2;
}
return neighbors;
}
@Override
public Neighbor<double[], E> nearest(double[] q) {
Set<Integer> candidates = obtainCandidates(q);
Neighbor<double[], E> neighbor = new Neighbor<double[], E>(null, null, -1, Double.MAX_VALUE);
for (int index : candidates) {
double[] key = keys.get(index);
if (q == key && identicalExcluded) {
continue;
}
double distance = Math.distance(q, key);
if (distance < neighbor.distance) {
neighbor.index = index;
neighbor.distance = distance;
neighbor.key = key;
neighbor.value = data.get(index);
}
}
return neighbor;
}
@Override
public double calculate(int[] samples) {
int n = 0;
double nu = 0.0;
double de = 0.0;
for (int i = 0; i < samples.length; i++) {
if (samples[i] > 0) {
n++;
double abs = Math.abs(y[i]);
nu += y[i];
de += abs * (1.0 - abs);
}
}
if (de < 1E-10) {
return nu / n;
}
return ((k - 1.0) / k) * (nu / de);
}
/** Test of learn method, of class ARM. */
@Test
public void testLearnPima() {
System.out.println("pima");
List<int[]> dataList = new ArrayList<int[]>(1000);
try {
InputStream stream =
getClass().getResourceAsStream("/smile/data/transaction/pima.D38.N768.C2");
BufferedReader input = new BufferedReader(new InputStreamReader(stream));
String line;
for (int nrow = 0; (line = input.readLine()) != null; nrow++) {
if (line.trim().isEmpty()) {
continue;
}
String[] s = line.split(" ");
int[] point = new int[s.length];
for (int i = 0; i < s.length; i++) {
point[i] = Integer.parseInt(s[i]);
}
dataList.add(point);
}
} catch (IOException ex) {
System.err.println(ex);
}
int[][] data = dataList.toArray(new int[dataList.size()][]);
int n = Math.max(data);
System.out.format("%d transactions, %d items\n", data.length, n);
ARM instance = new ARM(data, 20);
long numRules = instance.learn(0.9, System.out);
System.out.format("%d association rules discovered\n", numRules);
assertEquals(6803, numRules);
assertEquals(6803, instance.learn(0.9).size());
}
@Override
public int predict(double[] x) {
if (x.length != p) {
throw new IllegalArgumentException(
String.format("Invalid input vector size: %d, expected: %d", x.length, p));
}
double[] wx = project(x);
int y = 0;
double nearest = Double.POSITIVE_INFINITY;
for (int i = 0; i < k; i++) {
double d = Math.distance(wx, smu[i]);
if (d < nearest) {
nearest = d;
y = i;
}
}
return y;
}
/**
* Test the model on a validation dataset.
*
* @param x the test data set.
* @param y the test data labels.
* @param measures the performance measures of classification.
* @return performance measures with first 1, 2, ..., decision trees.
*/
public double[][] test(double[][] x, int[] y, ClassificationMeasure[] measures) {
int m = measures.length;
double[][] results = new double[T][m];
int n = x.length;
int[] label = new int[n];
if (k == 2) {
double[] prediction = new double[n];
Arrays.fill(prediction, b);
for (int i = 0; i < T; i++) {
for (int j = 0; j < n; j++) {
prediction[j] += shrinkage * trees[i].predict(x[j]);
label[j] = prediction[j] > 0 ? 1 : 0;
}
for (int j = 0; j < m; j++) {
results[i][j] = measures[j].measure(y, label);
}
}
} else {
double[][] prediction = new double[n][k];
for (int i = 0; i < T; i++) {
for (int j = 0; j < n; j++) {
for (int l = 0; l < k; l++) {
prediction[j][l] += shrinkage * forest[l][i].predict(x[j]);
}
label[j] = Math.whichMax(prediction[j]);
}
for (int j = 0; j < m; j++) {
results[i][j] = measures[j].measure(y, label);
}
}
}
return results;
}