Posit AI Weblog: Audio classification with torch

Variations on a theme

Easy audio classification with Keras, Audio classification with Keras: Wanting nearer on the non-deep studying elements, Easy audio classification with torch: No, this isn’t the primary put up on this weblog that introduces speech classification utilizing deep studying. With two of these posts (the “utilized” ones) it shares the final setup, the kind of deep-learning structure employed, and the dataset used. With the third, it has in frequent the curiosity within the concepts and ideas concerned. Every of those posts has a special focus – must you learn this one?

Effectively, in fact I can’t say “no” – all of the extra so as a result of, right here, you’ve got an abbreviated and condensed model of the chapter on this matter within the forthcoming e book from CRC Press, Deep Studying and Scientific Computing with R torch. By means of comparability with the earlier put up that used torch, written by the creator and maintainer of torchaudio, Athos Damiani, important developments have taken place within the torch ecosystem, the top consequence being that the code received lots simpler (particularly within the mannequin coaching half). That mentioned, let’s finish the preamble already, and plunge into the subject!

Inspecting the info

We use the speech instructions dataset (Warden (2018)) that comes with torchaudio. The dataset holds recordings of thirty completely different one- or two-syllable phrases, uttered by completely different audio system. There are about 65,000 audio recordsdata general. Our process can be to foretell, from the audio solely, which of thirty potential phrases was pronounced.

library(torch)
library(torchaudio)
library(luz)

ds <- speechcommand_dataset(
  root = "~/.torch-datasets", 
  url = "speech_commands_v0.01",
  obtain = TRUE
)

We begin by inspecting the info.

[1]  "mattress"    "fowl"   "cat"    "canine"    "down"   "eight"
[7]  "5"   "4"   "go"     "glad"  "home"  "left"
[32] " marvin" "9"   "no"     "off"    "on"     "one"
[19] "proper"  "seven" "sheila" "six"    "cease"   "three"
[25]  "tree"   "two"    "up"     "wow"    "sure"    "zero" 

Selecting a pattern at random, we see that the knowledge we’ll want is contained in 4 properties: waveform, sample_rate, label_index, and label.

The primary, waveform, can be our predictor.

pattern <- ds[2000]
dim(pattern$waveform)

[1]     1 16000

Particular person tensor values are centered at zero, and vary between -1 and 1. There are 16,000 of them, reflecting the truth that the recording lasted for one second, and was registered at (or has been transformed to, by the dataset creators) a price of 16,000 samples per second. The latter info is saved in pattern$sample_rate:

[1] 16000

All recordings have been sampled on the similar price. Their size nearly all the time equals one second; the – very – few sounds which can be minimally longer we will safely truncate.

Lastly, the goal is saved, in integer kind, in pattern$label_index, the corresponding phrase being accessible from pattern$label:

pattern$label
pattern$label_index

[1] "fowl"
torch_tensor
2
[ CPULongType{} ]

How does this audio sign “look?”

library(ggplot2)

df <- information.body(
  x = 1:size(pattern$waveform[1]),
  y = as.numeric(pattern$waveform[1])
  )

ggplot(df, aes(x = x, y = y)) +
  geom_line(dimension = 0.3) +
  ggtitle(
    paste0(
      "The spoken phrase "", pattern$label, "": Sound wave"
    )
  ) +
  xlab("time") +
  ylab("amplitude") +
  theme_minimal()

What we see is a sequence of amplitudes, reflecting the sound wave produced by somebody saying “fowl.” Put in a different way, we’ve got right here a time collection of “loudness values.” Even for consultants, guessing which phrase resulted in these amplitudes is an unattainable process. That is the place area data is available in. The professional might not be capable to make a lot of the sign on this illustration; however they could know a technique to extra meaningfully characterize it.

Two equal representations

Think about that as a substitute of as a sequence of amplitudes over time, the above wave have been represented in a approach that had no details about time in any respect. Subsequent, think about we took that illustration and tried to get well the unique sign. For that to be potential, the brand new illustration would someway need to include “simply as a lot” info because the wave we began from. That “simply as a lot” is obtained from the Fourier Rework, and it consists of the magnitudes and part shifts of the completely different frequencies that make up the sign.

How, then, does the Fourier-transformed model of the “fowl” sound wave look? We get hold of it by calling torch_fft_fft() (the place fft stands for Quick Fourier Rework):

dft <- torch_fft_fft(pattern$waveform)
dim(dft)

[1]     1 16000

The size of this tensor is similar; nevertheless, its values aren’t in chronological order. As a substitute, they characterize the Fourier coefficients, equivalent to the frequencies contained within the sign. The upper their magnitude, the extra they contribute to the sign:

magazine <- torch_abs(dft[1, ])

df <- information.body(
  x = 1:(size(pattern$waveform[1]) / 2),
  y = as.numeric(magazine[1:8000])
)

ggplot(df, aes(x = x, y = y)) +
  geom_line(dimension = 0.3) +
  ggtitle(
    paste0(
      "The spoken phrase "",
      pattern$label,
      "": Discrete Fourier Rework"
    )
  ) +
  xlab("frequency") +
  ylab("magnitude") +
  theme_minimal()

From this alternate illustration, we may return to the unique sound wave by taking the frequencies current within the sign, weighting them based on their coefficients, and including them up. However in sound classification, timing info should certainly matter; we don’t actually wish to throw it away.

Combining representations: The spectrogram

Actually, what actually would assist us is a synthesis of each representations; some type of “have your cake and eat it, too.” What if we may divide the sign into small chunks, and run the Fourier Rework on every of them? As you might have guessed from this lead-up, this certainly is one thing we will do; and the illustration it creates known as the spectrogram.

With a spectrogram, we nonetheless hold some time-domain info – some, since there’s an unavoidable loss in granularity. However, for every of the time segments, we study their spectral composition. There’s an essential level to be made, although. The resolutions we get in time versus in frequency, respectively, are inversely associated. If we cut up up the alerts into many chunks (referred to as “home windows”), the frequency illustration per window is not going to be very fine-grained. Conversely, if we wish to get higher decision within the frequency area, we’ve got to decide on longer home windows, thus shedding details about how spectral composition varies over time. What appears like an enormous downside – and in lots of instances, can be – received’t be one for us, although, as you’ll see very quickly.

First, although, let’s create and examine such a spectrogram for our instance sign. Within the following code snippet, the scale of the – overlapping – home windows is chosen in order to permit for cheap granularity in each the time and the frequency area. We’re left with sixty-three home windows, and, for every window, get hold of 2 hundred fifty-seven coefficients:

fft_size <- 512
window_size <- 512
energy <- 0.5

spectrogram <- transform_spectrogram(
  n_fft = fft_size,
  win_length = window_size,
  normalized = TRUE,
  energy = energy
)

spec <- spectrogram(pattern$waveform)$squeeze()
dim(spec)

[1]   257 63

We are able to show the spectrogram visually:

bins <- 1:dim(spec)[1]
freqs <- bins / (fft_size / 2 + 1) * pattern$sample_rate 
log_freqs <- log10(freqs)

frames <- 1:(dim(spec)[2])
seconds <- (frames / dim(spec)[2]) *
  (dim(pattern$waveform$squeeze())[1] / pattern$sample_rate)

picture(x = as.numeric(seconds),
      y = log_freqs,
      z = t(as.matrix(spec)),
      ylab = 'log frequency [Hz]',
      xlab = 'time [s]',
      col = hcl.colours(12, palette = "viridis")
)
fundamental <- paste0("Spectrogram, window dimension = ", window_size)
sub <- "Magnitude (sq. root)"
mtext(facet = 3, line = 2, at = 0, adj = 0, cex = 1.3, fundamental)
mtext(facet = 3, line = 1, at = 0, adj = 0, cex = 1, sub)

We all know that we’ve misplaced some decision in each time and frequency. By displaying the sq. root of the coefficients’ magnitudes, although – and thus, enhancing sensitivity – we have been nonetheless capable of get hold of an affordable consequence. (With the viridis shade scheme, long-wave shades point out higher-valued coefficients; short-wave ones, the alternative.)

Lastly, let’s get again to the essential query. If this illustration, by necessity, is a compromise – why, then, would we wish to make use of it? That is the place we take the deep-learning perspective. The spectrogram is a two-dimensional illustration: a picture. With photos, we’ve got entry to a wealthy reservoir of methods and architectures: Amongst all areas deep studying has been profitable in, picture recognition nonetheless stands out. Quickly, you’ll see that for this process, fancy architectures aren’t even wanted; a simple convnet will do an excellent job.

Coaching a neural community on spectrograms

We begin by making a torch::dataset() that, ranging from the unique speechcommand_dataset(), computes a spectrogram for each pattern.

spectrogram_dataset <- dataset(
  inherit = speechcommand_dataset,
  initialize = operate(...,
                        pad_to = 16000,
                        sampling_rate = 16000,
                        n_fft = 512,
                        window_size_seconds = 0.03,
                        window_stride_seconds = 0.01,
                        energy = 2) {
    self$pad_to <- pad_to
    self$window_size_samples <- sampling_rate *
      window_size_seconds
    self$window_stride_samples <- sampling_rate *
      window_stride_seconds
    self$energy <- energy
    self$spectrogram <- transform_spectrogram(
        n_fft = n_fft,
        win_length = self$window_size_samples,
        hop_length = self$window_stride_samples,
        normalized = TRUE,
        energy = self$energy
      )
    tremendous$initialize(...)
  },
  .getitem = operate(i) {
    merchandise <- tremendous$.getitem(i)

    x <- merchandise$waveform
    # be sure all samples have the identical size (57)
    # shorter ones can be padded,
    # longer ones can be truncated
    x <- nnf_pad(x, pad = c(0, self$pad_to - dim(x)[2]))
    x <- x %>% self$spectrogram()

    if (is.null(self$energy)) {
      # on this case, there's a further dimension, in place 4,
      # that we wish to seem in entrance
      # (as a second channel)
      x <- x$squeeze()$permute(c(3, 1, 2))
    }

    y <- merchandise$label_index
    checklist(x = x, y = y)
  }
)

Within the parameter checklist to spectrogram_dataset(), observe energy, with a default worth of two. That is the worth that, except advised in any other case, torch’s transform_spectrogram() will assume that energy ought to have. Underneath these circumstances, the values that make up the spectrogram are the squared magnitudes of the Fourier coefficients. Utilizing energy, you may change the default, and specify, for instance, that’d you’d like absolute values (energy = 1), another constructive worth (akin to 0.5, the one we used above to show a concrete instance) – or each the actual and imaginary elements of the coefficients (energy = NULL).

Show-wise, in fact, the total advanced illustration is inconvenient; the spectrogram plot would wish a further dimension. However we might nicely wonder if a neural community may revenue from the extra info contained within the “entire” advanced quantity. In spite of everything, when decreasing to magnitudes we lose the part shifts for the person coefficients, which could include usable info. Actually, my checks confirmed that it did; use of the advanced values resulted in enhanced classification accuracy.

Let’s see what we get from spectrogram_dataset():

ds <- spectrogram_dataset(
  root = "~/.torch-datasets",
  url = "speech_commands_v0.01",
  obtain = TRUE,
  energy = NULL
)

dim(ds[1]$x)

[1]   2 257 101

We now have 257 coefficients for 101 home windows; and every coefficient is represented by each its actual and imaginary elements.

Subsequent, we cut up up the info, and instantiate the dataset() and dataloader() objects.

train_ids <- pattern(
  1:size(ds),
  dimension = 0.6 * size(ds)
)
valid_ids <- pattern(
  setdiff(
    1:size(ds),
    train_ids
  ),
  dimension = 0.2 * size(ds)
)
test_ids <- setdiff(
  1:size(ds),
  union(train_ids, valid_ids)
)

batch_size <- 128

train_ds <- dataset_subset(ds, indices = train_ids)
train_dl <- dataloader(
  train_ds,
  batch_size = batch_size, shuffle = TRUE
)

valid_ds <- dataset_subset(ds, indices = valid_ids)
valid_dl <- dataloader(
  valid_ds,
  batch_size = batch_size
)

test_ds <- dataset_subset(ds, indices = test_ids)
test_dl <- dataloader(test_ds, batch_size = 64)

b <- train_dl %>%
  dataloader_make_iter() %>%
  dataloader_next()

dim(b$x)

[1] 128   2 257 101

The mannequin is a simple convnet, with dropout and batch normalization. The true and imaginary elements of the Fourier coefficients are handed to the mannequin’s preliminary nn_conv2d() as two separate channels.

mannequin <- nn_module(
  initialize = operate() {
    self$options <- nn_sequential(
      nn_conv2d(2, 32, kernel_size = 3),
      nn_batch_norm2d(32),
      nn_relu(),
      nn_max_pool2d(kernel_size = 2),
      nn_dropout2d(p = 0.2),
      nn_conv2d(32, 64, kernel_size = 3),
      nn_batch_norm2d(64),
      nn_relu(),
      nn_max_pool2d(kernel_size = 2),
      nn_dropout2d(p = 0.2),
      nn_conv2d(64, 128, kernel_size = 3),
      nn_batch_norm2d(128),
      nn_relu(),
      nn_max_pool2d(kernel_size = 2),
      nn_dropout2d(p = 0.2),
      nn_conv2d(128, 256, kernel_size = 3),
      nn_batch_norm2d(256),
      nn_relu(),
      nn_max_pool2d(kernel_size = 2),
      nn_dropout2d(p = 0.2),
      nn_conv2d(256, 512, kernel_size = 3),
      nn_batch_norm2d(512),
      nn_relu(),
      nn_adaptive_avg_pool2d(c(1, 1)),
      nn_dropout2d(p = 0.2)
    )

    self$classifier <- nn_sequential(
      nn_linear(512, 512),
      nn_batch_norm1d(512),
      nn_relu(),
      nn_dropout(p = 0.5),
      nn_linear(512, 30)
    )
  },
  ahead = operate(x) {
    x <- self$options(x)$squeeze()
    x <- self$classifier(x)
    x
  }
)

We subsequent decide an acceptable studying price:

mannequin <- mannequin %>%
  setup(
    loss = nn_cross_entropy_loss(),
    optimizer = optim_adam,
    metrics = checklist(luz_metric_accuracy())
  )

rates_and_losses <- mannequin %>%
  lr_finder(train_dl)
rates_and_losses %>% plot()

Based mostly on the plot, I made a decision to make use of 0.01 as a maximal studying price. Coaching went on for forty epochs.

fitted <- mannequin %>%
  match(train_dl,
    epochs = 50, valid_data = valid_dl,
    callbacks = checklist(
      luz_callback_early_stopping(endurance = 3),
      luz_callback_lr_scheduler(
        lr_one_cycle,
        max_lr = 1e-2,
        epochs = 50,
        steps_per_epoch = size(train_dl),
        call_on = "on_batch_end"
      ),
      luz_callback_model_checkpoint(path = "models_complex/"),
      luz_callback_csv_logger("logs_complex.csv")
    ),
    verbose = TRUE
  )

plot(fitted)

Let’s examine precise accuracies.

"epoch","set","loss","acc"
1,"prepare",3.09768574611813,0.12396992171405
1,"legitimate",2.52993751740923,0.284378862793572
2,"prepare",2.26747255972008,0.333642356819118
2,"legitimate",1.66693911248562,0.540791100123609
3,"prepare",1.62294889937818,0.518464153275649
3,"legitimate",1.11740599192825,0.704882571075402
...
...
38,"prepare",0.18717994078312,0.943809229501442
38,"legitimate",0.23587799138006,0.936418417799753
39,"prepare",0.19338578602993,0.942882159044087
39,"legitimate",0.230597475945365,0.939431396786156
40,"prepare",0.190593419024368,0.942727647301195
40,"legitimate",0.243536252455384,0.936186650185414

With thirty courses to tell apart between, a ultimate validation-set accuracy of ~0.94 appears to be like like a really first rate consequence!

We are able to affirm this on the check set:

consider(fitted, test_dl)

loss: 0.2373
acc: 0.9324

An fascinating query is which phrases get confused most frequently. (In fact, much more fascinating is how error possibilities are associated to options of the spectrograms – however this, we’ve got to go away to the true area consultants. A pleasant approach of displaying the confusion matrix is to create an alluvial plot. We see the predictions, on the left, “stream into” the goal slots. (Goal-prediction pairs much less frequent than a thousandth of check set cardinality are hidden.)

Wrapup

That’s it for at the moment! Within the upcoming weeks, count on extra posts drawing on content material from the soon-to-appear CRC e book, Deep Studying and Scientific Computing with R torch. Thanks for studying!

Picture by alex lauzon on Unsplash